This is one of the webpages of Libarid A. Maljian at the Department of Physics at CSLA at NJIT.

 

 

 

New Jersey Institute of Technology

College of Science and Liberal Arts

Department of Physics

Introductory Astronomy and Cosmology

Phys 202

Fall 2023

Second Examination lecture notes

 

 

 

Introduction to the Solar System

 

The Solar System is the Sun together with the planets orbiting the Sun, moons orbiting the planets, asteroids orbiting the Sun, comets orbiting the Sun, and other minor objects.  By far, the most important member of the Solar system is the Sun.  However, we will for the most part ignore the Sun during this survey of the Solar System.  We will study the Sun in tremendous detail in the context of the Sun being a star, not in the context of the Sun being a member of the Solar System.  During this survey of the Solar System, we will concentrate our attention on the planets, their moons, the asteroids, the comets, and the other minor objects of the Solar System.

 

There are eight planets orbiting the Sun.  The eight planets listed in the correct order from closest to the Sun are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune furthest from the Sun.  There is remarkable symmetry among the eight planets.  In particular, the four planets closer to the Sun all share similar physical properties, the four planets further from the Sun all share similar physical properties, and these two groups of planets have opposite physical properties from each other.  Evidently, there are two different categories of planets, with the four inner planets being of one category and the four outer planets being of the other category.  The four inner planets are small, while the four outer planets are large.  The four inner planets are dense, composed primarily of metal and rock; the four outer planets are tenuous (low density), composed primarily of hydrogen gas and helium gas.  The four inner planets have no moons or perhaps few moons, while the four outer planets each have many moons.  The four inner planets have no rings; the four outer planets do have rings.  The four inner planets have slow rotation, while the four outer planets have fast rotation.  Again, the four inner planets all share similar physical properties, the four outer planets all share similar physical properties, and these two groups of planets have opposite physical properties from each other.  The four inner planets are Mercury, Venus, Earth, and Mars, and these four planets are all classified as terrestrial planets.  The word terrestrial means Earth-like, but we must be careful with interpreting the term terrestrial (Earth-like) planet.  We do not mean that Mercury, Venus, and Mars are exactly like the Earth.  There are many differences among all four terrestrial planets.  When we say a planet is a terrestrial (Earth-like) planet, we mean that the planet is small, dense (composed primarily of metal and rock), with no moons or perhaps few moons, with no rings, and with slow rotation.  The four outer planets are Jupiter, Saturn, Uranus, and Neptune, and these four planets are all classified as jovian planets.  The word jovian means Jupiter-like, but we must be careful with interpreting the term jovian (Jupiter-like) planet.  We do not mean that Saturn, Uranus, and Neptune are exactly like Jupiter.  There are many differences among all four jovian planets.  When we say a planet is a jovian (Jupiter-like) planet, we mean that the planet is large, tenuous (composed primarily of hydrogen gas and helium gas), with many moons, with rings, and with fast rotation.  Another term for jovian planets is gas-giant planets, since they are large and tenuous (composed primarily of gas).  In summary, the four inner planets are all terrestrial planets, while the four outer planets are all jovian, gas-giant planets.

 

There are further remarkable symmetries among the eight planets of the Solar System.  All eight planets orbit the Sun in nearly the same plane.  The plane of the Earth’s orbit around the Sun is called the ecliptic plane.  All eight planets orbit the Sun in nearly the ecliptic plane.  Although the orbital planes of the planets are actually inclined relative to the ecliptic plane, these inclinations are nevertheless small.  In other words, the entire Solar System is very flat.  All eight planets have roughly circular (but nevertheless slightly elliptical) orbits around the Sun.  All eight planets orbit the Sun in the same direction, counterclockwise when observed from above the plane of the Solar System.  Most of the planets rotate in that same direction while they orbit Sun.  Most of the moons of most of the planets orbit their mother planet in that same direction.  Most of the moons of most of the planets rotate in that same direction while orbiting their mother planet in that same direction.  The Sun itself rotates in that same direction.

 

To explain all of these symmetries among the planets of the Solar System, we must discuss the formation of the Solar System.  The entire Solar System was born roughly 4.6 billion years ago from a diffuse nebula, which is a giant cloud of gas (many light-years across) composed mostly of hydrogen and helium and very small amounts of all the other atoms on the Periodic Table of Elements.  The gases within a diffuse nebula are pushed by many different forces, including thermal pressures, gravitational forces, magnetic pressures, and even cosmic rays (ultra high-energy particles).  All these different forces are comparable in strength with each other in interstellar space (the space between star systems).  Thus, the gases within a diffuse nebula are pushed in seemingly random directions, causing some parts of the diffuse nebula to be more dense than average and other parts to be less dense (or more tenuous) than average.  On occasion, a small part of a diffuse nebula may become dense enough that its self-gravity dominates over all other forces.  Thus, a small part of an ancient diffuse nebula collapsed from its self-gravity (under its own weight).  Most of the material collapsed toward the center, eventually forming the Sun.  As the rest of the material collapsed, collisions between particles within the collapsing cloud became more frequent, since the gravitational collapse brought the particles closer together.  These collisions tended to be sticky, with colliding particles merging into larger masses.  By the law of conservation of translational (linear) momentum, the resulting larger masses had less motion along the direction of the axis defined by the total angular momentum of the collapsing cloud, since the collisions averaged out their more random motions in this direction.  By the law of conservation of energy, the resulting larger masses were heated, since sticky collisions convert a significant fraction of the kinetic energy (moving energy) of the colliding particles into thermal energy (heat energy).  By the law of conservation of angular momentum, the resulting larger masses had more circular orbits, since the collisions averaged out their more random orbits, many of which were more elliptical.  In summary, the laws of physics together caused the gravitationally collapsing material to flatten into a circular, rotating disk perpendicular to the axis of the total angular momentum of the forming Solar System.  This disk is called the protoplanetary disk, since the planets would eventually form from this flat, circular, rotating disk.  We see that this nebular theory explains why the Solar System is very flat and why all eight planets orbit the Sun in the same direction with roughly circular (but nevertheless slightly elliptical) orbits.  During the first couple of hundred million years after the formation of the protoplanetary disk, there were frequent sticky, heat-generating collisions among particles, resulting in larger and larger masses.  This is called the heavy bombardment period in the history of the Solar System.  The inner part of the protoplanetary disk was closer to the Sun and therefore was more subject to the Sun’s heat.  The outer part of this protoplanetary disk was further from the Sun and therefore was less subject to the Sun’s heat.  Since the inner part of the protoplanetary disk was warmer, only materials with hotter melting temperatures were able to condense, in particular metal and rock.  However, most of the protoplanetary disk was composed of hydrogen and helium; metal and rock constituted only a tiny fraction of the protoplanetary disk.  Therefore, only these small amounts of metal and rock were able to condense closer to the Sun.  Since the outer part of the protoplanetary disk was cooler, a greater abundance of materials in addition to metal and rock was able to condense.  We see that this nebular theory explains why we will eventually have small, dense planets closer to the Sun and large, tenuous planets further from the Sun.  However, these condensing objects orbiting the Sun were not yet planets.  They were planetesimals, the technical term for baby planets.  As the planetesimals orbited the Sun, they collided with material along their orbits, which stuck to the planetesimals.  Thus, the planetesimals grew larger through accretion, the gaining of mass through sticky collisions.  The planetesimals grew larger and larger through accretion until the planetesimals became so large that their self-gravity became strong enough to force themselves into spherical shapes.  These objects were now so large with so much mass and therefore strong enough self-gravity that they began to attract even more material around them, causing them to grow even larger.  The outer planetesimals were sufficiently large with sufficiently strong gravity that they attracted nearby hydrogen and helium, which constituted most of the material of the protoplanetary disk.  Consequently, the outer planetesimals grew to enormous sizes as compared with the inner planetesimals.  Eventually, all the planetesimals grew large enough that they became planets.  In summary, the nebular theory explains why all the planets orbit the Sun in nearly the same plane (the flatness of the Solar System), why all eight planets orbit the Sun with roughly circular (but nevertheless slightly elliptical) orbits, why all eight planets orbit the Sun in the same direction, why the inner planets are all terrestrial planets, and why the outer planets are all jovian, gas-giant planets.  We will reveal further successes this nebular theory has with explaining what we observe during this overview of the Solar System.

 

The Sun is named for Sol, the ancient Roman mythological god of the Sun (Helios in ancient Greek mythology).  We use ☉ as the astronomical symbol for the Sun.  For example, astrophysicists use M☉ to denote the mass of the Sun, astrophysicists use R☉ to denote the radius of the Sun, and so on and so forth.  The planet Mercury is named for the ancient Roman mythological god of messengers (Hermes in ancient Greek mythology).  Since the planet Mercury is the closest planet to the Sun, it orbits the Sun with the fastest speed with the shortest orbital period (in the shortest amount of time).  Mercury even appears to move back and forth quickly across the Sun as observed in our sky.  This is why the ancient Greeks and Romans believed that this object was the god of messengers Mercury (Hermes), since a messenger must travel quickly to deliver messages promptly.  We use ☿ as the astronomical symbol for planet Mercury.  The planet Venus is named for the ancient Roman mythological goddess of love (Aphrodite in ancient Greek mythology).  We use ♀ as the astronomical symbol for planet Venus.  The planet Earth is named for Terra, the ancient Roman mythological goddess of the Earth (Gaia in ancient Greek mythology).  We use ⊕ as the astronomical symbol for planet Earth.  For example, astrophysicists use M⊕ to denote the mass of planet Earth, astrophysicists use R⊕ to denote the radius of planet Earth, and so on and so forth.  When spelled beginning with a lowercase letter, the word earth means ground or dirt or soil.  The Earth’s Moon is named for Luna, the ancient Roman mythological goddess of the Moon (Selene in ancient Greek mythology).  We use ☽︎ as the astronomical symbol for the Earth’s Moon.  The planet Mars is named for the ancient Roman mythological god of war (Ares in ancient Greek mythology).  In the modern ages after the telescope was invented, the two moons of planet Mars were discovered.  These moons were named Phobos and Deimos after the twin mythological sons of the god of war Mars (Ares).  Phobos was the ancient mythological god of fear (a phobia is a fear), and Deimos was the ancient mythological god of panic.  We use ♂ as the astronomical symbol for planet Mars.  The planet Jupiter is named for the ancient Roman mythological king of the gods (Zeus in ancient Greek mythology).  The planet Jupiter happens to be the largest and the most massive planet in the Solar System.  Therefore, naming this planet after the ancient mythological king of the gods seems to be appropriate.  However, the only way to determine the size of a planet is with a telescope, which was not invented until the Modern Ages.  Also, the only way to calculate the mass of a planet is using Kepler’s third law, which again was not formulated until the Modern Ages.  So, the fact that the ancient Romans named the planet Jupiter in the sky after their mythological king of the gods is actually a remarkable coincidence.  We use ♃ as the astronomical symbol for planet Jupiter.  The planet Saturn is named for the youngest of the ancient mythological titans (Kronos in ancient Greek mythology).  The mythological titan Saturn (Kronos) was the father of the mythological god Jupiter (Zeus).  In the Modern Ages after the telescope was invented, the planet Saturn was discovered to have many moons.  The largest moon was named Titan, since the mythological Saturn (Kronos) was the youngest of the mythological titans.  We use ♄ as the astronomical symbol for planet Saturn.  The planets Uranus and Neptune were not discovered until the Modern Ages after the telescope was invented.  We will include Pluto in this discussion, even though Pluto is not a planet, as we will discuss shortly.  Pluto was also not discovered until the Modern Ages after the telescope was invented.  Nevertheless, astronomers have decided to continue this ancient tradition of naming planets after ancient Roman mythological gods.  The planet Uranus is named for the ancient Greek mythological god of the sky (Caelus in ancient Roman mythology).  Note that Uranus is the only planet named for an ancient Greek mythological god instead of an ancient Roman mythological god.  The mythological god Caelus (Uranus) was the father of the mythological titans, including Saturn (Kronos).  Therefore, Caelus (Uranus) was also the grandfather of Jupiter (Zeus).  We use ⛢ as the astronomical symbol for planet Uranus.  The planet Neptune is named for the ancient Roman mythological god of the sea (Poseidon in ancient Greek mythology).  The largest moon of planet Neptune is Triton, named for the mythological son of the god of the sea Neptune (Poseidon).  The mythological god Triton carried a trident, a three-pronged spear.  We use ♆ as the astronomical symbol for planet Neptune.  The celestial body Pluto is named for the ancient Roman mythological god of the underworld (Hades in ancient Greek mythology).  The largest moon of Pluto is Charon, named for the mythological boatman who ferried souls across the mythological river Styx to the underworld.  As an extraordinary coincidence, the wife of American astronomer James W. Christy who discovered the moon Charon was named Charlene, who already used the nickname Char before her husband discovered the moon Charon!

 

During our survey of the Solar System, we will discuss each of the planets extensively.  Generally, we will discuss the planets in order, from closest to the Sun to furthest from the Sun.  However, we will begin with the Earth-Moon system, which we will discuss in tremendous detail.  We will discuss the Earth-Moon system in tremendous detail since we know more about planet Earth than any other planet in the Solar System.  The reason for this is obvious: we live on planet Earth and can therefore directly study the Earth.  After we discuss the Earth-Moon system in tremendous detail, we will then discuss the other terrestrial planets (Mercury, Venus, and Mars) by comparing them and contrasting them with the Earth.  We will then discuss the jovian, gas-giant planets.  Finally, we will conclude our survey with a discussion of the minor objects of the Solar System.

 

 

The Earth-Moon System

 

Planet Earth is the third planet from the Sun.  The solid part of planet Earth is layered.  The most dense layer of the Earth is the core at its center.  The core is composed primarily of metals, such as iron and nickel.  The next layer of the Earth surrounding the core is the mantle, which is less dense than the core.  The mantle is composed primarily of rock, which is itself composed primarily of silicates.  Silicates are minerals composed of silicon atoms, oxygen atoms, and other atoms chemically bonded to one another.  There are also fair amounts of metals in the mantle, such as iron.  Therefore, the mantle is actually composed of iron-rich silicate rock.  The outermost layer of the Earth surrounding the mantle is the crust.  The crust is the least dense layer of the Earth and the thinnest layer of the Earth.  The crust is also composed of silicate rock, but there are fewer metals such as iron in the crust as compared with the mantle.  Therefore, the crust is composed of iron-poor silicate rock.

 

The Earth’s core is itself layered.  At the very center of the Earth is the inner core, composed primarily of metals such as iron and nickel.  The temperature of the Earth’s core is very hot, for reasons we will discuss shortly.  These hot temperatures should be sufficient to melt metals into the molten state.  However, the pressure of the inner core is so enormous that the metals are compressed into the solid state even though they are at temperatures where they should be in the molten state.  Since the inner core is composed of solid metal, the inner core is also called the solid core.  The layer around the solid (inner) core is the outer core, which is also composed primarily of metals such as iron and nickel.  Again, the temperature of the outer core is sufficiently hot to melt metals into the molten state.  Although the pressure of the outer core is enormous by human standards, the pressure is nevertheless not as high as the pressure of the inner core.  Therefore, the pressure of the outer core is not sufficient to compress metals into the solid state.  The outer core is therefore molten, as metals should be at these hot temperatures.  Since the outer core is composed of molten metal, the outer core is also called the molten core.  Surrounding the molten (outer) core is the first layer of the mantle: the mesosphere.  The Greek root meso- means middle.  For example, Central America is sometimes called Mesoamerica, as in Middle America.  Therefore, the word mesosphere simply means middle sphere or middle layer.  The next layer of the mantle that surrounds the mesosphere is the asthenosphere.  This layer of the mantle is composed of weak rock.  Indeed, the Greek root astheno- means weak.  The asthenosphere is composed of weak rock that is still mostly solid, although parts of the asthenosphere are composed of rock that is partially molten.  Finally, the rest of the mantle together with the entire crust is called the lithosphere.  The lithosphere is of varying thickness.  Some parts of the lithosphere are so thick that they protrude out of the oceans.  These thick parts of the lithosphere are called continents.  The parts of the lithosphere that are thin are the ocean basins at the bottom of the ocean.

 

How have geophysicists determined the layers of the Earth, their thicknesses, their compositions, and their physical states (solid or molten)?  Have we drilled to the center of the Earth and directly studied the interior of the Earth?  No, we have come nowhere near drilling to the center of the Earth.  We have barely drilled through the Earth’s crust, which is by far the thinnest layer of the Earth.  We will never have technology advanced enough to drill far beyond the crust, and reaching the core is out of the question.  Geophysicists have determined the layers of the Earth, their thicknesses, their compositions, and their physical states (solid or molten) using seismic waves.  We will discuss earthquakes in more detail shortly.  For now, earthquakes cause waves that propagate (travel) throughout the entire planet Earth.  These waves are called seismic waves, and a seismometer is a device that detects seismic waves.  There are millions of earthquakes on planet Earth every day.  Most earthquakes are so weak that humans cannot feel them, but seismometers sensitive (accurate) enough can detect incredibly weak seismic waves.  Geophysicists have placed thousands of seismometers all over planet Earth to detect these seismic waves.  Surface seismic waves propagate (travel) along the surface of the Earth, while body seismic waves propagate (travel) throughout the interior of the Earth.  There are two different types of body seismic waves: pressure waves and shear-stress waves.  A pressure is a force exerted directly onto (perpendicularly onto) an area.  Consequently, a pressure wave is a longitudinal wave that may propagate (travel) through solids, liquids, and even gases, since all that is necessary for a longitudinal wave to propagate is for atoms or molecules to collide with other atoms or molecules in the direction of propagation.  A shear-stress is a force exerted along (parallel across) an area.  Consequently, a shear-stress wave is a transverse wave that can propagate (travel) through solids but not through liquids or gases, since there must be strong chemical bonding for atoms or molecules to pull other atoms or molecules perpendicular to the direction of propagation.  Also, pressure waves propagate faster than shear-stress waves.  Therefore, a seismometer will always detect pressure waves first.  For this reason, pressure waves are also called primary waves.  A seismometer will always detect shear-stress waves second, since they propagate slower than pressure (primary) waves.  For this reason, shear-stress waves are also called secondary waves.  By an amazing coincidence, the words pressure and primary both begin with the same letter.  Therefore, these waves are also called P-waves.  By another amazing coincidence, the words shear, stress, and secondary also all begin with the same letter!  Therefore, these waves are also called S-waves.  We can calculate how distant an earthquake occurred from a seismometer from the arrival times of the P-waves and the S-waves.  If a seismometer detects the S-waves a long duration of time after the P-waves, the earthquake must have occurred far from the seismometer, since the P-waves had sufficient distance to propagate (travel) far ahead of the S-waves, resulting in a long delay between them.  If the seismometer detects the S-waves immediately after the P-waves, the earthquake must have occurred near the seismometer, since the P-waves did not have sufficient distance to propagate (travel) that far ahead of the S-waves, resulting in a short delay between them.  In summary, we calculate the distance the seismic waves propagated from the arrival times of the P-waves and the S-waves.  We now have the distance of propagation, and we certainly know the time of propagation since we know when the earthquake occurred and when the seismometer detected the seismic waves.  We can then calculate the speed of the seismic waves, since the speed of anything equals its distance traveled divided by its time of travel.  Once we have the speed of the seismic waves, we can determine the properties of the materials that would cause that speed of propagation, whether the material was solid metal, molten metal, solid rock, or molten rock.  We can program a computer with all of these data, and the computer can calculate the layers of the Earth, their thicknesses, their compositions, and their physical states (solid or molten) from all these data.  Also, we are certain that the interior of the Earth is at least partially molten, since seismometers on the opposite side of planet Earth from an earthquake do not detect S-waves; these seismometers only detect P-waves.  As we discussed, S-waves cannot propagate through liquids; they can only propagate through solids.  However, P-waves can propagate through either solids or liquids, as we discussed.  In fact, the opposite side of planet Earth from any earthquake is called the shadow zones of that particular earthquake.  This term comes from the idea that the molten (outer) core casts a shadow, preventing those seismometers from detecting S-waves.  In actuality, the S-waves cannot propagate through the molten (outer) core, while the P-waves can propagate through the molten (outer) core.  Hence, seismometers in the shadow zones only detect P-waves from earthquakes on the opposite side of planet Earth.  In summary, by using thousands of seismometers all over planet Earth that detect seismic waves from millions of earthquakes each day and by running computer simulations, geophysicists have determined the layers of the Earth, their thicknesses, their compositions, and their physical states.

 

It cannot be accidental or coincidental that the solid part of the Earth is layered according to density.  Why are the inner layers more dense while the outer layers are less dense?  To explain this layering, we must discuss the formation of the Earth.  As we discussed, the entire Solar System is roughly 4.6 billion years old, and the Earth (indeed all the terrestrial planets) were born as small, dense planetesimals that grew larger through accretion.  Again, accretion is the gaining of mass through sticky collisions.  During a sticky collision, a significant fraction of the kinetic energy (moving energy) of the colliding objects is converted into thermal energy (heat energy).  Thus, objects that suffer from sticky collisions become significantly warmer.  Therefore, as the Earth was forming and growing larger through accretion, it became warmer.  Eventually, the Earth became so hot that it became almost entirely molten.  While the Earth was almost entirely molten, more dense materials were able to sink toward the center of the planet while less dense materials were able to rise toward the surface of the planet.  Most metals are more dense than most rocks.  That is, most rocks are less dense than most metals.  Therefore, most of the metals sank toward the center of the planet, forming the core.  Most of the rocks rose toward the surface of the planet, forming the mantle and the crust.  The process by which any planet separates materials according to density is called differentiation, and the planet is said to be differentiated.  A planet larger than the Earth would be more severely differentiated than the Earth, since it would have more mass and therefore stronger gravity that would pull the metals towards the center of the planet more strongly.  A planet smaller than the Earth would be less severely differentiated than the Earth, since it would have less mass and therefore weaker gravity that would pull the metals toward the center of the planet less strongly.  For example, planet Mars is smaller than the Earth.  Therefore, Mars has less mass and thus weaker gravity as compared with the Earth.  Hence, Mars is less severely differentiated as compared with the Earth.  Of course, planet Mars is still differentiated.  It has a dense core composed primarily of metals such as iron, and it has less dense outer layers composed primarily of rock.  Nevertheless, Mars is less severely differentiated as compared with the Earth, meaning that not all of the metals sank toward the center of Mars to form its core.  This is also the case with the Earth.  Although most of the metals sank toward the center of the Earth to form its core, there are still fair amounts of metals in the mantle and small amounts of metals in the crust.  Since Mars is less severely differentiated as compared with the Earth, we find more iron on the surface of Mars as compared with the amount of iron on the surface of the Earth.  The abundance of iron on the surface of Mars has oxidized.  Iron oxide is commonly known as rust, which has a reddish color.  This is why Mars is red.  In fact, the nickname of planet Mars is the Red Planet.  Mars even appears red to the naked eye (without the aid of a telescope or even binoculars) in our sky.

 

The Earth has a magnetic field, but we do not completely understand how this magnetic field is generated.  According to older theories, the Earth’s magnetic field is generated by its solid (inner) core.  This theory may seem reasonable, since the solid (inner) core is composed of ferromagnetic metals such as iron and nickel.  However, we now realize that this old model is too simplistic.  According to more modern theories, the Earth’s magnetic field is created by its molten (outer) core.  This more modern theory also seems reasonable, since the molten (outer) core is also composed of ferromagnetic metals such as iron and nickel.  These modern theories claim that the rotation of the Earth causes circulating currents of molten metal in the outer core.  These circulating currents of molten metal in turn generate the Earth’s magnetic field.  These more modern theories seem reasonable, but nevertheless these theories are not fully developed.  If these models are correct, then the two equally important variables that create a terrestrial planet’s magnetic field is a metallic core that is at least partially molten and reasonably rapid rotation.  Indeed, among all of the terrestrial (inner) planets of the Solar System, the Earth has the strongest magnetic field, since it is the only terrestrial planet that has both a partially molten metallic core and reasonably rapid rotation.  For example, Venus probably has a partially molten metallic core, but Venus has very slow rotation.  Hence, Venus has a very weak magnetic field.  As another example, Mars has reasonably rapid rotation, but Mars has a metallic core that is no longer partially molten.  Hence, Mars also has a very weak magnetic field.  The planet Mercury has neither a partially molten metallic core nor reasonably rapid rotation.  This may lead us to conclude that Mercury has the weakest magnetic field among all the terrestrial planets.  However, Mercury has a modest magnetic field, stronger than the magnetic fields of Venus and Mars.  We will discuss the theory to explain Mercury’s modest magnetic field shortly.  Nevertheless, Mercury’s magnetic field is still weak as compared with the Earth’s magnetic field.  Therefore, even Mercury’s modest magnetic field does support the theory that a terrestrial planet’s magnetic field is created by both a partially molten metallic core and reasonably rapid rotation.  Caution: in this discussion, we are only comparing the magnetic fields of the terrestrial (inner) planets.  Although the Earth has the strongest magnetic field among the terrestrial (inner) planets, its magnetic field is still weak as compared with all of the jovian, gas-giant (outer) planets.

 

The overall structure of the Earth’s magnetic field is very much similar to the magnetic field created by a bar magnet, such as a refrigerator magnet.  In fact, the only difference between the Earth’s magnetic field and a bar magnet’s magnetic field is strength.  The Earth’s magnetic field is thousands of times weaker than a bar magnet’s magnetic field.  That is, a bar magnet’s magnetic field is thousands of times stronger than the Earth’s magnetic field.  Students often cannot believe that a small refrigerator magnet could create a stronger magnetic field than an entire planet, but this stands to reason actually.  A refrigerator magnet’s magnetic field is strong enough to lift paper clips for example, but the Earth’s magnetic field is not this strong.  The Earth’s magnetic field is everywhere around us, yet we do not see paper clips floating around us!  A refrigerator magnet’s magnetic field is strong enough to lift paper clips against planet Earth’s gravitational field, but planet Earth’s magnetic field is not strong enough to lift paper clips against its own gravitational field.  Hence, the Earth’s magnetic field is indeed thousands of times weaker than a bar magnet’s magnetic field.

 

The Earth’s magnetic field reverses itself once every few hundred thousand years.  We do not understand how or why this occurs.  We do know that this does happen from the magnetization of iron within rocks.  The uppermost layer of rock has its iron magnetized in the same direction as the Earth’s magnetic field; this is called normal polarity.  However, a deeper layer of rock has its iron magnetized in the opposite direction of the Earth’s magnetic field; this is called reverse polarity.  An even deeper layer of rock has normal polarity again, and an even more deep layer of rock has reverse polarity again.  In other words, the magnetization of iron within rock (the polarity) alternates from normal to reverse and back again.  The reason for this is clear.  When new rock forms, the iron within that rock will become magnetized in whichever direction the Earth’s magnetic field happens to point at the time of that rock’s formation.  The Earth’s magnetic field must reverse itself periodically to cause the alternating polarity of rock layers.  Therefore, we are certain that the Earth’s magnetic field reverses itself once every few hundred thousand years, but again we do not understand how or why this occurs.

 

It is a common misconception that the Earth’s magnetic field begins at the north pole and ends at the south pole.  This is false for a couple of reasons.  Firstly, it is a basic law of physics that magnetic field lines are not permitted to begin or end anywhere.  Magnetic field lines must form closed loops.  The magnetic field lines of a bar magnet, such as a refrigerator magnet for example, do not begin at the north pole of the magnet, nor do they end at the south pole of the magnet.  The magnetic field lines of a bar magnet go straight through the magnet, coming out of its north pole, circulating around to go into its south pole, going straight through the magnet, and coming out its north pole again.  Similarly, the magnetic field lines of planet Earth go straight through the planet, coming out one end, circulating around to go into the opposite end, going straight through the planet, and coming out again.  Moreover, the Earth’s magnetic field lines do not come out from nor do they go into the terrestrial poles (the geographical poles).  The Earth’s magnetic field lines come out from and go into the magnetic poles, which are different from the terrestrial (geographical) poles.  Indeed, a magnetic compass does not point toward terrestrial (geographical) north as is commonly believed.  A magnetic compass points toward magnetic north, which again is different from terrestrial (geographical) north.  Admittedly, the Earth’s magnetic poles are somewhat close to the planet’s terrestrial (geographical) poles, but there is no reason to expect that the magnetic poles should be the same or even close to the terrestrial (geographical) poles.  The solid (inner) core is literally floating within the molten (outer) core.  Therefore, the solid (inner) core is actually detached from the rest of the planet.  Consequently, there is no reason to expect that the solid (inner) core is rotating in precisely the same direction as the rest of the planet.  In addition, there are circulating currents of molten metal within the molten (outer) core.  In brief, the rotation of the Earth is complicated; the entire planet does not rotate together as one solid unit.  Therefore, there is no reason to expect that the magnetic poles should be the same or even close to the terrestrial (geographical) poles.  To ask why the Earth’s magnetic poles are different from the terrestrial (geographical) poles is a wrong question to ask, since there is no reason to expect that the magnetic poles should be the same as the terrestrial (geographical) poles.  The correct question to ask is why are the Earth’s magnetic poles even close to the Earth’s terrestrial (geographical) poles.  We do not understand why this is the case.  Indeed, other planets have magnetic poles that are completely different from their geographical poles.

 

The solar wind is a stream of charged particles from the Sun composed primarily of protons (hydrogen nuclei), electrons, and alpha particles (helium nuclei).  This solar wind is capable of substantially ionizing the Earth’s atmosphere in a fairly short amount of time.  Fortunately, the Earth’s magnetic field, although weak compared with the magnetic field of bar magnets, is sufficiently strong to deflect most of the Sun’s solar wind.  Some of the charged particles in the solar wind do however become trapped within the Earth’s magnetic field.  These charged particles execute helical trajectories around the Earth’s magnetic field lines.  These regions of the Earth’s magnetic field are called the Van Allen belts, named for the American physicist James Van Allen who discovered these belts in the year 1958.  The charged particles within the Van Allen belts execute helical trajectories while drifting along the Earth’s magnetic field lines toward the magnetic poles.  The charged particles eventually collide with the molecules of the Earth’s atmosphere, surrendering their kinetic energy by emitting light.  The result is gorgeous curtains of light or sheets of light across the sky near the Earth’s magnetic poles.  This is called an aurora.  Near the Earth’s north magnetic pole it is called aurora borealis (or more commonly the northern lights), and near the Earth’s south magnetic pole it is called aurora australis (or more commonly the southern lights).  If the Sun happens to be less active, its solar wind would be weaker, the resulting aurorae would appear less spectacular, and we would only be able to enjoy them near the Earth’s magnetic poles.  If the Sun happens to be more active, its solar wind would be stronger, the resulting aurorae would appear more spectacular, and we would be able to enjoy them further from the Earth’s magnetic poles.  For example, the Battle of Fredericksburg in December 1862 during the American Civil War was interrupted by the appearance of the aurora borealis in the sky, even though Fredericksburg, Virginia is quite far from the Earth’s north magnetic pole.

 

The interior of the Earth is hot due to geothermal energy.  This geothermal energy drives geologic activity, as we will discuss shortly.  The source of this geothermal energy is primarily radioactive decay.  There are certain atoms that have an unstable nucleus, since the nucleus has too much energy.  To stabilize itself, the nucleus will emit particles to decrease its own energy.  These atoms are called radioactive atoms, and the emission of these particles is called radioactive decay.  A certain naturally occurring fraction (percentage) of all the atoms in the universe are radioactive.  A certain fraction (percentage) of the atoms that compose planet Earth are radioactive.  When these atoms suffer from radioactive decay, the emitted particles are themselves a source of energy.  This is the source of the Earth’s geothermal energy.  A planet larger than the Earth would have a longer geologic lifetime than the Earth, since it would have more mass and therefore more radioactive atoms and hence a greater supply of internal energy.  A planet smaller than the Earth would have a shorter geologic lifetime than the Earth, since it would have less mass and therefore less radioactive atoms and hence a smaller supply of internal energy.  Billions of years from now, most of the radioactive atoms of planet Earth will have decayed.  With very little radioactive atoms remaining to provide geothermal energy, geologic activity will end, and the Earth will become a geologically dead planet.  This geologic death has already occurred for other planets smaller than the Earth.  The planets Mercury and Mars for example are geologically dead planets, since they are significantly smaller than the Earth.  However, planet Venus has almost the same size as the Earth.  Presumably, the geologic lifetime of Venus is roughly the same as the geologic lifetime of the Earth.  Indeed, both Venus and the Earth are currently geologically alive.

 

The three mechanisms by which heat (energy) is transported from one location to another are conduction, convection, and radiation.  Conduction is the transfer of heat (energy) from one object to another because they are in direct contact with one another.  For example, our hand becomes hot when we grab a hot object because our hand is in direct contact with the hot object when we grab it.  The heat (energy) is transferred from the hot object to our hand by conduction, since our hand is in direct contact with the hot object.  Convection is the transfer of heat (energy) from one object to another by moving materials.  It is commonly known that hot air rises and cold air sinks.  This is not just true for air; this is true for any gas and for any liquid as well.  In physics, gases and liquids are both considered fluids.  Caution: in colloquial English, the word fluid refers to liquids only, but in physics the word fluid may apply to both liquids and gases.  Convection is the transfer of heat (energy) by moving fluids, since hot fluids rise and cool fluids sink.  For example, a heater on the first floor of a house also warms the second floor by convection.  The heater on the first floor warms the air on the first floor; since hot fluids rise, the hot air rises to the second floor and warms the second floor.  When the air that has risen to the second floor loses its heat and cools, it sinks back to the first floor, where it is warmed again by the heater.  Radiation is the transfer of heat (energy) without direct contact and without moving fluids.  Radiation typically transports heat (energy) using electromagnetic waves, which are actually composed of photons as we discussed earlier in the course.  For example, heat (energy) is not transported from the Sun to the Earth by conduction, since the Earth is not in direct contact with the Sun, thank God!  Heat (energy) is not transported from the Sun to the Earth by convection, since there is no fluid in outer space that takes the Sun’s heat (energy) and moves it to the Earth.  The Sun’s heat (energy) is transported to the Earth across outer space by radiation, through electromagnetic waves composed of photons.

 

The Theory of Plate Tectonics is the fundamental theory of the geology of planet Earth.  According to the Theory of Plate Tectonics, the Earth’s lithosphere is fractured (or broken) into roughly twenty pieces called tectonic plates.  The adjective tectonic is derived from a Greek word meaning construction or building.  In other words, the Theory of Plate Tectonics states that the Earth’s lithosphere is composed of (built from or constructed from) pieces.  These tectonic plates are floating on the asthenosphere and are being pushed very slowly by convection cells in the asthenosphere.  Mostly solid but nevertheless weak rock in the lower layers of the asthenosphere are heated by the Earth’s geothermal energy.  Since hot fluids rise, this hot rock rises until it reaches a tectonic plate of the lithosphere.  The risen rock then pushes the tectonic plate in a certain direction, since the thermal energy (heat energy) of the rock is transformed into the kinetic energy (moving energy) of the tectonic plate.  Since the tectonic plate gains kinetic energy at the expense of the thermal energy of the rock, the rock must become cooler as it pushes the tectonic plate.  Since cool fluids sink, the now cooler rock sinks back into the asthenosphere, where it is warmed again by the Earth’s geothermal energy.  In brief, there are circulating currents of weak rock within the asthenosphere.  These are called convection cells.  These convection cells push the tectonic plates very slowly, a few centimeters per year on average.  According to the Theory of Plate Tectonics, much geologic activity occurs at the boundary between two tectonic plates.  There are three different types of tectonic plate boundaries: divergent plate boundaries, convergent plate boundaries, and transform fault boundaries.

 

At a divergent plate boundary, two tectonic plates are being pushed away from each other.  The verb to diverge means to spread out.  As the tectonic plates are pushed away from each other, hot rock within the asthenosphere can rise and deposit itself onto the tectonic plates.  As the rock cools, it may crystallize into solid rock.  Hence, this is the youngest part of a tectonic plate, since newborn rock forms at divergent plate boundaries.  Entire mountain ranges can be built at divergent plate boundaries.  For example, the Mid-Atlantic Ridge runs along the middle of the Atlantic Ocean and assumes the same shape as the east coast of South America and the west coast of Africa.  The South American continent is actually a part of a much larger tectonic plate called the South American plate, and the African continent is actually a part of a much larger tectonic plate called the African plate.  The South American plate and the African plate are being pushed away from each other, permitting hot rock to rise out of the asthenosphere.  The hot rock has deposited onto both plates, has cooled, and has crystallized to form the Mid-Atlantic Ridge.  This is why the shape of the east coast of South America, the west coast of Africa, and the Mid-Atlantic Ridge between them are all similar to each other.  South America and Africa were connected to each other roughly two hundred million years ago, but they have been pushed apart from one another, thus forming the Mid-Atlantic Ridge at the boundary between these two tectonic plates.  North America and Europe were also connected to each other two hundred million years ago, and they are also being pushed apart from one another.  The Atlantic Ocean is continuously becoming wider very slowly, only a few centimeters per year.  The Red Sea between the Arabian peninsula and northeastern Africa is the result of another divergent plate boundary.  The Arabian peninsula was ripped off of the continent of Africa millions of years ago, opening up the Red Sea.  The African continent is still being ripped apart in southeastern Africa, forming the African Rift Valleys.  If we wait millions of years, the African Rift Valleys will rip open to become a narrow sea like the Red Sea.  If we wait millions of more years, that narrow sea will open even wider to become a growing ocean like the Atlantic Ocean.

 

At a convergent plate boundary, two tectonic plates are being pushed toward each other.  The verb to converge means to come together.  As the tectonic plates are pushed toward each other, they eventually collide.  The more dense tectonic plate will sink into the asthenosphere, while the less dense tectonic plate will rise out of the asthenosphere.  Hence, the more dense plate will sink underneath the less dense plate.  As the more dense tectonic plate sinks into the asthenosphere, it is heated by the Earth’s geothermal energy.  Eventually, the plate becomes so hot that it melts.  Hence, this is the oldest part of a tectonic plate, since the tectonic plate is being destroyed as it melts into molten rock.  Liquids are usually less dense than solids.  Hence, this less dense molten rock may rise and collide underneath the other tectonic plate; the molten rock may even push through the other tectonic plate, forming active volcanoes.  For example, the Nazca plate at the bottom of the Pacific Ocean and the South American plate are being pushed toward each other.  The Nazca plate is more dense, while the South American plate is less dense.  Thus, the Nazca plate is sinking underneath the South American plate.  As the Nazca plate sinks, it is heated by the Earth’s geothermal energy.  The Nazca plate melts, and the less dense molten rock rises.  The molten rock collides underneath and even pushes through the South American plate, forming the Andes Mountains on the west coast of South America.  Indeed, many of the mountains in the Andes are volcanically active.  The Nazca plate is an example of an oceanic plate, since it is at the bottom of the Pacific Ocean.  The South American plate is an example of a continental plate, since it is mostly the South American continent.  Hence, the Andes Mountains have formed at an oceanic-continental convergent plate boundary.  At an oceanic-oceanic convergent plate boundary, two oceanic plates collide.  Again, the more dense plate will sink underneath the less dense plate.  The more dense plate is heated and melts.  The molten rock rises and collides underneath and may even push through the other tectonic plate, again forming active volcanoes.  These are island volcanoes, such as the Aleutian Islands in Alaska or the Japanese Islands or the Philippine Islands.  A subduction zone is wherever one tectonic plate sinks underneath another tectonic plate.  There are two different types of subduction zones: oceanic-continental convergence and oceanic-oceanic convergence.  However, continental-continental convergence does not result in a subduction zone, since continental plates are too thick to permit one plate to sink underneath the other plate.  If two continental plates collide and if convection cells in the asthenosphere continue to push them toward each other, the rock of both plates becomes folded.  If we apply a large force to rock in a short duration of time, we will fault (break) the rock.  However, if we apply a small force to rock over a long duration of time, we will bend or deform or warp the rock.  The technical term for this bending or deforming or warping is folding.  If we apply a small force to rock over a long duration of time, we will fold the rock.  Hence, two colliding continental plates become folded.  The rocks are folded upward forming non-volcanic mountains, since there is no subduction.  The technical term for these non-volcanic mountains is fold mountains.  For example, millions of years ago the Indian plate was near the South Pole.  The Indian plate was pushed northward and closed up an ancient ocean that no longer exists.  The Indian plate eventually collided with the Eurasian plate.  As the plates continue to be pushed toward each other, they have folded upward forming the Himalayas, the tallest mountains in the world.  The Himalayas continue to grow taller, although very slowly, as the Indian plate and the Eurasian plate continue to be pushed toward each other.  Mount Everest is in the Himalayas, is the tallest mountain in the world, and is still growing taller, although only a few centimeters per year.  The Appalachian Mountains are another example of fold mountains.  Two hundred million years ago, the North American plate and the Eurasian plate collided and folded upward, forming the Appalachian Mountains.  The Appalachian Mountains were the tallest mountains in the world roughly two hundred million years ago.  However, over the past two hundred million years, the North American plate and the Eurasian plate have diverged from one another, and thus the Appalachian Mountains are no longer growing taller.  In fact, the Appalachian Mountains are continuously becoming shorter as natural forces such as wind and rain degrade (weaken and destroy) their rocks, ultimately breaking them down into sediment and moving the sediment to other landscapes.  The Ural Mountains are also fold mountains.  Hundreds of millions of years ago, Europe and Asia were two separate continents.  They collided, forming the Ural Mountains.  In summary, there are three different types of convergent plate boundaries: oceanic-continental convergence, oceanic-oceanic convergence, and continental-continental convergence.  At oceanic-continental convergence, we have volcanoes on a continent such as the Andes Mountains.  At oceanic-oceanic convergence, we have island volcanoes such as the Aleutian Islands, the Japanese Islands, and the Philippine Islands.  These two cases are subduction zones.  However, at continental-continental convergence, we do not have subduction; we have fold mountains such as the Himalayas, the Appalachians, or the Urals.

 

At a transform fault boundary, two tectonic plates slide across each other.  Tectonic plates are not smooth, since they are composed of rock.  Hence, the sliding of the tectonic plates across each other causes seismic activity, such as weak vibrations.  On occasion, the two tectonic plates become stuck, but the convection cells in the asthenosphere continue to try to push the plates across each other.  It may take years or even decades, but eventually the plates become unstuck and slide across each other by a tremendous amount, perhaps several meters.  An enormous amount of energy is liberated from years or even decades of accumulated stored energy within the rock, thus causing intense vibrations.  This powerful type of seismic activity is called an earthquake.  For example, the San Andreas Fault is the boundary between the North American plate and the Pacific plate.  The North American plate is being pushed south, while the Pacific plate is being pushed north.  The sliding of these two tectonic plates across each other causes seismic activity, including earthquakes.  This explains why there is an abundance of seismic activity, including earthquakes, in California, since it is on the west coast of North America at the boundary between the North American plate and the Pacific plate.  This also explains why the shape of Baja California fits into the shape of Mexico.  Millions of years ago, Baja California was connected to Mexico.  As these two tectonic plates were pushed in two opposite directions, Baja California was ripped off of the Mexican mainland, opening up the Sea of Cortez.  If we wait millions of years, all of Baja California together with upper California (the State of California) will be ripped off of the North American mainland forming an enormous island off the west coast of North America.  Geologists have given this future island a name even though it has not yet been born; it is called the Island of California.  The Island of California will then continue to move north as the Pacific plate continues to be pushed north.

 

Most geologic activity occurs at ocean basins (at the bottom of the ocean), simply because most of the world is covered with ocean.  For example, most seismic activity such as earthquakes occurs at the bottom of the ocean.  Most igneous activity such as volcanic eruptions occurs at the bottom of the ocean.  Most mountains are at the bottom of the ocean.  Even most landslides occur at the bottom of the ocean.  The San Andreas Fault is actually an example of a continental-continental transform fault boundary.  The Queen Charlotte Fault off the west coast of Canada is an example of an oceanic-oceanic transform fault boundary that causes earthquakes at the bottom of the Pacific Ocean and near the west coast of Canada.  Just as it is popularly known among many Americans that the San Andreas Fault continually causes earthquakes near their west coast, it is popularly known among many Canadians that the Queen Charlotte Fault continually causes earthquakes near their west coast.

 

According to the Theory of Plate Tectonics, geologic activity does not just occur at plate boundaries.  Geologic activity also occurs at hotspots, which are caused by mantle plumes.  A mantle plume is a rising mass of hot rock within the asthenosphere.  The rising mantle plume eventually collides underneath a tectonic plate.  This collision can occur anywhere underneath the tectonic plate depending on the location of the mantle plume.  The collision need not be located at a plate boundary; the collision could even occur in the middle of a tectonic plate.  After the collision, the hot rock may push through the tectonic plate, causing geologic activity at this location on the tectonic plate.  This is called a hotspot.  For example, there is volcanic activity in the Hawaiian Islands, but the Hawaiian Islands are nowhere near a plate boundary; the Hawaiian Islands are in the middle of the Pacific plate.  The volcanic activity in the Hawaiian Islands is caused by a hotspot, which is itself caused by a mantle plume.  Molten rock pushes out of the Pacific plate at the bottom of the Pacific Ocean.  The extruding molten rock builds a volcano at the bottom of the Pacific Ocean.  More extruding molten rock grows the volcano taller and taller until it protrudes out of the Pacific Ocean.  It is now a volcanic island.  We all learn in primary (elementary) school that Mount Everest in the Himalayas is the tallest mountain in the world.  Actually, if we measure the height of the Hawaiian Islands above their true base, which is at the bottom of the Pacific Ocean, then the Hawaiian Islands are in fact the tallest mountains in the world.  As measured from their true base at the bottom of the Pacific Ocean, the Hawaiian Islands are much taller than Mount Everest.  It is however strictly correct to state that Mount Everest has the highest elevation above sea level.

 

The rocks that compose the westernmost Hawaiian island are oldest, while the rocks that compose the Hawaiian Islands further and further east are younger and younger.  The rocks that compose the easternmost Hawaiian island (commonly known as the Big Hawaiian Island) are youngest, and that is the only Hawaiian island with active volcanism.  All the other volcanoes on all the other Hawaiian Islands are extinct.  This suggests that the hotspot is moving east, but in actuality the Pacific plate is moving west over the hotspot.  As the Pacific plate moves west, the hotspot pushes up a Hawaiian island with active volcanism.  As the Pacific plate continues to move west, that Hawaiian island moves west and off of the hotspot causing its volcanoes to become extinct, while the hotspot pushes up a new Hawaiian island with active volcanism.  As the Pacific plate continues to move west, that Hawaiian island moves west and off of the hotspot causing its volcanoes to become extinct, while the hotspot pushes up a new Hawaiian island, and so on and so forth.  If we wait millions of years, the Big Hawaiian Island will move off of the hotspot, its volcanoes will become extinct, and the hotspot will push up a new Hawaiian island to the east of the easternmost Big Hawaiian Island.  This is already beginning to occur.  To the east of the easternmost Big Hawaiian Island, there is a small active volcano at the bottom of the Pacific Ocean.  If we wait millions of years, that active volcano will grow to become a new Hawaiian island.

 

Imagine a terrestrial globe that depicts the shapes of the continents and the oceans.  The Theory of Plate Tectonics has revealed that the Earth has never looked this way before and that the Earth will never look this way again.  If the tectonic plates are slowly but continuously being pushed by convection cells in the asthenosphere, then the shapes of the continents and the oceans are slowly but continuously changing.  We do not notice this occurring, but we would notice significant changes if we wait millions of years.  During some eras of Earth’s history, the continents may have been more uniformly (evenly) distributed around the planet.  During other eras in Earth’s history, the continents may have all been together as one giant landmass called a supercontinent.  A supercontinent is surrounded by a superocean, the unity of all the oceans around the supercontinent.  According to the supercontinent cycle, once every roughly five hundred million years, all the continents are together as a supercontinent surrounded by a superocean.  If planet Earth is roughly 4.6 billion years old and if there is a supercontinent every roughly five hundred million years, this means that there have been roughly nine or ten supercontinents thus far in Earth’s history.  As we will discuss later in the course, in roughly five billion years the Sun will swell to become a red giant, thus destroying all four of the terrestrial (inner) planets, including the Earth.  If the Earth will be destroyed in roughly five billion years and if there is a supercontinent every roughly five hundred million years, then there will be roughly ten supercontinents in the Earth’s future.  Therefore, over the entire history of planet Earth, there have been and there will be very roughly twenty supercontinents.  Many students believe that we happen to be alive when the continents are uniformly (evenly) distributed around the planet, but this is not the case.  The continents are presently crowded together on the opposite side of planet Earth from the Pacific Ocean, which is by far the largest ocean in the entire world.  The continents are also presently more crowded toward the northern hemisphere as compared with the southern hemisphere.  Therefore, we happen to be alive not when the continents are more uniformly (evenly) distributed; we happen to be alive when the continents are rather crowded together.  This is because rather recently, roughly two hundred million years ago, all the continents were together in one giant supercontinent called Pangaea surrounded by a superocean called Panthalassa.  It is a common misconception that when the Earth formed, the continents were all together as Pangaea and have been spreading apart ever since.  This is false.  Again, there have been roughly ten supercontinents in Earth’s history thus far, and there will be another roughly ten supercontinents in the Earth’s future.  Not only was Pangaea not the first supercontinent in Earth’s history, Pangaea was in fact the most recent supercontinent in Earth’s history.  There were several other supercontinents before Pangea ever formed, and there will be several other supercontinents in the Earth’s future.

 

The Theory of Plate Tectonics has explained seismic activity, such as earthquakes in California.  The Theory of Plate Tectonics has explained subductive igneous activity, such as the volcanic activity in the Andes Mountains, the Aleutian Islands, the Japanese Islands, and the Philippine Islands.  The Theory of Plate Tectonics has explained the formation of non-volcanic mountains, such as the Himalayas, the Appalachians, and the Urals.  The Theory of Plate Tectonics has explained why the continents fit together like a jigsaw puzzle, such as the east coast of South America fitting into the west coast of Africa and the Arabian peninsula fitting into northeastern Africa and Baja California fitting into Mexico.  The Theory of Plate Tectonics has even explained the igneous activity of the Hawaiian Islands.  The Theory of Plate Tectonics is truly the fundamental theory of the geology of planet Earth.  Caution: the Theory of Plate Tectonics has not explained all of the geology of planet Earth; there are still many examples of geologic activity that geologists do not completely understand.  Nevertheless, whenever a geologist tries to understand any geologic activity on planet Earth, the geologist does so within the context of the Theory of Plate Tectonics.

 

During eras of Earth’s history when there was a supercontinent at the terrestrial equator, the climate of the entire planet would be warm, since the terrestrial equator is warm throughout the entire year.  During other eras of Earth’s history when there were continents that were relatively isolated at one or both terrestrial poles, the climate of the entire planet would be cold, since the terrestrial poles are cold throughout the entire year.  An ice age is a long period of time, lasting millions of years, when the climate of the entire planet is cold.  There have been a few ice ages throughout Earth’s history thus far.  It is truly remarkable how we have just applied the Theory of Plate Tectonics to climatology.  The Theory of Plate Tectonics is the fundamental theory of the Earth’s geology, the study of the solid part of the Earth.  We might suspect that this theory therefore has nothing to do with meteorology and climatology, which are the study of the Earth’s atmosphere.  However, we have just applied the Theory of Plate Tectonics to explain ice ages, a climatological phenomenon.  Therefore, the Theory of Plate Tectonics is not just the fundamental theory of geology of planet Earth; the Theory of Plate Tectonics is one of the fundamental theories of all the Earth Sciences.

 

Although the Theory of Plate Tectonics is the fundamental theory of the geology of planet Earth, the Theory of Plate Tectonics is not a universal law of geology.  In other words, the Theory of Plate Tectonics does not apply to every terrestrial planet in the universe.  The Theory of Plate Tectonics does not even apply to every terrestrial planet in our own Solar System.  In particular, the Theory of Plate Tectonics is not the correct theory to explain the geologic activity on Venus.  Geophysicists continue to search for the correct theory of the geology of planet Venus.

 

An atmosphere is a thin layer of gas gravitationally held to a moon, a planet, or a star.  The Earth’s atmosphere is roughly eighty percent nitrogen gas, roughly twenty percent oxygen gas, and tiny amounts of other gases.  The tiny amounts of other gases are quite important, as we will discuss shortly.  Every second of every day of our lives, we are breathing mostly nitrogen gas (roughly eighty percent) and a fair amount of oxygen gas (roughly twenty percent).  This roughly twenty-percent abundance of oxygen gas is an enormous fraction; other planets have nowhere nearly this much oxygen gas in their atmospheres.  Other planetary atmospheres have only tiny amounts of oxygen gas with a large abundance of carbon dioxide gas, as is the case with the atmospheres of planets Venus and Mars for example.  The Earth’s atmosphere has a large fraction of oxygen gas but only a tiny amount of carbon dioxide gas.  To understand why the Earth’s atmosphere is so different from other planetary atmospheres, we must discuss the history of the Earth’s atmosphere.  When the Earth formed roughly 4.6 billion years ago, its atmosphere was almost entirely hydrogen gas and helium gas; this is called the Earth’s primary atmosphere.  The primary atmosphere was almost entirely hydrogen and helium because the Earth together with the entire Solar System was born from a nebula composed of mostly hydrogen and helium, as we discussed.  The more massive (or heavier) an atom or molecule, the slower it moves; the less massive (or lighter) an atom or molecule, the faster it moves.  This is rather remarkable.  Suppose all the air in a room is at the same temperature, which means that all the air molecules in the room have the same average energy.  Nevertheless, the oxygen molecules are moving slower on average since they are more massive (or heavier), while the nitrogen molecules are moving faster on average since they are less massive (or lighter), even though all of the air is at the same temperature, which means both the nitrogen molecules and the oxygen molecules have the same average energy!  Hydrogen is the least massive (lightest) atom in the entire universe, and helium is the second least massive (second lightest) atom in the entire universe.  Hydrogen and helium are so light that they move so fast that they can escape from the Earth’s gravitational attraction.  Thus, the Earth lost its primary atmosphere because its own gravity was too weak to hold onto hydrogen and helium.  This occurred with all four of the terrestrial (inner) planets orbiting the Sun (Mercury, Venus, Earth, and Mars).  These four terrestrial (inner) planets have weaker gravity since they are smaller with less mass as compared with the four jovian, gas-giant (outer) planets orbiting the Sun (Jupiter, Saturn, Uranus, and Neptune).  These four jovian, gas-giant (outer) planets have stronger gravity since they are larger with more mass; thus, they have retained their primary (hydrogen and helium) atmospheres to the present day.  Even the gravity of the jovian, gas-giant (outer) planets is weak compared with the gravity of the Sun; therefore, the Sun has certainly retained its primary (hydrogen and helium) atmosphere to the present day.  To summarize, the Sun and the four jovian, gas-giant (outer) planets have retained their primary (hydrogen and helium) atmospheres, but the four terrestrial (inner) planets have lost their primary (hydrogen and helium) atmospheres.  After the Earth lost its primary atmosphere, this left behind a secondary atmosphere composed of an abundance of water vapor and nitrogen gas and carbon dioxide gas.  These gases came from volcanic outgassing.  Since the Earth was born almost entirely molten, volcanic eruptions everywhere on its surface ejected not just lava but gases as well.  These gases are significantly more massive (or heavier) than hydrogen and helium.  Therefore, they did not move fast enough to escape from the Earth’s gravitational attraction.  As the Earth cooled, the water vapor condensed into liquid water which precipitated back down onto the planet for such a long period of time that most of the surface of the Earth became flooded, thus forming the oceans.  At this point, the Earth may be regarded as having a normal atmosphere with an abundance of carbon dioxide gas similar to other planets such as Venus and Mars.  However, roughly one billion years after the Earth formed (roughly 3.6 billion years ago), something extraordinary occurred in the oceans that to our knowledge did not occur anywhere else in the entire universe: life appeared.  The first lifeforms were primitive unicellular microorganisms, such as bacteria and blue-green algae.  Some of the carbon dioxide gas of the atmosphere dissolved into the oceans, which these primitive lifeforms converted to oxygen gas.  Over the next roughly one billion years, the rock at the ocean floor was oxidized by the oxygen that these microorganisms continually synthesized.  When nearly all the rock at the ocean floor was oxidized, the oxygen gas that these primitive lifeforms continued to synthesize then began to accumulate within the oceans.  Some of this accumulating oxygen gas then dissolved back into the atmosphere.  After an additional roughly two billion years, these microorganisms actually succeeded in extracting almost all of the carbon dioxide gas from the atmosphere, replacing it with oxygen gas.  Thus, as of roughly 600 million years ago, planet Earth attained its tertiary atmosphere that we enjoy to the present day: roughly eighty percent nitrogen gas, roughly twenty percent oxygen gas, and tiny amounts of other gases.  Again, the tiny amounts of other gases are quite important, and we will discuss these trace gases shortly.

 

The pressure of the Earth’s atmosphere is typically a maximum at sea level and decreases exponentially with increasing elevation.  The equation that describes this decreasing pressure with increasing elevation is called the law of atmospheres, but we do not need this equation to understand why this is the case.  The Earth’s gravity pulls air downward; therefore, the air becomes thinner as we climb the atmosphere, making the air pressure less at higher elevations.  The average air pressure at sea level is called one atmosphere of pressure, equal to 101325 pascals of pressure.  One pascal of pressure is one newton of force per square meter of area.  This average air pressure of 101325 pascals is close enough to one hundred thousand pascals that meteorologists have defined another unit of air pressure: the bar.  One bar of air pressure is exactly one hundred thousand pascals of air pressure.  Thus, the average air pressure at sea level is equal to 1.01325 bars of pressure; this is also 1013.25 millibars of pressure.  When meteorologists report the air pressure on any given day, they may report that the air pressure is several millibars above average or several millibars below average.  A device to measure air pressure is called a barometer.  To build a primitive barometer, we insert a long, narrow container inverted into any liquid.  The air pressure will push downward onto the liquid, thus forcing the liquid upward into the long, narrow inverted column.  If the air pressure is greater than average, it will push downward more strongly onto the liquid, thus forcing the liquid further upward the inverted column, making the column of liquid taller.  If the air pressure is less than average, it will push downward less strongly onto the liquid, thus forcing the liquid not as far upward the inverted column, making the column of liquid shorter.  Thus, by measuring the height of the column of liquid and performing a calculation, we can determine the air pressure that has pushed downward onto the liquid.  Most barometers use the element mercury as the liquid; at average air pressure at sea level, liquid mercury will be pushed 760 millimeters (or 29.9 inches) up the narrow column.  Thus, the average air pressure at sea level is also equal to 760 millimeters of mercury (or 29.9 inches of mercury).  When meteorologists report the air pressure on any given day, they may report that the air pressure is several millimeters of mercury higher than average or several millimeters of mercury lower than average.  Barometers almost always use liquid mercury because mercury is between thirteen and fourteen times more dense than water.  In other words, mercury is between thirteen and fourteen times heavier than water; thus, gravity pulls mercury thirteen or fourteen times more strongly than water, making the column of mercury only 760 millimeters (or 29.9 inches) tall.  If a barometer used water instead of mercury, the column of water would be between thirteen or fourteen times taller; this would make barometers more than ten meters (almost thirty-four feet) tall!  It is not convenient to carry such a tall device; it is much more convenient to carry a barometer that is only 760 millimeters (or 29.9 inches) tall.  This is why almost all barometers use mercury instead of water.

 

Meteorologists have defined layers of the Earth’s atmosphere based on the variation of the temperature of the Earth’s atmosphere with elevation.  The lowest layer of the atmosphere is the troposphere.  With increasing elevation, the troposphere is followed by the stratosphere, then the mesosphere, and finally the thermosphere.  Beyond the thermosphere is the exosphere, where the air smoothly transitions from the Earth’s atmosphere to the surrounding outer space, as we will discuss shortly.  The temperature typically cools with increasing elevation within the troposphere, the lowest layer of the atmosphere.  However, we reach a certain elevation at which the temperature stops becoming cooler and begins instead to become warmer with increasing elevation.  This elevation defines the end of the troposphere and the beginning of the stratosphere.  This precise elevation is called the tropopause.  We may regard the tropopause as the boundary between the troposphere and the stratosphere, but the tropopause is more correctly defined as the end of the troposphere.  The temperature then typically becomes warmer with increasing elevation within the stratosphere.  The reason for this warming is a heat source within the stratosphere that we will discuss shortly.  However, we reach a certain elevation at which the temperature stops becoming warmer and begins instead to become cooler with increasing elevation.  This elevation defines the end of the stratosphere and the beginning of the mesosphere.  This precise elevation is called the stratopause.  We may regard the stratopause as the boundary between the stratosphere and the mesosphere, but the stratopause is more correctly defined as the end of the stratosphere.  The temperature then typically becomes cooler with increasing elevation within the mesosphere.  However, we reach a certain elevation at which the temperature stops becoming cooler and begins instead to become warmer with increasing elevation.  This elevation defines the end of the mesosphere and the beginning of the thermosphere.  This precise elevation is called the mesopause.  We may regard the mesopause as the boundary between the mesosphere and the thermosphere, but the mesopause is more correctly defined as the end of the mesosphere.  The temperature then typically becomes warmer with increasing elevation within the thermosphere.  The reason for this warming is a heat source within the thermosphere that we will discuss shortly.  However, we reach a certain elevation at which the temperature stops becoming warmer and begins instead to become cooler with increasing elevation.  This elevation defines the end of the thermosphere and the beginning of the exosphere.  This precise elevation is called the thermopause.  We may regard the thermopause as the boundary between the thermosphere and the exosphere, but the thermopause is more correctly defined as the end of the thermosphere.  The temperature then typically becomes cooler with increasing elevation within the exosphere, smoothly transitioning into the very cold temperatures of the surrounding outer space.  To summarize, the temperature typically becomes cooler with increasing elevation within the troposphere, the mesosphere, and the exosphere, while the temperature typically becomes warmer with increasing elevation within the stratosphere and the thermosphere.

 

It may seem reasonable to ask for the precise elevation at which the Earth’s atmosphere ends and outer space begins, but this is in fact an ill-defined question.  The concentration of gases in the Earth’s atmosphere becomes thinner and thinner with increasing elevation until we reach a certain elevation at which the concentration of gases matches the concentration of gases of the surrounding outer space.  It is a common misconception that outer space is a perfect vacuum, but this is false.  There is no such thing as a perfect vacuum; in fact, a perfect vacuum would violate the laws of physics.  In actuality, the entire universe is filled with extremely diffuse gas.  Therefore, the Earth’s atmosphere smoothly transitions into the gases of the surrounding outer space.  We may actually interpret the Earth’s atmosphere as extending forever, filling the entire universe.  The same interpretation can be applied to all other planetary atmospheres.  In other words, there is no well-defined exopause.  The tropopause is the end of the troposphere, the stratopause is the end of the stratosphere, the mesopause is the end of the mesosphere, and the thermopause is the end of the thermosphere.  If there were an end of the exosphere (which would also be the end of the entire atmosphere), that end would be called the exopause, but there is no well-defined exopause.  Nevertheless, if we insist upon a boundary between the Earth’s atmosphere and outer space, we may arbitrarily use the elevation of the tropopause, since the Earth’s gravity pulls most of the air in the entire atmosphere down into the troposphere.  Indeed, the vast majority of all meteorological phenomena (commonly known as weather) occurs within the troposphere, the lowest layer of the atmosphere.  So, we may arbitrarily regard the thickness of the Earth’s atmosphere as the elevation of the tropopause as a rough estimate.  The elevation of the tropopause is roughly ten kilometers above sea level.  Using this as a rough estimate for the thickness of the Earth’s atmosphere, we conclude that the atmosphere is extremely thin as compared with the average radius of the Earth, roughly 6400 kilometers.  To summarize, the Earth’s atmosphere extends indefinitely far according to strict interpretations, but the Earth’s atmosphere is only a few kilometers thick for all practical purposes.  The Earth’s atmosphere keeps us alive in a variety of different ways.  After we discuss all these ways the atmosphere keeps us alive, we will be humbled.  In this vast universe, we are only able to survive within a very thin layer of air surrounding a single planet: the atmosphere of planet Earth.

 

The most obvious way the Earth’s atmosphere keeps us alive is with its abundance of oxygen.  Humans and all animals must inhale oxygen gas to survive.  This is because humans and animals must react oxygen with glucose (a simple sugar) to extract the energy they need for their survival.  Humans ingest various sugars as well as complex carbohydrates such as bread, rice, cereal, and pasta.  Our bodies digest complex carbohydrates as well as sugars, breaking them down into glucose (a simple sugar).  There is a tremendous amount of energy stored within the chemical bonds of the glucose molecule, which our bodies access by reacting it with oxygen.  The human body is composed of roughly one hundred trillion cells.  Within these cells, the following reaction occurs: glucose plus oxygen yields energy plus carbon dioxide and water as waste products.  This reaction is called cellular respiration and is more properly written C6H12O6 + 6 O2 → energy + 6 CO2 + 6 H2O.  When we inhale, the oxygen gas that goes into our lungs is transferred to our blood; our blood then carries the oxygen to the trillions of cells of our bodies.  The oxygen enters our cells and reacts with glucose to yield energy.  The carbon dioxide that is produced as a waste product from the reaction is transferred back into our blood; our blood then carries the carbon dioxide back to our lungs, and we then exhale.  Cellular respiration not only explains why humans and animals must inhale oxygen gas; cellular respiration also explains why humans and animals must exhale carbon dioxide gas.  Plants inhale carbon dioxide gas to use together with water as the raw materials to synthesize glucose.  Plants use the energy of sunlight to initiate this reaction, which is why this reaction is called photosynthesis.  The photosynthesis reaction is more properly written 6 CO2 + 6 H2O + energy → C6H12O6 + 6 O2.  Notice that the photosynthesis reaction is precisely the reverse of the cellular respiration reaction.  Note also that oxygen is a waste product of this photosynthesis reaction.  Plants inhale carbon dioxide gas and exhale oxygen gas, the precise reverse of humans and animals.  Therefore, the relationship between animals (including humans) and plants is a symbiotic relationship.  Animals (including humans) exhale carbon dioxide gas, which plants then inhale.  Plants then exhale oxygen gas, which animals (including humans) then inhale.  Animals (including humans) then exhale carbon dioxide gas, which plants then inhale, and so on and so forth.

 

Another way the Earth’s atmosphere keeps us alive is by maintaining a habitable temperature for life.  Based on the Earth’s distance from the Sun, our planet should be too cold for life to exist.  The temperature of our planet should be much colder than the freezing temperature of water; not only should all the oceans be frozen, but the continents should be frozen over as well.  However, there are tiny amounts of gases within the Earth’s atmosphere that absorb and then emit some of the heat that our planet radiates.  These gases are called greenhouse gases.  The most important greenhouse gas is water vapor; carbon dioxide gas is a secondary greenhouse gas.  These gases absorb some of the heat that the Earth radiates, and these gases then reradiate this heat themselves.  Although these gases reradiate some of this heat into outer space, these gases also reradiate some of this heat back to the Earth.  This causes the temperature of planet Earth to be significantly warmer than it would have been otherwise, based on its distance from the Sun.  In fact, the Earth is sufficiently warmed that its average surface temperature is habitable for life.  This warming is called the greenhouse effect, since it is rather like a greenhouse that is warm even in the wintertime.  The Earth’s atmosphere is mostly nitrogen gas and oxygen gas, but neither of these gases can absorb or radiate heat efficiently.  In other words, neither nitrogen gas nor oxygen gas are greenhouse gases.  Water vapor and carbon dioxide gas are able to absorb and radiate heat efficiently.  The tiny amounts of water vapor and carbon dioxide in the Earth’s atmosphere warm the planet to a habitable temperature.  This is a second way the Earth’s atmosphere keeps us alive.

 

The Sun not only radiates visible light; the Sun radiates all forms of electromagnetic radiation.  As we discussed earlier in the course, the Electromagnetic Spectrum is a list of all the different types of electromagnetic waves in order as determined by either the frequency or the wavelength.  Starting with the lowest frequencies (which are also the longest wavelengths), we have radio waves, microwaves, infrared, visible light (the only type of electromagnetic wave our eyes can see), ultraviolet, X-rays, and gamma rays at the highest frequencies (which are also the shortest wavelengths).  The visible part of the Electromagnetic Spectrum is actually quite narrow.  Nevertheless, the visible part of the Electromagnetic Spectrum can be subdivided.  In order, the subcategories of the visible part of the Electromagnetic Spectrum starting at the lowest frequency (which is also the longest wavelength) are red, orange, yellow, green, blue, indigo, and violet at the highest frequency (which is also the shortest wavelength).  As we discussed earlier in the course, we now realize why electromagnetic waves just before visible light are called infrared, since their frequencies (or wavelengths) are just beyond red visible light.  In other words, infrared light is more red than red!  We also realize why electromagnetic waves just after visible light are called ultraviolet, since their frequencies (or wavelengths) are just beyond violet visible light.  In other words, ultraviolet light is more purple than purple!  The Sun radiates all of these electromagnetic waves.  For example, the near ultraviolet from the Sun causes suntans, and too much near ultraviolet from the Sun causes sunburns.  The far ultraviolet has even more energy, and the Sun radiates sufficient far ultraviolet that we should be killed from its far ultraviolet radiation.  X-rays have even greater energy; thus, the X-rays from the Sun should kill us in a fairly short amount of time.  Something must be shielding us from the Sun’s far ultraviolet and from the Sun’s X-rays.  Our atmosphere provides these shields.  The symbol for the oxygen atom is O.  Under normal temperatures and pressures, the oxygen atom will never remain by itself; it will always chemically bond to another atom.  If there are no other atoms nearby, the oxygen atom will chemically bond to another oxygen atom.  Two oxygen atoms chemically bonded to each other is called the oxygen molecule, which is written O2.  Molecular oxygen is also known as normal oxygen, since oxygen is almost always in this state under normal temperatures and pressures.  Roughly twenty percent of the Earth’s atmosphere is molecular (normal) oxygen for example, and this is the form of oxygen that plants exhale as well as the form humans and all animals must inhale.  Notice this is the form of oxygen appearing in the cellular respiration reaction and the photosynthesis reaction written above.  Whenever we use the simple word oxygen, we are not being clear.  Do we mean atomic oxygen O or do we mean molecular oxygen O2?  We probably mean molecular oxygen, since this is normal oxygen.  If molecular oxygen absorbs far ultraviolet, a chemical reaction will synthesize a strange form of oxygen: three oxygen atoms chemically bonded to each other.  This strange form of oxygen is written O3 and is called ozone.  The synthesis of ozone is more properly written 3 O2 + energy → 2 O3.  Ozone is toxic, since inhaling O3 causes severe respiratory problems.  This is ironic, since ozone also keeps us alive.  The molecular oxygen in the Earth’s atmosphere absorbs the far ultraviolet from the Sun, synthesizing ozone.  Therefore, the far ultraviolet from the Sun never reaches the surface of the Earth, since it is absorbed by molecular oxygen to synthesize ozone.  In fact, there is a layer of ozone in the stratosphere below which far ultraviolet does not penetrate.  This layer is commonly known as the ozone layer, but it is more correctly called the ozonosphere.  The ozonosphere is the heat source within the stratosphere that is responsible for warming temperatures with increasing elevation within that atmospheric layer.  Much higher in the atmosphere within the thermosphere, various atoms and molecules absorb X-rays from the Sun.  X-rays have so much energy that absorbing them strips electrons completely free from an atom or molecule.  In other words, atoms or molecules are ionized by X-rays.  Therefore, the X-rays from the Sun never reach the surface of the Earth, since they are absorbed by atoms and molecules to synthesize ionized atoms and molecules.  In fact, there is a layer of ionized atoms and molecules in the thermosphere below which X-rays do not penetrate.  This layer is called the ionosphere, and it is the heat source within the thermosphere that is responsible for warming temperatures with increasing elevation within that atmospheric layer.

 

Let us summarize all the ways the Earth’s atmosphere keeps us alive.  Firstly, humans and animals would not have oxygen to react with glucose to extract energy for their survival if unicellular microorganisms did not remove most of the carbon dioxide gas from the atmosphere, replacing it with molecular oxygen.  Secondly, planet Earth would be too cold for life to exist without the presence of greenhouse gases that make the planet warm enough to be habitable for life.  Thirdly, life on Earth would be killed from the far ultraviolet from the Sun if it were not for the ozonosphere.  Fourthly, life on Earth would be killed from the X-rays from the Sun if it were not for the ionosphere.  We also discussed that the atmosphere would be substantially ionized by the Sun’s solar wind without the Earth’s magnetic field deflecting most of these charged particles from the Sun that continually bombard our planet.  This is a fifth way our planet keeps us alive.  If only one of these were the case, we would not be here from the lack of the other four.  If two were the case, we would not be here from the lack of the other three.  If three were the case, we would not be here from the lack of the other two.  If four were the case, we would not be here from the lack of the remaining one.  The fact that all five of these are the case on the same planet is truly miraculous.  Again, we are humbled.  In this vast universe, we are only able to survive within a very thin layer of air surrounding a single planet: the atmosphere of planet Earth.

 

The surface temperature of the Earth causes the Earth to radiate heat from its surface.  The explains why the troposphere becomes cooler with increasing elevation; as we climb the troposphere, we are further and further from the surface of the Earth and thus further and further from this source of heat.  Air in the lower troposphere (near sea level) is often heated by the Earth’s surface.  Since hot fluids rise, this hot air may rise to the upper troposphere (near the tropopause).  This rising air may cool.  Since cool air sinks, air in the upper troposphere (near the tropopause) may sink to the lower troposphere (near sea level), where it may be warmed again thus causing it to rise again.  In summary, there is significant convection within the troposphere caused by continually circulating air within the troposphere.  This convection (circulation) of air within the troposphere is ultimately responsible for meteorological phenomena (commonly known as weather).  This explains why the vast majority of all meteorological phenomena (weather) occurs within the troposphere, the lowest layer of the atmosphere.  This also explains why the lowest layer of the Earth’s atmosphere is called the troposphere, since the Greek root tropo- means turning.  The ozonosphere is in the upper stratosphere, near the stratopause.  This explains why the temperature warms as we climb the stratosphere.  After passing the tropopause, we approach the ozonosphere, which serves as a heat source, thus causing warming temperatures.  After passing the stratopause, we are further and further from the ozonosphere.  This explains why the temperature cools as we climb the mesosphere.  Note that cooler air resides in the lower stratosphere while warmer air resides in the upper stratosphere.  Since cool fluids do not rise, the cool air in the lower stratosphere does not rise to the upper stratosphere.  Conversely, since warm fluids do not sink, the warm air in the upper stratosphere does not sink to the lower stratosphere.  Therefore, there is no convection (circulation) of air within the stratosphere.  The air in the stratosphere remains layered based on temperature.  This explains why this layer of the atmosphere is called the stratosphere, since the air is stratified or layered.  The word stratify is derived from a Latin word meaning layer.  The air in the mesosphere cools as we climb the mesosphere, just as air in the troposphere cools as we climb the troposphere.  This may lead us to conclude that there is significant convection (circulation) of air within the mesosphere just as in the troposphere, thus causing an abundance of meteorological phenomena (weather) within the mesosphere.  However, the Earth’s gravity pulls most of the air in entire atmosphere down into the troposphere.  Although there is convection (circulation) of air within the mesosphere, the air within this layer is too thin for this convection (circulation) to result in an abundance of meteorological phenomena (weather) within the mesosphere.  The Greek root meso- means middle.  For example, Central America is sometimes called Mesoamerica, as in Middle America.  Therefore, the word mesosphere simply means middle sphere or middle layer.  The ionosphere is in the upper thermosphere, near the thermopause.  This explains why the temperature warms as we climb the thermosphere.  After passing the mesopause, we approach the ionosphere, which serves as a heat source, thus causing warming temperatures.  After passing the thermopause, we are further and further from the ionosphere.  This explains why the temperature cools as we climb the exosphere.  Note that cooler air resides in the lower thermosphere while warmer air resides in the upper thermosphere.  Since cool fluids do not rise, the cool air in the lower thermosphere does not rise to the upper thermosphere.  Conversely, since warm fluids do not sink, the warm air in the upper thermosphere does not sink to the lower thermosphere.  Therefore, there is no convection (circulation) of air within the thermosphere.  The air in the thermosphere remains layered based on temperature.  This is similar to the air in the stratosphere, but note that the air in the thermosphere is much thinner than the air in the stratosphere, since the Earth’s gravity pulls air downward.  As we climb the exosphere, the air becomes cooler and cooler, smoothly transitioning into the very cold temperatures of the surrounding outer space.  The Greek root exo- means outside or external.  For example, an exoskeleton is a skeleton that is outside (surrounding) an organism.  Therefore, the word exosphere simply means external sphere or external layer.  The exosphere is a layer of gas that is not strictly part of the Earth’s atmosphere but is outside (surrounding) the Earth’s atmosphere that smoothly transitions into the gas of the surrounding outer space.

 

All of us have a basic understanding of the seasons: it is warmer in summertime and colder in wintertime.  It is a common misconception that the seasons occur because of the varying distance of planet Earth from the Sun.  Supposedly when our planet Earth is closer to the Sun, it is warmer causing summertime, and supposedly when our planet Earth is further from the Sun, it is colder causing wintertime.  This argument seems reasonable, but it is completely wrong.  The orbit of the Earth around the Sun is almost a perfect circle, meaning that the Earth is roughly the same distance from the Sun throughout the entire year.  Of course, the true shape of the Earth’s orbit around the Sun is an ellipse; sometimes the Earth is closer to the Sun than average, and other times the Earth is further from the Sun than average.  However, the eccentricity of the Earth’s elliptical orbit is so close to zero that the orbit is almost a perfect circle.  The eccentricity of an ellipse quantifies the elongation of the ellipse.  When the eccentricity is zero, the ellipse is a perfect circle, as we discussed earlier in the course.  When the eccentricity is close to zero, the ellipse is almost a perfect circle.  The eccentricity of the Earth’s elliptical orbit around the Sun is so close to zero that its orbit is almost a perfect circle.  When the Earth is at perihelion (closest to the Sun), it is roughly 2.5 million kilometers (roughly 1.5 million miles) closer to the Sun than average.  When the Earth is at aphelion (furthest from the Sun), it is roughly 2.5 million kilometers (roughly 1.5 million miles) further from the Sun than average.  These closer or further distances may seem large, but the Earth is on average roughly 150 million kilometers (roughly 93 million miles) from the Sun.  Therefore, these closer or further distances are less than two-percent variations from the average distance between the Earth and the Sun, and this is not enough of a difference to cause the seasons.  There is a spectacular piece of evidence that will forever bury the misconception that the varying distance of the Earth from the Sun causes the seasons: the Earth is closest to the Sun in wintertime and furthest from the Sun in summertime!  The Earth is at its perihelion on roughly January 03rd every year, but early January is in wintertime!  The Earth is at its aphelion on roughly July 03rd every year, but early July is in summertime!  Therefore, it is absolutely not the Earth’s varying distance from the Sun that causes the seasons.  Caution: we do not argue that distance from the Sun is completely irrelevant.  Obviously, if we were to move the Earth fifty million kilometers closer to the Sun, of course the planet would become so hot that it would no longer be habitable for life (all life, including all of us, would die).  Obviously, if we were to move the Earth fifty million kilometers further from the Sun, of course the planet would become so cold that it would no longer be habitable for life (all life, including all of us, would die).  However, if we were to move the Earth only a couple million kilometers closer to or further from the Sun, this would not be enough to affect the Earth’s average temperature.  The proof of this assertion is that this already occurs; every year as the Earth orbits the Sun on its elliptical orbit, the Earth moves roughly 2.5 million kilometers closer to the Sun at perihelion and roughly 2.5 million kilometers further from the Sun at aphelion, and these variations do not affect the average temperature of the planet.  In fact, planet Earth is closest to the Sun in wintertime and furthest from the Sun in summertime!

 

After discussing in tremendous detail what does not cause the seasons, we must finally discuss what does cause the seasons.  The Earth’s rotational axis is tilted from the vertical, the vertical being defined as perpendicular to the ecliptic plane (the plane of the Earth’s orbit around the Sun).  The tilt of any planet’s rotational axis is called the obliquity of the planet.  The seasons are caused by the Earth’s obliquity, the tilt of its rotational axis.  The obliquity of planet Earth is roughly 23½ degrees.  As the Earth orbits the Sun, this 23½ degrees of obliquity remains fixed to an excellent approximation.  Thus, as the Earth orbits the Sun, sometimes the Earth’s northern hemisphere will be tilted toward the Sun, causing that hemisphere to receive more direct sunlight thus causing warmer summertime.  The warmer summertime is also caused by daytime being longer than nighttime, as we will discuss shortly.  At the same time the Earth’s northern hemisphere is tilted toward the Sun, the Earth’s southern hemisphere is tilted away from the Sun, causing that hemisphere to receive less direct sunlight thus causing colder wintertime.  The colder wintertime is also caused by nighttime being longer than daytime, as we will discuss shortly.  Six months later when the Earth is on the opposite side of its orbit, the Earth’s northern hemisphere will be tilted away from the Sun, causing that hemisphere to receive less direct sunlight and causing that hemisphere to have longer nighttime than daytime, thus causing colder wintertime.  At the same time the Earth’s northern hemisphere is tilted away from the Sun, the Earth’s southern hemisphere is tilted toward the Sun, causing that hemisphere to receive more direct sunlight and causing that hemisphere to have longer daytime than nighttime, thus causing warmer summertime.  This is remarkable; the seasons are reversed in the two hemispheres at the same time!  As another example, when it is springtime in the northern hemisphere, it is autumntime in the southern hemisphere at the same time.  This means that the Earth is at perihelion (closest to the Sun) during the southern hemisphere’s summertime, and the Earth is at aphelion (furthest from the Sun) during the southern hemisphere’s wintertime.  We may be tempted to conclude that the southern hemisphere’s summertime is especially hot, and the southern hemisphere’s wintertime is especially cold.  This is false; the opposite is true!  Summers are typically hotter in the northern hemisphere as compared with summers in the southern hemisphere, and winters are typically colder in the northern hemisphere as compared with winters in the southern hemisphere!  In other words, both summers and winters are more mild in the southern hemisphere as compared with the northern hemisphere, where both summers and winters are more severe.  This is because the continents are presently somewhat crowded together in the northern hemisphere, making the southern hemisphere mostly covered with ocean (water).  Water has a large heat capacity, meaning that it is difficult to change the temperature of water.  Therefore, the abundance of water in the southern hemisphere stabilizes temperatures, causing smaller temperature variations in the southern hemisphere as compared with larger temperature variations in the northern hemisphere.  This spectacularly emphasizes that variations in the distance from the Sun do not determine seasonal temperatures.  Again, summers are more mild (less hot) in the southern hemisphere, even though the Earth is closest to the Sun during summertime in the southern hemisphere, while summers are more severe (more hot) in the northern hemisphere, even though the Earth is furthest from the Sun during summertime in the northern hemisphere!  Similarly, winters are more mild (less cold) in the southern hemisphere, even though the Earth is furthest from the Sun during wintertime in the southern hemisphere, while winters are more severe (more cold) in the northern hemisphere, even though the Earth is closest to the Sun during wintertime in the northern hemisphere!  The large heat capacity of liquid water is also responsible for moderating the temperature difference between daytime and nighttime on our planet Earth.  The daytime side of any planet faces toward the Sun, while the nighttime side of any planet faces away from the Sun.  For most planets, nighttime is much colder than daytime, but the nighttime side of planet Earth is only slightly cooler than its daytime side, thanks to the stabilizing effect of all the water that covers most of the planet.  Extraordinarily, the nighttime side of planet Earth may at times become warmer than the daytime side depending upon weather patterns.  As another example of how water stabilizes temperatures on our planet Earth, other planets have north poles and south poles that are much colder than their equators.  Although the Earth’s poles are cold and the Earth’s equator is hot by human standards, the difference in temperature is nevertheless moderate as compared with other planets.  Without the abundance of water that covers our planet Earth, our poles would be too cold and our equator would be too hot to be habitable for life.

 

The moment when the Earth’s northern hemisphere is tilted the most toward the Sun is called the summer solstice.  This occurs on average June 21st every year; some years it could occur one or two days earlier, while other years it could occur one or two days later.  Since the northern hemisphere is tilted the most toward the Sun on the summer solstice, the Sun appears to be highest in the sky, since the northern hemisphere receives the most direct sunrays.  This is also the longest daytime and the shortest nighttime of the year in the northern hemisphere.  The precise duration of daytime and nighttime depends upon our latitude.  At the midlatitudes, there are roughly fifteen hours of daytime and only roughly nine hours of nighttime on the summer solstice.  Note that the sum of fifteen hours and nine hours is twenty-four hours.  Six months later when the Earth is on the other side of its orbit around the Sun, there is a moment when the Earth’s northern hemisphere is tilted the most away from the Sun.  This moment is called the winter solstice, occurring on average December 21st every year; some years it could occur one or two days earlier, while other years it could occur one or two days later.  Since the northern hemisphere is tilted the most away from the Sun on the winter solstice, the Sun appears to be lowest in the sky, since the northern hemisphere receives the least direct sunrays.  This is also the longest nighttime and the shortest daytime of the year in the northern hemisphere.  The precise duration of nighttime and daytime depends upon our latitude, but it will always be the reverse of the summer solstice.  At the midlatitudes for example, there are roughly fifteen hours of nighttime and only roughly nine hours of daytime on the winter solstice.  Note again that the sum of fifteen hours and nine hours is twenty-four hours.  Halfway in between the solstices are two other moments called the equinoxes when the Earth’s axis is not tilted toward or away from the Sun, resulting in equal amounts of daytime and nighttime (twelve hours each).  This is why they are called equinoxes, since there are equal amounts of daytime and nighttime.  Roughly three months after the summer solstice (roughly three months before the winter solstice) is the autumn equinox, occurring on average September 21st every year; some years it could occur one or two days earlier, while other years it could occur one or two days later.  Roughly three months after the winter solstice (roughly three months before the summer solstice) is the vernal equinox (or the spring equinox).  The vernal equinox (spring equinox) occurs on average March 21st every year; some years it could occur one or two days earlier, while other years it could occur one or two days later.  It is a common misconception that since every day is twenty-four hours, supposedly every day has twelve hours of daytime and twelve hours of nighttime.  This is false for almost every day the entire year.  In fact, there are only two days of the entire year when this is the case: the equinoxes.  Once we pass the vernal equinox (spring equinox), every day for the next six months there is more daytime than nighttime, with maximum daytime on the summer solstice.  Once we pass the autumn equinox, every day for the next six months there is more nighttime than daytime, with maximum nighttime on the winter solstice.

 

The term summer solstice has three different yet interrelated meanings.  We may interpret the summer solstice as the location on the Earth’s orbit where its northern hemisphere is tilted the most toward the Sun.  We may also interpret the summer solstice as the moment in time when the Earth’s northern hemisphere is tilted the most toward the Sun, occurring on average June 21st every year.  Thirdly, we may interpret the summer solstice as the point on the Celestial Sphere (the point on the sky) where the ecliptic has a positive maximum declination of +23½°, as we discussed earlier in the course.  Obviously, the Earth is actually located at its orbital summer solstice and the Sun appears to be located at the sky’s summer solstice at the moment of the temporal summer solstice.  The terms winter solstice, vernal equinox, and autumn equinox have similar interpretations.  The term winter solstice has three different yet interrelated meanings.  We may interpret the winter solstice as the location on the Earth’s orbit where its northern hemisphere is tilted the most away from the Sun.  We may also interpret the winter solstice as the moment in time when the Earth’s northern hemisphere is tilted the most away from the Sun, occurring on average December 21st every year.  Thirdly, we may interpret the winter solstice as the point on the Celestial Sphere (the point on the sky) where the ecliptic has a negative maximum declination of −23½°, as we discussed earlier in the course.  Obviously, the Earth is actually located at its orbital winter solstice and the Sun appears to be located at the sky’s winter solstice at the moment of the temporal winter solstice.  The term vernal equinox (spring equinox) has three different yet interrelated meanings.  We may interpret the vernal equinox (spring equinox) as the location on the Earth’s orbit where its axis is not tilted toward or away from the Sun as it journeys from the orbital winter solstice toward the orbital summer solstice.  We may also interpret the vernal equinox (spring equinox) as the moment in time occurring on average March 21st every year when the Earth’s axis is not tilted toward or away from the Sun after the temporal winter solstice but before the temporal summer solstice.  Thirdly, we may interpret the vernal equinox (spring equinox) as the point on the Celestial Sphere (the point on the sky) where the ecliptic intersects the Celestial Equator and where the Sun appears to have an increasing declination, as we discussed earlier in the course.  Obviously, the Earth is actually located at its orbital vernal equinox and the Sun appears to be located at the sky’s vernal equinox at the moment of the temporal vernal equinox.  Finally, the term autumn equinox has three different yet interrelated meanings.  We may interpret the autumn equinox as the location on the Earth’s orbit where its axis is not tilted toward or away from the Sun as it journeys from the orbital summer solstice toward the orbital winter solstice.  We may also interpret the autumn equinox as the moment in time occurring on average September 21st every year when the Earth’s axis is not tilted toward or away from the Sun after the temporal summer solstice but before the temporal winter solstice.  Thirdly, we may interpret the autumn equinox as the point on the Celestial Sphere (the point on the sky) where the ecliptic intersects the Celestial Equator and where the Sun appears to have a decreasing declination, as we discussed earlier in the course.  Obviously, the Earth is actually located at its orbital autumn equinox and the Sun appears to be located at the sky’s autumn equinox at the moment of the temporal autumn equinox.

 

As we discussed earlier in the course, the latitude of any location on planet Earth is defined as its angle from the terrestrial equator, whether north or south.  The colatitude of any location on planet Earth is defined as its angle from the north terrestrial pole.  Since there are ninety degrees of latitude from the terrestrial equator to the north terrestrial pole, this makes the colatitude equal to ninety degrees minus the latitude.  For example, if our latitude is ten degrees north, this means we are ten degrees of latitude north of the terrestrial equator, making us eighty degrees from the north terrestrial pole; therefore, our colatitude is eighty degrees.  Indeed, ninety minus ten equals eighty.  As another example, if our latitude is seventy degrees north, this means we are seventy degrees of latitude north of the terrestrial equator, making us twenty degrees from the north terrestrial pole; therefore, our colatitude is twenty degrees.  Indeed, ninety minus seventy equals twenty.  The only location on planet Earth where our latitude and our colatitude equal the same number is at forty-five degrees north latitude, since that would place us halfway between (equidistant from) the terrestrial equator and the north terrestrial pole.  Indeed, ninety minus forty-five equals forty-five.  The altitude of the Sun at noon on the summer solstice equals our colatitude plus the obliquity.  The altitude of the Sun at noon on the winter solstice equals our colatitude minus the obliquity.  The altitude of the Sun at noon on either equinox equals our colatitude.  Everything we have discussed applies not just to planet Earth but also to any other planet orbiting the Sun.  The obliquity of any planet is the angular tilt of its rotational axis from the vertical direction that is perpendicular to its own orbital plane around the Sun.  The poles of any planet are where its own rotational axis intersects the planet.  The equator of any planet is halfway between the two poles of the planet.  Our latitude on that planet would be our angle north or south from that planet’s equator.  The planet’s equator would be 0° latitude on that planet.  The planet’s north pole would be 90°N latitude on that planet, and the planet’s south pole would be 90°S latitude on that planet.  Our colatitude on that planet would be our angle from that planet’s north pole, which would again be ninety degrees minus our latitude.  The summer solstice of any planet is the moment when its northern hemisphere is tilted the most towards the Sun.  The winter solstice for any planet is the moment when its northern hemisphere is tilted the most away from the Sun.  The equinoxes of any planet is halfway between the solstices when its rotational axis is not tilted toward or away from the Sun.  The altitude of the Sun at noon on each of these dates would be the same equations: colatitude plus obliquity on the summer solstice, colatitude minus obliquity on the winter solstice, and colatitude on the equinoxes.  The only difference in this analysis for other planets are the actual dates of the solstices and the equinoxes.  For any planet orbiting the Sun, the time from one solstice to the next solstice (which is also the time from one equinox to the next equinox) is one-half of the planet’s orbital period around the Sun.  The time from one solstice to the next equinox (which is also the time from one equinox to the next solstice) is one-quarter of the planet’s orbital period around the Sun.  As an example, consider a hypothetical planet with an obliquity of thirty degrees, and suppose we live at fifty degrees north latitude on this hypothetical planet.  Since our latitude is fifty degrees north, our colatitude is forty degrees, since ninety minus fifty equals forty.  Hence, the altitude of the Sun at noon on the summer solstice would be seventy degrees, since the colatitude plus the obliquity is forty plus thirty, which equals seventy.  The altitude of the Sun at noon on the winter solstice would be ten degrees, since the colatitude minus the obliquity is forty minus thirty, which equals ten.  The altitude of the Sun at noon on either equinox would be forty degrees, since that is our colatitude.

 

It is a common misconception that the Sun is at the zenith (directly overhead) at noon.  This misconception comes from the phrase high noon.  Of course, the Sun has the greatest altitude (is highest in the sky) at noon, giving the phrase some validity.  Nevertheless, the Sun is never ever at the zenith (directly overhead) at most locations on Earth.  For example, suppose we live at forty degrees north latitude.  Our colatitude would be fifty degrees, since ninety minus forty equals fifty.  The highest the Sun would ever be at this location is on the summer solstice, when its altitude at noon is 73½ degrees, since our colatitude plus obliquity is fifty plus 23½, which is indeed 73½ degrees.  Although 73½ degrees is a high altitude, it is not at the zenith (directly overhead).  As we discussed earlier in the course, the zenith is +90° altitude.  If the Sun is not at the zenith at noon on the summer solstice, it would only be lower in the sky every other day of the year.  This shows that the Sun is never ever at the zenith (directly overhead) at most locations on Earth.  Is there anywhere on planet Earth where the Sun is at the zenith (directly overhead) at noon on the summer solstice?  Yes, at a latitude the same number of degrees north of the terrestrial equator as the obliquity of planet Earth.  To prove this, suppose we live at 23½ degrees north latitude, then our colatitude would be 66½ degrees, since ninety minus 23½ equals 66½.  Thus, the altitude of the Sun at noon would be our colatitude 66½ degrees plus the obliquity of planet Earth 23½ degrees, but 66½ plus 23½ equals +90° altitude, the zenith!  This location of 23½ degrees north latitude is so important that it deserves a special name: the Tropic of Cancer.  There is only one location on planet Earth where the Sun is directly overhead at noon on the winter solstice: 23½ degrees south latitude.  This location is so important that it deserves a special name: the Tropic of Capricorn.  The words Cancer and Capricorn refer to astronomical constellations of the zodiac, as we discussed earlier in the course.  There is only one location on planet Earth where the Sun is at the zenith (directly overhead) at noon on the equinoxes: the terrestrial equator at zero degrees latitude.  Thousands of years ago, primitive humans did not understand that the Earth is a planet with a tilted rotational axis orbiting the Sun.  For thousands of years, humans believed that the motion of the Sun was responsible for the seasons.  Although today we understand that it is actually the Earth that is orbiting the Sun, we must also confess that when we look up into the sky, it does appear as if the Sun is moving.  Therefore, we should understand the seasons from the frame of reference of the Earth, which was the only understanding of humans for thousands of years.  From the frame of reference of the Earth, the Sun appears to be directly on top of the Tropic of Cancer on the summer solstice.  For the next six months, the Sun appears to move south, arriving on top of the terrestrial equator three months later on the autumn equinox and arriving on top of the Tropic of Capricorn three months after that on the winter solstice.  For the following six months, the Sun appears to move north, arriving on top of the terrestrial equator three months later on the vernal equinox (spring equinox) and arriving on top of the Tropic of Cancer three months after that on the summer solstice.  Again, it is not the Sun that is actually moving north and south; in actuality, the Earth is orbiting the Sun.  Nevertheless, we live on planet Earth, and so we must understand the seasons from the frame of reference of the Earth.  To summarize, it is only possible for the Sun to appear at the zenith (directly overhead) at noon if we live somewhere between the Tropic of Cancer and the Tropic of Capricorn.  If we live north of the Tropic of Cancer or south of the Tropic of Capricorn, the Sun never ever appears to be at the zenith (directly overhead).

 

The Arctic Circle is 66½ degrees north latitude, making its colatitude 23½ degrees, since ninety minus 66½ equals 23½.  The altitude of the Sun at noon at the Arctic Circle on the winter solstice would be zero degrees, since our colatitude minus the obliquity would be 23½ minus 23½, which is obviously zero.  As we discussed earlier in the course, 0° altitude means the Sun is on the horizon, such as during sunrise.  At even more northern latitudes, the altitude of the Sun on the winter solstice will be a negative number, which means it is below the horizon as we discussed earlier in the course.  In other words, we cannot see the Sun, making it nighttime even though it is noon!  Before noon or after noon, the Sun will be even further below the horizon.  Thus, the entire day is in perpetual nighttime!  The same occurs on the Antarctic Circle at 66½ degrees south latitude: the altitude of the Sun at noon on the summer solstice is zero degrees, meaning that it is on the horizon.  At even more southern latitudes, the altitude of the Sun on the summer solstice will be a negative number, which means it is below the horizon.  Again, we cannot see the Sun, making it nighttime even though it is noon!  Before noon or after noon, the Sun will be even further below the horizon.  Thus, the entire day is in perpetual nighttime!  These extreme northern latitudes and extreme southern latitudes are the only places on planet Earth where the Sun may never rise on some days of the year and may never set on other days of the year.  At the north terrestrial pole, six months of continuous nighttime occurs from the autumn equinox all the way to the vernal equinox (spring equinox), and then six months of continuous daytime occurs from the vernal equinox (spring equinox) all the way to the autumn equinox.  The reverse occurs at the south terrestrial pole: six months of continuous nighttime occurs from the vernal equinox (spring equinox) all the way to the autumn equinox, while six months of continuous daytime occurs from the autumn equinox all the way to the vernal equinox (spring equinox).  Even when the clock time is midnight, the Sun may still be in the sky causing daytime at these extreme latitudes.  This is the origin of the phrase midnight Sun.

 

By one interpretation, nighttime begins at sunset and extends all the way to sunrise.  However, from the interpretation of the brightness of the sky, true nighttime does not immediately begin upon sunset, nor does true nighttime extend all the way to sunrise.  The Earth’s atmosphere refracts the Sun’s light even when the Sun is below the horizon.  In fact, the sky remains somewhat bright for quite some time after sunset, and the sky becomes somewhat bright for quite some time before sunrise.  The somewhat bright times after sunset are called the evening twilights, while the somewhat bright times before sunrise are called the morning twilights.  After sunset, the sky is still quite bright for several minutes.  This is called the evening civil twilight, ending with civil dusk.  After civil dusk, the sky becomes noticeably darker with some stars becoming visible, but the western sky is still bright enough for sailors at sea to find the western horizon.  For this reason, this time is called the evening nautical twilight, ending with nautical dusk.  After nautical dusk, the sky becomes dark enough that the western horizon is no longer visible, but the sky is still bright enough to prevent astronomers from making observations of faint (dim) objects in the sky.  For this reason, this time is called the evening astronomical twilight, ending with astronomical dusk.  It is only after astronomical dusk that true nighttime begins.  Before sunrise, these three twilights are reversed.  First is astronomical dawn followed by the morning astronomical twilight, when the sky is still dark enough that the eastern horizon is still not visible yet sufficiently bright that astronomers can no longer observe faint (dim) objects in the sky.  This morning astronomical twilight ends with nautical dawn followed by the nautical twilight, when the sky is still dark with some stars still visible, but the eastern sky becomes bright enough for sailors at sea to find the eastern horizon.  This morning nautical twilight ends with civil dawn followed by the morning civil twilight, when the sky becomes quite bright.  Finally, the morning civil twilight ends with sunrise.  Civil dusk and civil dawn are strictly defined as the moments when the Sun has an altitude of −6° (six degrees below the horizon).  Nautical dusk and nautical dawn are strictly defined as the moments when the Sun has an altitude of −12° (twelve degrees below the horizon).  Astronomical dusk and astronomical dawn are strictly defined as the moments when the Sun has an altitude of −18° (eighteen degrees below the horizon).  The durations of time of all of these twilights depends upon our latitude and the time of year.  At the midlatitudes, these twilights (civil, nautical, and astronomical) are each roughly thirty minutes in duration on average.  Thus, at the midlatitudes, there are roughly ninety minutes on average of evening twilight and roughly ninety minutes on average of morning twilight.  Therefore, at the midlatitudes, there are roughly three hours of total twilight on average.  As we discussed, the vernal equinox (spring equinox) and the autumn equinox each have equal amounts of daytime and nighttime (twelve hours each); this is why they are called equinoxes.  However, we now realize there are only roughly nine hours of true nighttime at the midlatitudes because of the evening twilights and the morning twilights, at least at the midlatitudes.  Every other day of the year also has a correspondingly shorter true nighttime, because of the evening twilights and the morning twilights.

 

As we discussed, at extreme latitudes either north of the Arctic Circle at 66½°N latitude or south of the Antarctic Circle at 66½°S latitude, we may have continuous daytime (no nighttime) or continuous nighttime (no daytime), depending on the time of year.  At every other latitude on planet Earth, there will be some daytime and some nighttime every day throughout the entire year.  However, we now realize that all of these nighttimes may not necessarily be true nighttimes.  At the extreme latitudes north of the Arctic Circle at 66½°N latitude or south of the Antarctic Circle at 66½°S latitude, continuous nighttime may actually be continuous twilight, depending on the time of year.  Moreover, there are even less extreme latitudes where true nighttime may not occur, depending on the time of year.  Between 60½° latitude and 66½° latitude (in both the northern hemisphere and the southern hemisphere), there may be some days of the year when daytime is followed by civil twilight followed by daytime again.  In other words, nautical twilight, astronomical twilight, and true nighttime never occur.  Between 54½° latitude and 60½° latitude (in both the northern hemisphere and the southern hemisphere), there may be some days of the year when daytime is followed by civil twilight, then nautical twilight, then civil twilight, then finally daytime again.  In other words, astronomical twilight and true nighttime never occur.  Between 48½° latitude and 54½° latitude (in both the northern hemisphere and the southern hemisphere), there may be some days of the year when daytime is followed by civil twilight, then nautical twilight, then astronomical twilight, then nautical twilight, then civil twilight, then finally daytime again.  In other words, true nighttime never occurs.  At every other latitude on planet Earth (from 48½°N latitude to 48½°S latitude), there is some daytime, some twilights (of all six varieties) and some true nighttime every day of the entire year.

 

As we discussed earlier in the course, the Sun appears to wander around the Celestial Sphere (around the sky).  The giant circle that the Sun appears to wander around the Celestial Sphere (around the sky) is called the ecliptic, and it takes the Sun one year to appear to take one complete journey around the ecliptic.  The constellations along the ecliptic are called the zodiac constellations.  Thousands of years ago, the Sun appeared to be wandering through Cancer (the crab) on the summer solstice, when the Sun appears to be on top of 23½ degrees north latitude.  This is why 23½ degrees north latitude is called the Tropic of Cancer.  Thousands of years ago, the Sun appeared to be wandering through Capricornus (the sea goat) on the winter solstice, when the Sun appears to be on top of 23½ degrees south latitude.  This is why 23½ degrees south latitude is called the Tropic of Capricorn.  Also thousands of years ago, the Sun appeared to be wandering through Aries (the ram) on the vernal equinox (spring equinox), and the Sun appeared to be wandering through Libra (the scales) on the autumn equinox.  As we will discuss shortly, the Earth’s rotational axis suffers from a very slow precession, causing the entire Celestial Sphere to slowly shift over thousands of years thus causing the Sun to appear to wander through different zodiac constellations on the solstices and the equinoxes over the course of many thousands of years.  Today, the Sun appears to be wandering through Gemini (the twins) on the summer solstice, not Cancer (the crab).  Perhaps 23½ degrees north latitude should be renamed the Tropic of Gemini!  Today, the Sun appears to be wandering through Sagittarius (the centaur archer) on the winter solstice, not Capricornus (the sea goat).  Perhaps 23½ degrees south latitude should be renamed the Tropic of Sagittarius!  Also today, the Sun appears to be wandering through Pisces (the fish) on the vernal equinox (spring equinox) instead of Aries (the ram), and the Sun appears to be wandering through Virgo (the virgin) on the autumn equinox instead of Libra (the scales).  Thousands of years from now, the Sun will appear to be wandering through Taurus (the bull) on the summer solstice.  Perhaps 23½ degrees north latitude should then be renamed the Tropic of Taurus!  Thousands of years from now, the Sun will appear to be wandering through Scorpius (the scorpion) on the winter solstice.  Perhaps 23½ degrees south latitude should then be renamed the Tropic of Scorpius!  Also thousands of years from now, the Sun will appear to be wandering through Aquarius (the water bearer) on the vernal equinox (spring equinox), and the Sun will appear to be wandering through Leo (the lion) on the autumn equinox.  This precession of the solstices and the equinoxes completes one full cycle around the ecliptic in roughly twenty-six thousand years, as we will calculate shortly.  Therefore, it is convenient to leave the names of 23½ degrees north latitude and 23½ degrees south latitude as the Tropic of Cancer and the Tropic of Capricorn, respectively, since the Sun will return to wandering through those zodiac constellations on the solstices every twenty-six thousand years.

 

There are several religious holidays that have their origins in the solstices and the equinoxes.  For example, Christmas Day is observed on December 25th every year.  Notice that this is shortly after the winter solstice.  Before Christmas Day became the celebration of the birth of Jesus Christ, this was a pagan holiday celebrating the winter solstice.  Why would pagans celebrate the day when the Sun appeared to be lowest in the sky at noon with the most number of nighttime hours?  Primitive humans observed the Sun appear lower and lower in the sky after the summer solstice; perhaps many primitive humans were terrified that the Sun would continue to move downward until it disappeared below the horizon.  However, by simply paying attention every year, we observe that the Sun stops moving downward on the winter solstice, and then begins to move upward.  This was a reason to celebrate for many ancient pagans.  This pagan celebration became the celebration of the birth of Jesus Christ, since early Christians saw the birth of Jesus Christ as bringing more and more light into a spiritually dark world.  In actuality, Jesus was not born on December 25th.  We will never be certain of the exact day of the birth of Jesus.  Most of the details of the vast majority of persons throughout human history, including Jesus, were never recorded.  We will also never be certain of the exact year of the birth of Jesus.  Although it is commonly believed that the year of the birth of Jesus was anno Domini 1, in actuality no one recorded the year that Jesus was born.  Again, most of the details of the vast majority of persons throughout human history, including Jesus, were never recorded.  The people of the world did not declare the year to be anno Domini 1 when Jesus was born.  The ancient Romans designated years using a few different numbering schemes, among which was the number of years since the founding of the city of Rome, which was more than seven centuries before the birth of Jesus.  Using this particular convention, the ancient Romans designated years using either of the Latin phrases “ab urbe condita” or “anno urbis conditae,” meaning “in the year since the founding of the city.”  Either Latin phrase was abbreviated AUC.  This numbering scheme continued to be used by Europeans even after the fall of the Western Roman Empire.  More than five centuries after the birth of Jesus and roughly fifty years after the Western Roman Empire fell, the Christian monk Dionysius Exiguus tried to determine the year that Jesus was born.  This monk declared that AUC 1278 should be reset to A.D. 525, where A.D. is the abbreviation for the new Latin phrase “anno Domini” meaning “in the year of our Lord,” effectively meaning the number of years since the birth of Jesus.  Over the next few centuries, Europeans retroactively changed the years of historical dates from AUC to A.D. based on this declaration by Dionysius Exiguus.  Europeans even changed the years of historical dates before the birth of Jesus from AUC to B.C., which is simply an abbreviation for “before Christ.”  Modern scholarship has revealed that the year that Jesus was born as determined by Dionysius Exiguus is probably a few years in error.  Modern scholarship estimates that 6 B.C. is a more accurate estimate for the year of the birth of Jesus.  Many students are offended by this assertion.  Students claim that it would be contradictory for Jesus to have been born in the year 6 B.C., since B.C. is the abbreviation for before Christ and no one can be born before the year of their own birth!  Again, we must remember that no one recorded the date that Jesus was born.  We must remember that the belief that the year of the birth of Jesus was A.D. 1 is based upon an estimate by a monk who lived roughly five centuries after Jesus was born.  In fact, we should marvel that the estimate made by Dionysius Exiguus for an unrecorded event that occurred roughly five centuries earlier was only a few years in error!  As another example of a religious holiday that has its origin in the solstices and the equinoxes, Easter is always the first Sunday after the first Full Moon after the vernal equinox (spring equinox) every year.  Since Jesus was Jewish, what is traditionally called the Last Supper was in actuality a Passover celebration.  The Jewish calendar is a lunar calendar, and hence Jewish holy days are determined by the cycles of the Moon.  Placing Easter on the first Sunday after the first Full Moon after the vernal equinox (spring equinox) is an attempt to keep the date of Easter as close as possible to the date of Passover.

 

A thermometer is a device to measure temperature.  The operation of a thermometer is based on the principle of thermal expansion and thermal contraction.  Most substances expand when they become warmer, and most substances contract when they become colder.  To build a primitive thermometer, we take any object and measure its length at one temperature, and we measure its different length at a different temperature.  We draw marks at each of these lengths, and we draw other marks between these two marks.  To determine the temperature, we simply read off whichever mark the end of the object meets based on its length at that temperature.  Unfortunately, most substances expand and contract by only tiny amounts when their temperature changes.  Hence, the marks are often too close together, making differences in length difficult to measure.  However, the element mercury expands by quite a noticeable amount as it becomes warmer and contracts by quite a noticeable amount as it becomes colder.  Therefore, most thermometers use liquid mercury, since the marks are then well separated and easy to read.  An actinometer is a device that measures solar radiation.  To build a primitive actinometer, we take any object and use a thermometer to measure its initial temperature.  Then, we place the object in sunlight for a certain amount of time, perhaps one hour.  As the object absorbs solar radiation, it becomes hotter.  We use a thermometer to measure its hotter temperature afterwards, and from the difference in temperature between its hotter final temperature and its colder initial temperature, we can calculate the amount of solar radiation the object absorbed.  Note that we must wrap the object in black cloth to ensure that it absorbs all of the solar radiation.  Otherwise, the object will only become hotter by some of the solar radiation that it absorbed, since the object will reflect the rest of the solar radiation.  It is convenient to use a bucket of water as the object, since we know the heat capacity of water.  An actinometer would measure the greatest amount of solar radiation on the summer solstice, and an actinometer would measure the least amount of solar radiation on the winter solstice.  However, the summer solstice is almost never the hottest day of the year; a thermometer measures the hottest air temperature roughly a month later, in late July in the northern hemisphere.  Similarly, the winter solstice is almost never the coldest day of the year; a thermometer measures the coldest air temperature roughly a month later, in late January in the northern hemisphere.  These delays occur because the Earth is mostly covered with water, which has a large heat capacity.  In other words, it is difficult to change the temperature of water.  The northern hemisphere receives the most direct sunrays on the summer solstice around June 21st, but it still takes another month for the air to warm to maximum temperature sometime in late July.  In fact, it takes yet another month for the ocean waters to warm to maximum temperature, in late August in the northern hemisphere.  This is why most people in the northern hemisphere take their summer vacations in August, so that they may enjoy swimming in the ocean when it is warmest.  The northern hemisphere receives the least direct sunrays on the winter solstice around December 21st, but the oceans have retained so much heat from the summertime that it still takes another month for the air to cool to minimum temperature sometime in late January.  In fact, it takes yet another month for the ocean waters to cool to minimum temperature, in late February in the northern hemisphere.

 

The time it takes the Earth to complete one rotation is one day, but we must clearly define what we mean by one day.  Suppose it is noon; thus, the Sun is at its greatest altitude (appears highest in the sky).  In the time it takes the Earth to complete one full rotation, it has moved a small amount in its orbit around the Sun.  Therefore, it is not yet noon after this full rotation.  We must wait a short time longer for the Earth to rotate a little bit more to bring the Sun to greatest altitude (highest in the sky) again.  We now realize that the time it takes the Earth to complete one rotation is less than the time it takes the Sun to go from noon to noon.  In other words, the time it takes the Sun to go from noon to noon is longer than the time it takes the Earth to complete one rotation.  The time it takes the Sun to go from noon to noon is called a solar day, and this is equal to twenty-four hours.  However, this twenty-four-hour solar day is longer than the time it takes the Earth to rotate once.  The time it takes the Earth to rotate once is called the sidereal day, which is shorter than the twenty-four-hour solar day.  We can roughly calculate the duration of time of the sidereal day.  There are roughly 365 days in a year, although even this requires clarifications that we will discuss shortly!  For now, we will use 365 days as a rough estimate.  Recall that there are 360 degrees in a full circle, and notice that these two numbers 365 and 360 are roughly equal to each other.  This means that every day the Earth moves roughly one degree in its orbit around the Sun.  Thus, after one complete rotation, the Earth has moved roughly one degree along its orbit.  Therefore, we must calculate the time it takes the Earth to rotate an additional one degree, which is a 1/360 fraction of a complete rotation.  As a rough estimate, we will use 24 hours or 1440 minutes as a complete rotation.  Therefore, the time it takes the Earth to turn one degree is roughly 1/360 of 1440 minutes.  Remarkably, 1440 minutes divided by 360 is a simple whole number: four minutes.  Therefore, the sidereal day is roughly four minutes shorter than the solar day.  In other words, the solar day is roughly four minutes longer than the sidereal day.  In conclusion, the solar day is twenty-four hours, but this is roughly four minutes longer than the sidereal day, which is the true amount of time it takes the Earth to complete one rotation.  Whenever we hear anyone claim that it takes the Earth twenty-four hours to rotate once, we should correct their error.  The time it takes the Earth to rotate once is roughly twenty-three hours and fifty-six minutes, the sidereal day!

 

The time it takes the Earth to complete one orbit around the Sun is one year, but we must clearly define what we mean by one year.  After 365 solar days, the Earth does not return precisely to where it began in its orbit.  We must wait an additional roughly six hours before the Earth returns to where it began in its orbit.  In other words, one year is not an integer number (not a whole number) of solar days.  It is difficult to construct a calendar based on this orbit.  Are we supposed to have a calendar with 365 solar days followed by six hours of limbo before we begin the new year?  Many of us would enjoy such a calendar, since this would give us an additional six hours to party every New Year’s Eve!  Nevertheless, we cannot construct a calendar this way.  If we had six hours of limbo after midnight ending New Year’s Eve before declaring that it is a new midnight beginning New Year’s Day, then the Sun would be preparing to rise.  Thus, the Sun would rise at roughly midnight on average throughout that new year.  Also notice that the Sun would culminate (reach its highest altitude in the sky) at roughly 06:00 a.m. on average throughout that new year, and the Sun would set at roughly noon on average throughout that new year.  This is unacceptable.  We want the Sun to rise at 06:00 a.m. on average, we want the Sun to culminate (reach its highest altitude) at noon, and we want the Sun to set at 06:00 p.m. on average every year indefinitely.  We can accomplish this by using a calendar with 365 solar days without adding six hours of limbo between New Year’s Eve and New Year’s Day, but then the Earth would be roughly six hours behind from where it began on its orbit one year earlier.  After an additional 365 solar days, the Earth would then be roughly twelve hours behind from where it began on its orbit two years earlier.  After a third 365 solar days, the Earth would then be roughly eighteen hours behind from where it began on its orbit three years earlier.  After a fourth 365 solar days, the Earth would be roughly twenty-four hours behind from where it began on its orbit four years earlier, but twenty-four hours is one full solar day!  This inspires us to construct a calendar as follows.  One calendar year will have 365 solar days, but once every four years we will add an extra solar day to the calendar.  This brings the Earth back to where it began on its orbit four years earlier.  This fourth year is commonly known as the leap year, and the extra day we add is commonly known as the leap day.  Many primitive humans across many ancient cultures thousands of years ago constructed their calendars in this way.  They did not understand that the Earth orbited the Sun, but they did notice that 365 solar days after the summer solstice for example, the Sun would not return to exactly where it appeared in the sky one year earlier.  After another 365 solar days, they noticed that the Sun still did not return to exactly where it appeared in the sky two years earlier.  After a third 365 solar days, they noticed that the Sun still did not return to exactly where it appeared in the sky three years earlier.  After a fourth 365 solar days, many ancient humans noticed that after one additional solar day, the Sun finally returned to where it appeared in the sky four years earlier.

 

The ancient Roman Republic used a calendar with not only 365 solar days plus one extra solar day every four years, but they also divided their calendar into ten months.  Some of these months were named for ancient Roman mythological gods, such as March for Mars (Ares), the god of war.  Several of these months were named simply after their numerical month of the calendar, such as October for the eighth month.  The Greek root octo- means eight.  For example, an octopus has eight legs, an octagon has eight sides and eight angles, and octuplets are eight babies born from the same pregnancy.  Although ancient Rome was born a kingdom that did evolve into a republic, ancient Rome nevertheless degenerated from a republic to a dictatorship by the first century before Christ.  The last of the ancient Roman dictators was Julius Caesar, who declared himself perpetual dictator.  Several Roman senators conspired to assassinate him, including one of his closest friends Brutus.  After the assassination of Julius Caesar, the Roman dictatorship plunged into a civil war that ended when Julius Caesar’s great-nephew Octavius Augustus declared himself the first emperor of Rome.  This completed the degeneration of ancient Rome from a republic to a dictatorship to an empire.  Also during this time, two new months were inserted into the calendar, turning the ten-month ancient Roman calendar into a twelve-month ancient Roman calendar.  One of the new months that was inserted into the calendar was named July after Julius Caesar, and the other new month that was inserted into the calendar was named August after Octavius Augustus.  This new calendar was named the Julian calendar, after Julius Caesar.  The Julian calendar was used by more persons for a longer period of time than any other calendar in all of human history.  This Julian calendar was used throughout the roughly 500-year (half a millennium) imperial history of ancient Rome, and even after the Western Roman Empire fell Europeans continued to use this Julian calendar for another 1000 years (a millennium).  This Julian calendar lasted for 1500 years, a millennium and a half!  Again, more people used this Julian calendar for a longer period of time than any other calendar in all of human history.  For this reason, we will now discuss the Julian calendar in tremendous detail, even though this is not the calendar we use presently.  According to the Julian calendar, the calendar year is divided into twelve months.  In the correct order, these months are January with thirty-one solar days, February with twenty-eight solar days (except for leap years, which we will discuss shortly), March with thirty-one solar days, April with thirty solar days, May with thirty-one solar days, June with thirty solar days, July with thirty-one solar days, August with thirty-one solar days, September with thirty solar days, October with thirty-one solar days, November with thirty solar days, and December with thirty-one solar days.  Notice how difficult it is to memorize this calendar.  The word September means seventh month, since the Latin root sept- means seven.  For example, septuplets are seven babies born from the same pregnancy.  However, in the Julian calendar, September is the ninth month instead!  The word October means eighth month, since the Greek root octo- means eight.  Again, an octopus has eight legs, an octagon has eight sides and eight angles, and octuplets are eight babies born from the same pregnancy.  However, in the Julian calendar, October is the tenth month instead!  The word November means ninth month, since the Latin root nov- means nine.  However, in the Julian calendar, November is the eleventh month instead!  The word December means tenth month, since the Greek root dec- means ten.  For example, a decimal is one-tenth, there are ten decimeters in a meter, and a decagon has ten sides and ten angles.  However, in the Julian calendar, December is the twelfth month instead!  Finally, the Julian calendar adds the leap day once every four years to February, meaning that February actually has 28 and ¼ solar days.  If we add all the solar days in all twelve months of the Julian calendar, we obtain 365 and ¼ solar days, which is roughly the number of solar days in one year.

 

If one Earth year were exactly 365 and ¼ solar days, the Julian calendar would be a perfect calendar.  However one Earth year is roughly but not exactly equal to 365 and ¼ solar days.  Therefore, even if we add one solar day every four years, the Earth does not return to precisely where it began in its orbit four years earlier.  There is a small error, and this error will accumulate, becoming larger and larger as decades, centuries, and millennia pass.  After 1500 years of using this calendar, the Earth was roughly ten days displaced from where it was 1500 years earlier.  Hence, the dates of the solstices and the equinoxes were also displaced by roughly ten days.  If an additional 1500 years had passed while we continued to use the Julian calendar, the dates of the solstices and the equinoxes would be roughly twenty days displaced.  If a third 1500 years had passed while we continued to use the Julian calendar, the dates of the solstices and the equinoxes would be displaced by roughly thirty days.  Thus, using the Julian calendar for 4500 years would cause the dates of the solstices and the equinoxes to drift by roughly one month.  Using the Julian calendar for 27000 years would cause the dates of the solstices and the equinoxes to become displaced by roughly six months.  This is unacceptable.  A proper calendar should ensure that summertime (in the northern hemisphere) remains in June, July, and August indefinitely and wintertime (in the northern hemisphere) remains in December, January, and February indefinitely.  In the year 1582, Pope Gregory XIII realized these problems would arise from continuing to use the Julian calendar.  To correct these problems, Pope Gregory XIII firstly erased ten solar days from the year 1582.  In particular, the day after October 04, 1582, was the day October 15, 1582, skipping October 05th through October 14th that year, by decree of the pope.  This returned the Earth to where it belonged in its orbit, thus resetting the dates of the solstices and the equinoxes.  However, Pope Gregory XIII realized that this was only a temporary solution.  Again, the dates of the solstices and the equinoxes would continue to drift if we continue to use the Julian calendar.  The pope ordered astronomers to construct a more accurate calendar that would maintain the dates of the solstices and the equinoxes indefinitely.  This new calendar was named the Gregorian calendar, after Pope Gregory XIII.  This is the calendar that Catholics have used for more than four hundred years, and this is also the calendar the entire world uses for civil (nonreligious) purposes.  We will now discuss the Gregorian calendar in tremendous detail, since all of us must be familiar with the calendar that we actually use!  According to the Gregorian calendar, the year is still divided into the same twelve months in the same order as the Julian calendar.  This unfortunately still leaves illogically-named months in the calendar, such as October for the tenth month instead of the eighth month.  According to the Gregorian calendar, the number of solar days in each month is also the same as the number of solar days in each month of the Julian calendar, including February which still has twenty-eight solar days on non-leap years but twenty-nine solar days on leap years.  The Gregorian calendar at first glance seems to be identical to the Julian calendar.  Indeed, the only difference between the Gregorian calendar and the Julian calendar is the leap-year calculation.  The Julian calendar leap-year calculation is simple; there is a leap year once every four years.  However, the leap-year calculation in the Gregorian calendar is more complex than the leap-year calculation in the Julian calendar to ensure that the dates of the solstices and the equinoxes do not drift.  According to the Gregorian calendar, the leap year calculation is as follows.  If the year is divisible by four, then it is a leap year, unless the year is divisible by one hundred in which case it is not a leap year, unless the year is divisible by four hundred in which case it is a leap year.  In other words, February has 28 plus 1/4 minus 1/100 plus 1/400 solar days according to the Gregorian calendar.  If we add the total number of solar days from all the months in the Gregorian calendar, we obtain a number of solar days so close to the true amount of time it takes the Earth to orbit the Sun that the dates of the solstices and the equinoxes will not drift for countless thousands of years.  Therefore, we should continue use the Gregorian calendar for many thousands of years.  Let us work through some examples using the Gregorian calendar.  The years 1629, 1781, and 1857 were not leap years, since those years are not divisible by four.  The years 1648, 1732, and 1816 were leap years, since those years are divisible by four.  The years 1700, 1800, and 1900 may be divisible by four, but they are also divisible by one hundred; therefore, those years were not leap years.  The years 1600 and 2000 are divisible by four and are divisible by one hundred, but they are also divisible by four hundred!  Therefore, the years 1600 and 2000 were leap years.  The first time this four-hundred rule was ever invoked was the year 1600, and the second time this four-hundred rule was ever invoked was the year 2000.  The third time this four-hundred rule will ever be invoked will be the year 2400.  Leap years happen to coincide with presidential election years in the United States, but there have been two exceptions thus far.  The year 1800 was a United States presidential election year (Thomas Jefferson versus John Adams), but the year 1800 was not a leap year.  The year 1900 was a United States presidential election year (William McKinley versus William Jennings Bryan), but the year 1900 was not a leap year.  Note that the year 2000 was a United States presidential election year (George W. Bush versus Albert Gore, Jr.), and the year 2000 was indeed a leap year.  The next United States presidential election that will not be a leap year will be the year 2100.  This assumes that the United States will last for another seventy-seven years, which based on student performance in this course is not likely!  To memorize the months and the number of solar days in each month for both the Julian calendar and the Gregorian calendar, we may memorize the following poem.  “Thirty days hath September, April, June, and November; All the rest have thirty-one, Excepting February alone, Which has twenty-eight days clear, But twenty-nine in each leap year.”

 

For most of the history of planet Earth, the hot temperatures at the terrestrial equator and the cold temperatures at the terrestrial poles have been moderated by the oceans due to the relatively large heat capacity of water.  However, the moving tectonic plates of the lithosphere slowly change the configuration of the continents and the oceans over enormous timescales (millions of years).  If there happens to be relatively isolated continents at the terrestrial poles, the relatively small heat capacity of these landmasses will permit the temperatures at the terrestrial poles to become extremely cold.  The result is an ice age, an extremely long period of time (millions of years) when the temperature at the terrestrial poles is so cold that enormous icecaps cover these landmasses.  To our knowledge, there have been only five ice ages throughout the entire history of planet Earth, each lasting many millions of years.  The Current Ice Age began roughly thirty million years ago and still continues to the present day.  The Current Ice Age will last many more millions of years as long as the continent Antarctica remains relatively isolated at the south terrestrial pole.  There are only two scenarios that can end the Current Ice Age.  In one scenario, Antarctica may move off of the south terrestrial pole, which would make it less cold.  In the other scenario, another continent may move to the south terrestrial pole and collide with Antarctica.  This would end the isolation of Antarctica, also making it less cold.  Whether Antarctica moves away from the south terrestrial pole or another continent moves toward the south terrestrial pole, it takes millions of years for tectonic plates to move significantly, as we discussed.  Therefore, the Current Ice Age will continue for millions of more years to come.  During the Current Ice Age, the southern icecap covers the continent Antarctica, and the northern icecap covers Greenland, a giant island near (but not exactly at) the north terrestrial pole.

 

Within the Current Ice Age, there have been many periods of time when the Earth has become even colder.  These are glacial periods of the Current Ice Age.  Between two glacial periods is an interglacial period when the Earth is not as cold.  The Earth becomes so cold during a glacial period that the icecaps expand beyond the terrestrial poles and advance onto other continents.  A major glacial period lasts roughly one hundred thousand years, while a minor glacial period lasts between roughly twenty-five thousand years and roughly fifty thousand years.  We are currently within an interglacial period of the Current Ice Age.  This interglacial period began roughly twelve thousand years ago at the end of a major glacial period that lasted roughly one hundred thousand years.  Plate tectonics cannot be responsible for the alternation between glacial periods and interglacial periods within the Current Ice Age, since tectonic plates do not move appreciably over timescales of thousands of years.  The alternation between glacial periods and interglacial periods within the Current Ice Age is caused by the Milanković cycles, named for the Serbian climatologist and astronomer Mulutin Milanković who formulated this theory.  The Earth’s orbit around the Sun is presently almost a perfect circle.  In other words, the eccentricity of the Earth’s orbit around the Sun is close to zero, but this has not always been the case nor will it always be the case.  Gravitational perturbations (tugs) from the other planets, primarily Jupiter, change the eccentricity of the Earth’s orbit.  When the Earth’s orbit is perturbed to become more elliptical, the Earth will be significantly further from the Sun, causing the Earth to become significantly colder thus causing a major glacial period of the Current Ice Age.  Calculations show that the eccentricity of the Earth’s orbit changes once every one hundred thousand years (roughly), which is roughly the duration of time of a major glacial period within the Current Ice Age.  Minor glacial periods are caused by the precession and the nutation of the Earth’s rotational axis.  Precession is the turning of an axis around another axis.  Nutation is the nodding of an axis resulting in a change in obliquity.  The Earth’s rotational axis precesses and nutates, and this changes the amount of sunlight the Earth receives from the Sun, which in turn causes minor glacial periods within the Current Ice Age.  Calculations show that the Earth’s rotational axis precesses once every twenty-six thousand years (roughly), and the Earth’s rotational axis nutates once every forty-one thousand years (roughly).  These are roughly equal to the duration of time of minor glacial periods within the Current Ice Age.

 

Long-term variations in global temperature (over millions of years) are caused by slowly moving tectonic plates, resulting in ice ages when continents happen to be relatively isolated at or near the terrestrial poles, as with the Current Ice Age.  Intermediate-term variations in global temperature (over thousands of years) cause glacial periods and interglacial periods within the Current Ice Age.  These intermediate-term variations in global temperature (over thousands of years) are caused by the Milanković cycles (the variations of the eccentricity of the Earth’s orbit around the Sun, the precession of the Earth’s rotational axis, and the nutation of the Earth’s rotational axis).  However, there are also short-term variations in global temperature, from centuries to decades, and even as short as a few years.  Extremely short-term variations in global temperature (over a few years) are caused by violent igneous eruptions.  A single igneous eruption can cause global cooling for a few years, since igneous eruptions eject ash into the atmosphere, reducing the amount of incoming sunlight to the Earth.  Short-term variations in global temperature (from decades to centuries) are caused by a combination of the Pacific Decadal Oscillation (PDO), the Atlantic Multidecadal Oscillation (AMO), and variations in solar activity.  The Pacific Decadal Oscillation (PDO) is the alternation between decades of El Niño domination in the Pacific Ocean and decades of La Niña domination in the Pacific Ocean.  The Atlantic Multidecadal Oscillation (AMO) is a similar oscillation in the Atlantic Ocean.  Although direct observations of the PDO and the AMO only stretch back several decades, measurements of the radioactive isotope carbon-fourteen  within trees have revealed that the PDO and the AMO each undergo roughly sixty-year cycles, where one complete PDO for example consists of roughly three decades of El Niño domination followed by roughly three decades of La Niña domination.  Quantitative observations of solar activity stretch back a few centuries, giving us a stronger understanding of how variations in solar activity affect global temperatures.  At times, the Sun is more active, radiating more energy that warms planet Earth; at other times, the Sun is more quiet, radiating less energy that cools planet Earth.  These variations in solar activity manifest themselves through sunspots, regions on the surface of the Sun where magnetic field strengths are particularly strong, as we will discuss later in the course.  These sunspots have been directly observed for roughly four hundred years, since the invention of the telescope.  Astronomers have observed that the number of sunspots goes through a roughly eleven-year cycle.  In one complete cycle, the number of sunspots increases then decreases over a time period of roughly eleven years.  For example, the Sun experienced a period of increasing activity during the last few years of the twentieth century and the first few years of the twenty-first century (the current century).  This period of increasing solar activity was followed by a period of decreasing solar activity.  During that particular period of decreasing solar activity, some of the coldest temperatures over the last one hundred years occurred.  Furthermore, measurements of the radioactive isotope carbon-fourteen  within trees have revealed that this roughly eleven-year solar cycle itself goes through a roughly two-hundred-year cycle.  This is the de Vries cycle, named for the Dutch physicist Hessel de Vries, one of the pioneers of radiocarbon dating.  According to the de Vries cycle, the Sun gradually increases in activity to what is called a solar maximum then gradually decreases in activity to what is called a solar minimum.  Caution: the eleven-year solar cycles continue to occur throughout each two-century de Vries cycle.  Since one complete de Vries cycle lasts for roughly two centuries, each solar maximum and each solar minimum lasts for roughly one hundred years.  Over the past twelve thousand years (since the beginning of the current interglacial period of the Current Ice Age), there have been roughly sixty complete de Vries cycles, with each de Vries cycle having one solar maximum and one solar minimum.  The Modern Maximum occurred throughout most of the twentieth century, and the Modern Minimum began toward the beginning of the twenty-first century (the current century).  These de Vries cycles have caused variations in global temperatures over the past several thousand years.  For example, a solar maximum contributed to the Roman Warm Period, lasting from the ancient Late Roman Republic to the ancient Early Roman Empire.  As another example, another solar maximum contributed to the Medieval Warm Period during the High Middle Ages.  As yet another example, a solar minimum contributed to the Little Ice Age, lasting from the Late Middle Ages to the Early Modern Ages.  Most recently, the Modern Maximum that occurred throughout most of the twentieth century contributed to the warming temperatures of that century, and the Modern Minimum that began toward the beginning of the twenty-first century (the current century) has already caused cooling temperatures that will continue for the rest of the current century.  By combining the roughly sixty-year PDO, the roughly sixty-year AMO, the roughly eleven-year solar cycle, and the roughly two-century de Vries cycle, we obtain a nearly perfect model of global temperature variations over the past couple of thousand years.  As we just discussed, this model predicts that there will be gradual global cooling during the current century.  Caution: an unexpected violent igneous eruption may cause additional global cooling in addition to these cyclic variations.

 

To summarize the climate of planet Earth, the average temperature of the atmosphere is determined primarily by the Earth’s distance from the Sun together with the concentration of greenhouse gases in the atmosphere, primarily water vapor, which warms the Earth sufficiently so that it is habitable for life.  Temperatures are hot near the terrestrial equator, temperatures are cold near the terrestrial poles, and temperatures vary at the midlatitudes based on the seasons (warmer in the summertime and cooler in the wintertime).  The abundance of liquid water that covers the Earth (the oceans) stabilizes global temperatures due to the large heat capacity of water.  Long-term variations in global temperature (over millions of years) are caused by slowly moving tectonic plates, resulting in ice ages when continents happen to be relatively isolated at or near the terrestrial poles, as with the Current Ice Age that began roughly thirty million years ago and continues to the present day.  Intermediate-term variations in global temperature (over thousands of years) cause glacial periods and interglacial periods within the Current Ice Age.  These intermediate-term variations in global temperature (over thousands of years) are caused by the Milanković cycles (the variations of the eccentricity of the Earth’s orbit around the Sun, the precession of the Earth’s rotational axis, and the nutation of the Earth’s rotational axis).  We are currently in an interglacial period of the Current Ice Age, and this interglacial period began roughly twelve thousand years ago.  Short-term variations in global temperature (over a few decades or a few centuries) are caused by the roughly eleven-year solar cycle, the roughly two-century de Vries cycle, the roughly sixty-year PDO, and the roughly sixty-year AMO.  We just began a century of gradual global cooling resulting from these short-term solar cycles and oceanic cycles.  Finally, extremely short-term variations in global temperature (over a few years) may result from powerful igneous eruptions.

 

The very slow precession and nutation of the Earth’s rotational axis also causes the entire Celestial Sphere to very slowly wobble along with the Earth’s rotational axis, since the celestial poles and the celestial equator are all defined as projections of the terrestrial poles and the terrestrial equator onto the sky.  As we discussed earlier in the course, the star α (alpha) Ursae Minoris is presently the north star, since the Earth’s rotational axis almost perfectly points toward that star.  However, this has not always been the case nor will it always be the case.  Thousands of years ago, a different star was the north star, since the Earth’s rotational axis pointed in a different direction toward a different star in the northern half of the Celestial Sphere.  After thousands of years of precession and nutation, the Earth’s rotational axis presently points toward α (alpha) Ursae Minoris.  After thousands of more years of precession and nutation, yet another star will become the new north star.  We also discussed earlier in the course that presently there is no south star, since the Earth’s rotational axis does not point toward any particularly bright star in the southern half of the Celestial Sphere.  However, this has not always been the case nor will it always be the case.  Thousands of years ago, there may have been a south star, since the Earth’s rotational axis pointed in a different direction toward a bright star in the southern half of the Celestial Sphere.  After thousands of years of precession and nutation, the Earth’s rotational axis presently does not point toward any particularly bright star in the southern half of the Celestial Sphere.  After thousands of more years of precession and nutation, perhaps another star will become a new south star.  In summary, as the Earth’s rotational axis slowly precesses and nutates over thousands of years, during some centuries there will be a north star but no south star (as is presently the case), during other centuries there will be a south star but no north star, during yet other centuries there will be both a north star and a south star, while during yet other centuries there will be neither a north star nor a south star.

 

The precession and the nutation of the Earth’s rotational axis causes another complication.  The time it takes the Earth to complete one orbit around the Sun is one year, but in that time the Earth’s axis has precessed and nutated by a tiny amount.  Therefore, the orientation of its rotational axis relative to its orbit around the Sun has already passed its original orientation by a tiny amount.  This discrepancy manifests itself in the precession of the equinoxes and the solstices.  The time it takes the Earth to complete one orbit around the Sun is strictly defined as the sidereal year, while the time it takes the Earth to go from the vernal equinox to the next vernal equinox is strictly defined as the tropical year.  The tropical year is slightly shorter than the sidereal year.  In other words, the sidereal year is slightly longer than the tropical year.  The difference between these two years is roughly twenty minutes.  We can use this difference to estimate the time for one complete cycle of the precession of the equinoxes and the solstices.  One complete precession of the Earth’s rotational axis would cause the Sun to appear to precess around the entire ecliptic, but every year the Sun also appears to wander around the entire ecliptic.  Therefore, the time for one complete precession of the equinoxes and the solstices must be the ratio between one year and twenty minutes.  If we regard one year as 365 and ¼ solar days as a rough estimate, then one year is also 8766 hours, which is also 525960 minutes.  The ratio between 525960 minutes and roughly 20 minutes of precession per year is roughly 26000 years for one complete precession around the entire ecliptic.  This finally justifies our earlier assertion that the Earth’s rotational axis precesses once every roughly 26000 years.  Somewhat more accurate calculations reveal that the tropical year is 365.24219 solar days, while the sidereal year is 365.25636 solar days, the difference being 20.4 minutes.  Note that human calendars are almost always based upon the tropical year, not the sidereal year.  The tropical year is defined in terms of the equinoxes and the solstices, which in turn determine the seasons.  The seasons directly affect life on Earth, including human life.  Thus, the seasons have a direct affect upon human history, human societies, and human cultures.  The Julian year is exactly 365 and ¼ solar days, since the Julian year is defined by the Julian calendar.  Note that one Julian year is 365.25 solar days expressed as a decimal.  The Gregorian year is exactly 365 plus 1/4 minus 1/100 plus 1/400 solar days, since the Gregorian year is defined by the Gregorian calendar.  Note that one Gregorian year is 365.2425 solar days expressed as a decimal.  Notice that the Gregorian year (365.2425 solar days) is much closer to the tropical year (365.24219 solar days) than the sidereal year (365.25636 solar days).  The difference between the Gregorian year and the tropical year is less than thirty seconds.  This finally justifies our earlier assertion that using the Gregorian calendar will prevent the dates of the solstices and the equinoxes from drifting for countless thousands of years.

 

The Earth has one moon, called the Moon.  The Moon has a diameter roughly one-fourth of the Earth’s diameter.  No other planetary moon in the Solar System is this enormous as compared with its mother planet.  All the other planetary moons in the Solar System are very small as compared with the size of their mother planet.  The Moon is so enormous that it is not even strictly correct to say that the Moon is orbiting the Earth.  More correctly, the Earth and the Moon are both orbiting their common center of mass, while that common center of mass orbits the Sun.  For this reason, many astrophysicists do not even consider the Moon to be a moon.  Instead, many astrophysicists regard the Earth-Moon system to be a double planet orbiting the Sun.  If we regard Mercury as the first planet from the Sun and Venus as the second planet from the Sun, we should regard the Earth as planet 3A and the Moon as planet 3B.  Mars would then remain the fourth planet from the Sun, and so on and so forth.

 

Although the Moon is very large as compared with the size of other planetary moons relative to their mother planets, the Moon is nevertheless only one-fourth the diameter of the Earth.  Being significantly smaller than the Earth, the Moon was born with much less radioactive atoms (as compared with the Earth) to provide itself with internal energy for geologic processes.  Therefore, the Moon was geologically alive for only a brief amount of time, perhaps a few hundred million years.  For most of its lifetime, the Moon has been geologically dead.  While the Moon was geologically alive, it did have a partially molten metallic core, and thus the young ancient Moon generated a magnetic field.  However, since the Moon has been geologically dead for most of its lifetime, its metallic core is no longer even partially molten.  Therefore, the Moon has not generated a substantial magnetic field for most of its lifetime.  Also due to its small size and small mass, the Moon’s gravity is sufficiently weak that it cannot retain an atmosphere.  Without geologic activity for most of its lifetime to provide volcanic outgassing to replenish a lost atmosphere, the Moon has had virtually no atmosphere for most of its lifetime.  At best, there is an exosphere that begins at the surface of the Moon that smoothly transitions into the very cold temperatures of the surrounding outer space.  Since the Moon has been geologically dead for most of its lifetime, there has been no geologic activity for most of its history to cover or eradicate craters caused by asteroid impacts and comet impacts.  Hence, the Moon is much more cratered as compared with the Earth.

 

We are not certain how the Moon formed.  The jovian, gas-giant (outer) planets are large enough with sufficient mass and therefore strong enough gravity to capture moons, as we will discuss shortly.  However, the terrestrial (inner) planets are small enough with insufficient mass and therefore insufficient gravity to capture moons.  This explains why both Mercury and Venus have no moons.  (The terrestrial planet Mars has two moons that it probably captured, and we will discuss this exception shortly.)  Since the Earth is a terrestrial planet and is therefore small as compared with the jovian, gas-giant planets, it is unlikely that the Earth captured the Moon, especially considering the large size of the Moon.  It is also unlikely that the young, forming Earth fragmented itself to form the Moon.  If the Moon was not captured by the Earth and if the Moon did not form from the Earth through self-fragmentation, then where did the Moon come from?  Our strongest theory for the formation of the Moon is the violent-collision theory.  When the Earth was still forming, it was almost entirely molten, as we discussed.  During this time, a large planetesimal accidentally collided with the Earth, ripping huge chunks of molten rock from the outer layers of the Earth.  Most of these chunks of molten rock did not have enough energy to escape from the Earth’s gravitational attraction.  Thus, these chunks of molten rock remained in orbit around the Earth.  These chunks of molten rock then suffered sticky collisions with each other, coalescing into a larger and larger mass through accretion.  The growing mass eventually became large enough that its self-gravity forced itself into a spherical shape, becoming the Moon.  The damaged Earth also had enough self-gravity to restore itself back to its original spherical shape.  One piece of evidence in favor of this violent-collision theory is that the composition of the Moon is similar to the composition of the outer layers of the Earth, namely iron-poor silicate rock.  The Apollo astronauts who landed on the Moon more than fifty years ago returned to the Earth with Moon rocks, and these rocks are indeed composed of iron-poor silicate rock.  We may argue that these rocks should be composed of iron-poor silicate rock regardless, since the Moon should have differentiated itself into a dense metallic core, a less dense mantle, and a least dense outer crust while it first formed.  However, the Apollo astronauts also left seismometers on the surface of the Moon.  Although the Moon is geologically dead, gravitational tidal forces from the Earth nevertheless cause weak moonquakes on the Moon that these seismometers have measured.  Just as the detection of earthquakes by seismometers on Earth together with computer simulations have revealed the layers of the Earth, their thicknesses, their compositions, and their physical states, the detection of moonquakes by seismometers on the Moon together with computer simulations have revealed the layers of the Moon, their thicknesses, their compositions, and their physical states.  These measurements and calculations have revealed that the Moon does indeed have a dense metallic core, a less dense mantle, and a least dense outer crust.  However, the Moon’s dense metallic core is unusually small for a terrestrial planet with the Moon’s overall size.  This is a strong piece of evidence in favor of the violent-collision theory for the Moon’s formation.  The Moon has a very small metallic core since it formed from a violent collision ripping chunks of molten rock from the outer layers of the Earth, which are composed of iron-poor silicate rock.

 

It takes roughly one month for the Earth and the Moon to orbit their common center of mass.  In fact, the word month is derived from the word moon.  If we take the word month, remove the suffix -th, and insert an extra letter o, we obtain the word moon!  The Moon always faces the same side toward the Earth as the Earth and the Moon orbit each other.  This side of the Moon is called the near side of the Moon, and the side of the Moon that always faces away from the Earth is called the far side of the Moon.  Therefore, for most of human history, the far side of the Moon remained a complete mystery.  Beginning in the mid-to-late twentieth century, humans have sent satellites to orbit the Moon.  These satellites have taken photographs of every part of the Moon, including the far side.  All of us can observe the near side of the Moon in the sky.  Without a telescope and even without binoculars, we can see with the naked eye that the near side of the Moon has some landscapes lighter in color and other landscapes darker in color.  When Galileo Galilei observed the near side of the Moon through his primitive telescope more than four hundred years ago, the darker landscapes looked so smooth and flat to him that he believed they were bodies of water.  In fact, Galileo Galilei named these darker areas maria, which is plural for the singular mare, the Latin word for sea.  Today, we know that these lunar maria are not bodies of water; they are low-elevation plains that are actually hardened lava flows.  When the Moon was young, it had a molten interior.  Collisions from asteroids and comets penetrated the outer layers of the Moon, permitting this molten rock from the interior to extrude out and flow onto the surface of the Moon.  This molten rock cooled and crystallized into solid rock, forming the lunar maria.  The parts of the near side of the Moon that appear lighter in color are mountainous highlands.  Craters on any planet or moon are caused by asteroid impacts and comet impacts.  The lunar maria are more sparsely cratered, while the lunar mountainous highlands are more heavily cratered.  This stands to reason.  The lunar maria formed later than the lunar mountainous highlands.  Since the lunar maria are younger, there has been less time for impact cratering to occur, making them sparsely cratered.  The lunar mountainous highlands are older.  Therefore, there has been more time for impact cratering to occur, making them heavily cratered.  In fact, since the early Solar System was the heavy bombardment period as we discussed, the lunar mountainous highlands are heavily cratered in an even greater proportion than their age as compared with the lunar maria.  The far side of the Moon has fewer sparsely-cratered maria and more heavily-cratered mountainous highlands as compared with the near side of the Moon, which has more sparsely-cratered maria and fewer heavily-cratered mountainous highlands as compared with the far side of the Moon.  Again, this topographical difference between the near side of the Moon and the far side of the Moon was not discovered until the mid-to-late twentieth century, when humans began to send artificial satellites to the Moon to orbit the Moon and photograph every part of the Moon, including the far side.

 

It is a common misconception that the Moon must not be rotating, since it always faces the same side toward the Earth.  This is false.  The Moon does rotate, and this rotation is essential in keeping the same side of the Moon pointed toward the Earth.  The time it takes the Moon to rotate once is exactly equal to the time it takes the Earth and the Moon to orbit each other once.  In other words, the rotational period of the Moon is exactly equal to its orbital period.  More plainly, the Moon turns at the same rate at which it orbits, thus keeping the same side always facing toward the Earth.  This is not a coincidence or an accident.  Millions of years ago, the rotational period of the Moon was not equal to its orbital period.  Hence, the Moon did not always face the same side toward the Earth.  However, gravitational tidal forces from the Earth exerted different forces on different parts of the Moon, distorting the shape of the Moon by giving it small tidal bulges.  More plainly, the Earth’s gravitational attraction stretches the Moon into a slightly elongated shape.  Since the Moon’s tidal bulges are slightly closer to the Earth with each lunar rotation, the Earth’s gravitational attraction pulls on the Moon’s tidal bulges more strongly.  If the ancient Moon was rotating faster than its current rotation, then the Earth’s greater gravitational attraction of the Moon’s tidal bulges would have slowed down the Moon’s rotation.  If the ancient Moon was rotating slower than its current rotation, then the Earth’s greater gravitational attraction of the Moon’s tidal bulges would have sped up the Moon’s rotation.  In either case, the Earth’s gravitational attraction adjusted the rotational period of the Moon over millions of years until one of its tidal bulges was forced to always face toward the Earth.  This mechanism is called tidal locking, and we say that the Moon is tidally locked to the Earth.  Tidal locking occurs frequently throughout the Solar System; many moons are tidally locked to their mother planet, meaning that their rotational periods are equal to their orbital periods causing them to always face the same side toward their mother planet.  In particular, both of the moons of Mars are tidally locked to Mars, the four largest moons of Jupiter are tidally locked to Jupiter, the seven largest moons of Saturn are tidally locked to Saturn, the five largest moons of Uranus are tidally locked to Uranus, and the two largest moons of Neptune are tidally locked to Neptune.  Pluto and its largest moon Charon are both tidally locked to one another.  Not only does Charon always face the same side toward Pluto, but Pluto always faces the same side toward Charon.  This stands to reason, since gravitation is universal; everything in the universe exerts a gravitational force on everything else in the universe, as we discussed earlier in the course.  Not only has Pluto adjusted the rotational period of Charon until it became tidally locked to Pluto, but Charon has adjusted the rotational period of Pluto until it became tidally locked to Charon.  The same will eventually occur with the Earth-Moon system in many millions of years.  The Earth has already succeeded in causing the Moon to be tidally locked to the Earth, but the Moon will someday succeed in causing the Earth to be tidally locked to the Moon.  The Earth’s rotation is presently slowing down by tiny unnoticeable amounts.  Eventually, the Earth will become tidally locked to the Moon, meaning that in millions of years there will be a near side of the Earth that always faces toward the Moon and a far side of the Earth that always faces away from the Moon.  When this finally occurs millions of years from now, anyone who happens to live on the far side of the Earth would never ever see the Moon, and anyone who happens to live on the near side of the Earth would always see the Moon in the sky.  This is already the case on the Moon.  Anyone who happens to live on the far side of the Moon never ever sees the Earth, and anyone who happens to live on the near side of the Moon always sees the Earth in the sky.  As the Earth’s rotation slows, this rotational angular momentum must be transferred back to the Moon, by the law of conservation of angular momentum.  If the Moon is gaining angular momentum, then the size of its orbit must grow, meaning that the Moon must be drifting away from the Earth.  The Apollo astronauts who landed on the Moon more than fifty years ago left mirrors on the Moon so that NASA could send laser signals to the Moon that would reflect off of those mirrors.  By timing how long it takes a laser signal to propagate to the Moon and for its reflection off of those mirrors to return to the Earth, we have measured the distance to the Moon within an accuracy of a few centimeters!  These measurements reveal that the Moon is indeed drifting away from the Earth very slowly, a few centimeters per year.  This recessional motion of the Moon will not continue until the Moon escapes from the Earth however.  This gradual recession of the Moon from the Earth will cease when the Earth becomes tidally locked to the Moon.  The angular momentum transfer will then end, and the orbit of the Earth-Moon system will attain a stable (unchanging) equilibrium.

 

It is a common misconception that the far side of the Moon is in perpetual darkness.  This is false.  This misconception comes from confusing the far side of the Moon with the dark side of the Moon.  Again, the far side of the Moon faces away from the Earth.  The dark side or more correctly the nighttime side of the Moon faces away from the Sun.  In fact, the nighttime side of any planet or moon in the Solar System is the side that faces away from the Sun, while the daytime side of any planet or moon in the Solar System is the side that faces toward the Sun.  The nighttime side of the Moon faces away from the Sun, but this is different from the far side of the Moon, which faces away from the Earth.  Similarly, the daytime side of the Moon faces toward the Sun, but this is different from the near side of the Moon, which faces toward the Earth.  We emphasize this again: the far side of the Moon and the nighttime (dark) side of the Moon are two different things, just as the near side of the Moon and the daytime side of the Moon are two different things.  The far side of the Moon is not in perpetual nighttime (darkness), just as the near side of the Moon is not in perpetual daytime.  Since it takes roughly one month for the Earth and the Moon to orbit their common center of mass as that common center of mass orbits the Sun and since the rotational period of the Moon is also roughly one month, every part of the Moon (both the near side and the far side) experiences roughly two weeks of continuous daytime followed by roughly two weeks of continuous nighttime.

 

For thousands of years, humans noticed that the appearance of the Moon in the sky appears to change daily, even hourly.  These are called the phases of the Moon.  We use the word crescent throughout the time when the Moon appears to be less than half-illuminated, and we use the word gibbous throughout the time when the Moon appears to be more than half-illuminated.  We use the word waxing throughout the time when the Moon appears to be growing in illumination, and we use the word waning throughout the time when the Moon appears to be shrinking in illumination.  The verb to wax means to grow or to become stronger, and the verb to wane means to shrink or to become weaker.  The entire lunar cycle lasts for roughly one month.  Beginning with New Moon which is when we cannot see the Moon, gradually over a period of roughly one week the Moon appears to grow in illumination, although it still appears to be less than half-illuminated.  This is Waxing Crescent Moon, since it appears growing in illumination (waxing) but still appears less than half-illuminated (crescent).  At the end of this first week, the Moon appears to be half-illuminated.  This is First Quarter Moon, since we have completed the first quarter of the entire lunar cycle.  Gradually over the period of the second week, the Moon continues to grow in illumination, now appearing more than half-illuminated.  This is Waxing Gibbous Moon, since it continues to appear growing in illumination (waxing) and now appears more than half-illuminated (gibbous).  At the end of this second week, the Moon appears to be completely illuminated.  This is Full Moon.  Gradually over the period of the third week, the Moon appears to shrink in illumination, although it still appears to be more than half-illuminated.  This is Waning Gibbous Moon, since it appears shrinking in illumination (waning) but still appears more than half-illuminated (gibbous).  At the end of this third week, the Moon appears to be half-illuminated.  This is Third Quarter Moon, since we have completed the third quarter of the entire lunar cycle.  Gradually over the period of the fourth week, the Moon continues to shrink in illumination, now appearing less than half-illuminated.  This is Waning Crescent Moon, since it continues to appear shrinking in illumination (waning) and now appears less than half-illuminated (crescent).  Finally at the end of the fourth week, we have returned to New Moon.  Notice that during the first half of the lunar cycle (roughly two weeks), the Moon is waxing, while during the second half of the lunar cycle (also roughly two weeks), the Moon is waning.  While the Moon is waxing, the west side of the Moon appears illuminated.  This is because the illumination of the Moon is actually sunlight that the Moon reflects, and the Sun is west of the Moon (the Moon is east of the Sun) while the Moon is waxing.  Conversely, while the Moon is waning, the east side of the Moon appears illuminated.  Again, the illumination of the Moon is actually sunlight that the Moon reflects, and the Sun is east of the Moon (the Moon is west of the Sun) while the Moon is waning.

 

The phases of the Moon occur because the Moon orbits the Earth while the Earth orbits the Sun.  When the Moon is approximately between the Sun and the Earth, the far side of the Moon is facing toward the Sun, making it daytime on the far side.  The near side of the Moon must therefore be facing away from the Sun, making it nighttime on the near side, but this means that anyone on the Earth looking at the near side of the Moon sees its nighttime side, which means we cannot see the Moon!  This is New Moon, when we cannot see the Moon.  Over the following two weeks, more and more of the near side of the Moon enters into daytime.  This is why the Moon appears waxing during this time.  When the Moon has arrived on the opposite side of its orbit, the Earth is approximately between the Sun and the Moon.  Hence, the near side of the Moon is facing toward the Sun, making it daytime on the near side.  This means that anyone on the Earth looking at the near side of the Moon sees its entire face illuminated.  This is Full Moon.  Note that the Full Moon is the only phase of the Moon when the far side of the Moon coincides with the nighttime side of the Moon.  Over the following two weeks, more and more of the near side of the Moon enters into nighttime.  This is why the Moon appears waning during this time.  Eventually, the Moon returns to where it began in its orbit, meaning that we have returned to New Moon.  Note that the near side of the Moon is entirely nighttime and the far side of the Moon is entirely daytime during the New Moon.

 

When the Moon is crescent (either waxing or waning), less than half of its near side is in daytime and more than half of its near side is in nighttime.  However, the sunlight that reflects off of the daytime side of the Earth does illuminate this nighttime part of the near side of the Moon.  This is called ashen light or earthshine.  We can always see the nighttime part of the near side of the Moon when the Moon is crescent, thanks to this ashen light or earthshine.

 

Many people boast about being able to determine the time of day from the position of the Sun in the sky, but our discussion enables us to do something more impressive.  We now discuss how we can determine the time of day from the position of the Moon in the sky together with its phase.  During Full Moon for example, the Earth is approximately between the Sun and the Moon, as we discussed.  Therefore, the Sun and the Moon appear to be on opposite sides of the sky.  If we observe the Full Moon rising in the east, the Sun must be on the opposite side of the sky.  In other words, the Sun must be setting in the west, making the clock time roughly 06:00 p.m. on average over the course of the entire year.  If we observe the Full Moon culminating (highest altitude in the sky while crossing the Celestial Meridian, as we discussed earlier in the course), the Sun must be on the opposite side of the sky.  In other words, the Sun must be crossing the Celestial Meridian below the horizon, making the clock time roughly midnight.  If we observe the Full Moon setting in the west, the Sun must be on the opposite side of the sky.  In other words, the Sun must be rising in the east, making the clock time roughly 06:00 a.m. on average over the course of the entire year.  As another example of this exercise, the First Quarter Moon is halfway through the waxing part of the lunar cycle, as we discussed.  Therefore, the Sun is west of the Moon and the angle formed by the Sun, the Earth, and the Moon is approximately a right angle.  In other words, the Sun will appear to be roughly ninety degrees to the west of the Moon in the sky.  If we observe the First Quarter Moon rising in the east, the Sun must be roughly ninety degrees to its west.  In other words, the Sun must be culminating (highest altitude in the sky while crossing the Celestial Meridian), making the clock time roughly noon on average over the course of the entire year.  If we observe the First Quarter Moon culminating (highest altitude in the sky while crossing the Celestial Meridian), the Sun must be roughly ninety degrees to its west.  In other words, the Sun must be setting in the west, making the clock time roughly 06:00 p.m. on average over the course of the entire year.  If we observe the First Quarter Moon setting in the west, the Sun must be roughly ninety degrees to its west.  In other words, the Sun must be crossing the Celestial Meridian below the horizon, making the clock time roughly midnight on average over the course of the entire year.  As yet another example of this exercise, the Third Quarter Moon is halfway through the waning part of the lunar cycle, as we discussed.  Therefore, the Sun is east of the Moon and the angle formed by the Sun, the Earth, and the Moon is approximately a right angle.  In other words, the Sun will appear to be roughly ninety degrees to the east of the Moon in the sky.  If we observe the Third Quarter Moon rising in the east, the Sun must be roughly ninety degrees to its east.  In other words, the Sun must be crossing the Celestial Meridian below the horizon, making the clock time roughly midnight on average over the course of the entire year.  If we observe the Third Quarter Moon culminating (highest altitude in the sky while crossing the Celestial Meridian), the Sun must be roughly ninety degrees to its east.  In other words, the Sun must be rising in the east, making the clock time roughly 06:00 a.m. on average over the course of the entire year.  If we observe the Third Quarter Moon setting in the west, the Sun must be roughly ninety degrees to its east.  In other words, the Sun must be culminating (highest altitude in the sky while crossing the Celestial Meridian), making the clock time roughly noon on average over the course of the entire year.  We can also apply this logic to determine the time of day from the position of the Moon in the sky when its phase is Waxing Crescent Moon, Waxing Gibbous Moon, Waning Gibbous Moon, and Waning Crescent Moon.

 

If the plane of the Moon’s orbit around the Earth were the same as the ecliptic plane (the plane of the Earth’s orbit around the Sun), then whenever the Moon was New Moon it would be directly between the Sun and the Earth.  Thus, it would cast a shadow upon the Earth.  Also in this case, whenever the Moon is Full Moon then the Earth would be directly between the Sun and the Moon.  Thus, the Earth would cast a shadow upon the Moon.  However, the plane of the Moon’s orbit around the Earth is not the same as the ecliptic plane (the plane of the Earth’s orbit around the Sun).  The plane of the Moon’s orbit around the Earth is inclined to the ecliptic plane.  Hence, when the Moon is New Moon, it does not cast a shadow on the Earth on most occasions, and when the Moon is Full Moon, the Earth does not cast a shadow on the Moon on most occasions.  However, if the Moon happens to be New Moon while passing through the ecliptic plane, it will cast a shadow upon the Earth.  This is called a solar eclipse.  If the Moon happens to be Full Moon while passing through the ecliptic plane, the Earth will cast a shadow upon the Moon.  This is called a lunar eclipse.  If the plane of the Moon’s orbit around the Earth were the same as the ecliptic plane, then a solar eclipse would occur with every New Moon and a lunar eclipse would occur with every Full Moon.  In other words, both solar eclipses and lunar eclipses would occur much more frequently if the plane of the Moon’s orbit around the Earth were the same as the ecliptic plane.

 

A lunar eclipse occurs when the Moon happens to be Full Moon while passing through the ecliptic plane.  Thus, the Earth casts a shadow upon the Moon.  Only those who happen to live on the nighttime side of the Earth witness a lunar eclipse occurring.  Anyone who happens to live on the daytime side of the Earth will not witness the lunar eclipse as it occurs.  The entire lunar eclipse lasts for several hours.  During a lunar eclipse, the Moon begins as a Full Moon.  Then, the Earth’s penumbra gradually passes over the Full Moon, darkening the Moon somewhat.  The less dark part of any shadow is its penumbra, while the more dark part of any shadow is its umbra.  After the Full Moon has become somewhat darkened by the Earth’s penumbra, the Earth’s umbra then gradually passes over the already darkened face of the Moon.  Eventually, the entire face of the Moon is in the Earth’s umbra.  This is called the totality of the lunar eclipse, which lasts for roughly one hour, although the duration of totality may be longer or shorter depending on the particular lunar eclipse.  After totality, the Earth’s umbra gradually recedes off of the Moon, followed by the Earth’s penumbra gradually receding off of the Moon, returning the Moon to Full Moon.  Again, the entire lunar eclipse lasts for several hours.  Everything we have described is actually called a total lunar eclipse.  At times, the Moon is Full Moon while only partially passing through the ecliptic plane.  Hence, the Earth’s shadow does not completely cover the Full Moon.  The Earth’s shadow only covers a part of the Full Moon.  In other words, totality never occurs.  This is called a partial lunar eclipse.  On most occasions, the Full Moon misses the ecliptic plane entirely, and no lunar eclipse occurs.

 

A solar eclipse occurs when the Moon happens to be New Moon while passing through the ecliptic plane.  Thus, the Moon casts a shadow on the Earth.  Only those who happen to live within that small shadow on the daytime side of the Earth will witness a solar eclipse occurring.  Anyone who happens to live on the nighttime side of the Earth and even all those who happen to live on the daytime side of the Earth but outside of the Moon’s shadow will not witness the solar eclipse as it occurs.  Even when a solar eclipse does occur, on most occasions the Moon’s shadow lands in the middle of the ocean, since the Earth is mostly covered with water.  Therefore, although lunar eclipses and solar eclipses occur with roughly the same frequency, it is much more rare for a human to witness solar eclipses as compared to witnessing lunar eclipses.  For those who witness a solar eclipse, the Moon appears to gradually move in front of the Sun.  This causes greater and greater darkness until the Moon completely eclipses the Sun.  This is called the totality of the solar eclipse, which lasts for only a few minutes, although the duration of totality may be longer or shorter depending on the particular solar eclipse.  During totality, the sky becomes nearly as dark as nighttime; even stars become visible in the sky.  Now we must briefly digress and discuss an amazing coincidence.  The physical diameter of the Sun is roughly four hundred times the physical diameter of the Moon, but the Sun happens to be roughly four hundred times further than the Moon, causing the Sun to appear four hundred times smaller than it would appear at the same distance as the Moon.  Stated the other way around, the physical diameter of the Moon is roughly four hundred times smaller than the physical diameter of the Sun, but the Moon happens to be roughly four hundred times closer than the Sun, causing the Moon to appear four hundred times larger than it would appear at the same distance as the Sun.  It is a remarkable coincidence that the ratio of the physical diameters of the Sun to the Moon is equal to the ratio of the distances of the Sun and the Moon from the Earth.  As a result of this remarkable coincidence, the Moon and the Sun appear to be the same size in the sky as seen from the Earth.  More technically, the Moon and the Sun have the same angular diameter, roughly one-half of one degree, as observed from the Earth.  Therefore, during the totality of a solar eclipse, the Moon eclipses the Sun so perfectly that we can see the solar corona around the Moon.  As we will discuss later in the course, the solar corona is the Sun’s atmosphere.  Millions of years ago, the Moon was closer to the Earth, and the Moon has been drifting further and further from the Earth due to the transfer of the Earth’s rotational angular momentum to the Moon, as we discussed.  Since the Moon was closer to the Earth millions of years ago, the Moon appeared to be larger than the Sun in the sky and therefore eclipsed not just the Sun but its corona as well.  Millions of years from now, the Moon will be further from the Earth and therefore will appear smaller than the Sun in the sky.  Therefore, totality will not occur.  We happen to be alive when the Moon is at the ideal distance from the Earth to appear to have the same angular diameter of the Sun as seen in the sky, thus causing a totality that still leaves the solar corona visible around the Moon.  After the totality of the solar eclipse, the Moon appears to gradually move off of the Sun, and daylight gradually returns.  Everything we have described is actually called a total solar eclipse.  At times, the Moon is New Moon while only partially passing through the ecliptic plane.  Hence, the Moon does not appear to pass directly in front of the Sun; the Moon appears to partially miss the Sun.  In other words, totality never occurs.  It does become darker and darker as the Moon moves in front of the Sun, but the sky does not become as dark as nighttime.  This is called a partial solar eclipse.  Note that even during a total solar eclipse, only those who happen to be within the Moon’s umbra (the more dark part of its shadow) will witness the total solar eclipse; those who happen to be within the Moon’s penumbra (the less dark part of its shadow) just outside of the Moon’s umbra will witness a partial solar eclipse instead.  There is a third type of solar eclipse called the annular solar eclipse.  The Moon’s orbit around the Earth is an ellipse.  Hence, the distance between the Moon and the Earth varies.  The Moon’s closest position to the Earth is the Moon’s perigee, while the Moon’s furthest position from the Earth is the Moon’s apogee.  Suppose the Moon happens to be at its apogee when it happens to be New Moon while it happens to be passing through the ecliptic plane.  The result is still a solar eclipse, but the Moon would appear to be smaller than usual (smaller than the Sun in the sky), since the Moon is at its apogee (furthest from the Earth).  Hence, totality never occurs.  At best, a smaller-appearing Moon would be in front of the larger-appearing Sun.  Thus, the Sun will appear to be a ring around the Moon.  The technical term for a ring is an annulus.  Hence, the Sun will appear to be an annulus around the Moon.  This is why this is called an annular solar eclipse.  To summarize, there are three different types of solar eclipses: total solar eclipses, partial solar eclipses, and annular solar eclipses.  Millions of years ago when the Moon was closer to the Earth, the Moon always appeared larger than the Sun in the sky.  Therefore, there were no annular solar eclipses millions of years ago; there were only total solar eclipses (that also eclipsed the solar corona in addition to the Sun itself) as well as partial solar eclipses.  Millions of years from now when the Moon is further from the Earth, the Moon will always appear smaller than the Sun in the sky.  Therefore, there will no longer be total solar eclipses millions of years from now; there will only be annular solar eclipses as well as partial solar eclipses.  We happen to be alive when the Moon is at the ideal distance from the Earth for us to enjoy all three varieties of solar eclipses: total, partial, and annular.  Note that today on most occasions, the New Moon misses the ecliptic plane entirely, and no solar eclipse of any type occurs.  Eclipse hunters are persons who are wealthy enough to travel wherever necessary to be within the Moon’s shadow during a solar eclipse to witness the solar eclipse as it occurs.  Ideally, eclipse hunters travel wherever necessary to be within the Moon’s umbra during a total solar eclipse.  On most occasions, the Moon’s shadow lands in the middle of the ocean.  Therefore, the most wealthy eclipse hunters have their own yachts that they take into the ocean to wherever the Moon’s shadow happens to be located during a solar eclipse.  We conclude the topic of solar eclipses with a stern warning about the Sun in general, not just during solar eclipses.  Never ever observe the Sun through a telescope.  Never ever observe the Sun through binoculars.  Never ever observe the Sun even with the naked eye.  Solar observations done incorrectly causes permanent blindness.  It is a common misconception that during a solar eclipse, it is supposedly somewhat safe to look at the Sun, since some of its light is being eclipsed by the Moon.  This is false.  The part of the Sun that has not been eclipsed by the Moon is just as dangerous to observe as during any other circumstance.  The only exception to this stern warning is during the totality of a total solar eclipse.  The Moon fits so perfectly over the Sun in the sky that during these brief few minutes, it is safe to observe with the naked eye the solar corona around the Moon.

 

Let us discuss eclipses purely from the frame of reference of the Earth.  As we discussed, the plane of the Earth’s orbit around the Sun is called the ecliptic plane.  As a result of the Earth’s orbit around the Sun, the Sun appears to wander around the Celestial Sphere (around the sky) along a circle called the ecliptic, which is actually the projection of the ecliptic plane onto the Celestial Sphere (onto the sky).  Since the plane of the Moon’s orbit around the Earth is inclined to the ecliptic plane, the Moon appears to wander around the sky along a different circle, the projection of its orbit onto the sky.  However, this circle does intersect the ecliptic at two points.  When the Moon happens to pass through one of these intersections while the Sun happens to be at the other intersection on the opposite side of the sky, we have a lunar eclipse.  When the Moon happens to pass through one of these intersections while the Sun happens to be at the same intersection, we have a solar eclipse.  This finally justifies why the Sun’s apparent path around the sky is called the ecliptic.  The word ecliptic is derived from the word eclipse.  The Sun is always on the ecliptic by definition, but eclipses occur when the Moon happens to pass through the ecliptic while the Sun is either at the same intersection or at the opposite intersection of the Sun’s apparent path around the sky (the ecliptic) and the Moon’s apparent path around the sky.

 

As we discussed, the orbital period of the Moon is one month, but we must clearly define what we mean by one month.  Suppose it is New Moon, which is when the Moon is approximately between the Sun and the Earth.  In the time it takes the Moon to complete one full orbit, the Earth has moved significantly in its orbit around the Sun.  Therefore, it is not yet New Moon after this full lunar orbit.  We must wait somewhat longer for the Moon to move somewhat more so that it is again New Moon (again approximately between the Sun and the Earth).  We now realize that the time it takes the Moon to complete one orbit is less than the time it takes the Moon to go from New Moon to New Moon.  In other words, the time it takes the Moon to go from New Moon to New Moon is longer than the time it takes the Moon to complete one orbit.  The time it takes the Moon to go from New Moon to New Moon is called a synodic month.  However, this synodic month is longer than the time it takes the Moon to complete one orbit.  The time it takes the Moon to complete one orbit is called the sidereal month, which is shorter than the synodic month.  We can roughly calculate the duration of time of the sidereal month.  We will regard a synodic month as roughly thirty days as a rough estimate.  Although a year is somewhat accurately 365 and ¼ solar days, this is close enough to 360 solar days that we will use this as a rough estimate.  If we divide 360 days by roughly thirty days for each synodic month, we conclude that there are roughly twelve synodic months in one year.  Notice that both the Julian calendar and the Gregorian calendar divide the year into twelve months.  If there are roughly twelve synodic months in one year and if there are 360 degrees around the complete orbit of the Earth, then the Earth moves roughly one-twelfth of 360 degrees in its orbit with each synodic month.  One-twelfth of 360 degrees is thirty degrees.  Therefore, the Earth moves roughly thirty degrees in its orbit with each synodic month.  This stands to reason.  We have already estimated that the Earth moves roughly one degree in its orbit with each passing day.  If there are roughly thirty days in a synodic month and if the Earth moves roughly one degree in its orbit in each day, then the Earth moves roughly thirty degrees in its orbit with each synodic month.  Therefore, we must calculate the time it takes the Moon to move an additional thirty degrees in its orbit, which is a 30/360 fraction of a complete orbit.  The fraction 30/360 reduces to the fraction 1/12.  Therefore, we must calculate the time it takes the Moon to move an additional 1/12 of a complete orbit.  As a rough estimate, we will use 30 days as a complete orbit.  Therefore, the time it takes the Moon to move 1/12 of its orbit is 1/12 of thirty days, or 2.5 days.  Therefore, the sidereal month is between two and three days shorter than the synodic month.  In other words, the synodic month is between two and three days longer than the sidereal month.  Somewhat more accurate calculations reveal that the synodic month is roughly 29.5 solar days, and the sidereal month is roughly 2.2 solar days shorter than the synodic month.  In other words, the sidereal month is roughly 27.3 solar days.

 

Just as geography is the naming of topographical features on Earth such as oceans, mountains, and rivers, selenography is the naming of topographical features on the Moon such as maria and craters.  The largest mare on the Moon is Oceanus Procellarum, which is Latin for the Ocean of Storms.  The first humans who stepped foot on the Moon landed on Mare Tranquillitatis, which is Latin for the Sea of Tranquility.  The three astronauts of the Apollo 11 mission were Neil Armstrong, Buzz Aldrin, and Michael Collins.  After traveling to the Moon and entering into lunar orbit in the command module named the Columbia, Neil Armstrong and Buzz Aldrin climbed into the small lunar module named the Eagle that detached from the Columbia.  Michael Collins remained in the command module Columbia while orbiting the Moon.  Hence, Michael Collins never stepped foot on the Moon.  Neil Armstrong and Buzz Aldrin piloted the Eagle and landed in Mare Tranquillitatis (the Sea of Tranquility) on Sunday, July 20, 1969.  Neil Armstrong’s exact words upon landing on the Moon were “The Eagle has landed,” since the name of the lunar module was the Eagle.  After spending several hours checking instruments and taking measurements, Neil Armstrong opened the door of the Eagle, climbed down a ladder, and became the first human being to step foot on the Moon.  His exact words upon stepping foot on the Moon were “This is one small step for a man, but one giant leap for mankind.”  Then, Buzz Aldrin climbed down the ladder and became the second human being to step foot on the Moon.  They planted an American flag, gathered some Moon rocks, climbed back into the Eagle, and launched off of Mare Tranquillitatis (the Sea of Tranquility).  They piloted the Eagle to lunar orbit, reconnected with Michael Collins in the command module Columbia, and all three of these astronauts returned safely to the Earth.  The same procedure was carried out by the astronauts of the Apollo 12, Apollo 14, Apollo 15, Apollo 16, and Apollo 17 missions.  The same procedure should have been carried out by the Apollo 13 astronauts, but an accident occurred while traveling to the Moon.  All three astronauts of the Apollo 13 mission traveled to the Moon, orbited the Moon, and returned safely to the Earth; however, none of them were able to step foot on the Moon.  Thus, only twelve human beings have stepped foot on the Moon.  There have been twelve human beings who have traveled to the Moon and who have orbited the Moon but who have not stepped foot on the Moon.  Note that this includes the astronauts of the Apollo 8 and Apollo 10 missions, two earlier missions that sent astronauts to orbit the Moon without landing on the Moon.  Therefore, there have been twenty-four human beings in all of human history who have traveled to the Moon and who have orbited the Moon.  Half of those twenty-four astronauts have actually stepped foot on the Moon.

 

 

The Terrestrial Planets and their Moons

 

During the young forming Solar System, the inner part of the protoplanetary disk was closer to the Sun and therefore was more subject to the Sun’s heat.  Since the inner part of the protoplanetary disk was warmer, only materials with hotter melting temperatures were able to condense, in particular metal and rock.  However, most of the protoplanetary disk was composed of hydrogen and helium; metal and rock constituted only a small fraction of the protoplanetary disk.  Therefore, only these small amounts of metal and rock were able to condense closer to the Sun.  Therefore, small and dense planetesimals condensed in the inner protoplanetary disk closer to the Sun.  These planetesimals grew larger and larger through accretion until the planetesimals became so large that their self-gravity became strong enough to force themselves into spherical shapes.  These objects were now so large with so much mass and therefore strong enough self-gravity that they began to attract even more material around them, causing them to grow even larger.  Eventually, they became the four terrestrial planets closer to the Sun: Mercury, Venus, Earth, and Mars.

 

As these metallic and rocky planetesimals grew to become terrestrial planets, they continuously collided with material in the protoplanetary disk during the heavy bombardment period of the young Solar System.  These collisions were sticky collisions, converting a significant fraction of the kinetic energy (moving energy) of the colliding objects into thermal energy (heat energy).  Therefore, the terrestrial planets became warmer and warmer as they formed.  Eventually, the terrestrial planets became so hot that they became almost entirely molten.  We conclude that accretion is a source of internal energy.  However, accretion only served as an important source of internal energy during the heavy bombardment period of the young Solar system.  When most planetesimals had accreted together to form planets, few planetesimals remained to collide with planets, thus ending the heavy bombardment period.  While the terrestrial planets were almost entirely molten, they differentiated themselves as more dense metals sank toward their centers while less dense rock rose toward their surfaces, ultimately forming dense metallic cores surrounded by less dense mantles surrounded by even less dense and thin crusts.  Differentiation is also a source of internal energy.  As more dense materials sink, gravitational energy is converted to thermal energy (heat energy).  Differentiation is completed when materials have mostly separated based on their densities.  The differentiation of the terrestrial planets was completed in a relatively short amount of time, roughly one hundred million years.  After this brief early history of the Solar System, neither accretion nor differentiation served as significant sources of internal energy for the terrestrial planets.  For most of the history of the Solar System, the terrestrial planets derived most of their internal energy from radioactive decay.  Any given radioactive sample becomes less and less radioactive over time, since more and more of the radioactive parent atoms are transmuted into daughter atoms leaving fewer and fewer radioactive atoms to decay.  Therefore, any given radioactive sample was more radioactive in the past.  Consequently, the terrestrial planets derived even more internal energy from radioactive decay billions of years ago while they were still forming.  In summary, the most important source of internal energy for the terrestrial planets is radioactive decay.  This is the only source of internal energy for most of the geologic lifetime of a terrestrial planet, and it is an even greater source of internal energy when a young terrestrial planet is forming, when it also derives internal energy from accretion and from differentiation.

 

The internal energy within a terrestrial planet drives its geologic activity, and the most important source of internal energy is radioactive decay.  The internal energy heats the interior of the terrestrial planet, causing some layers of rock to be weak, perhaps even partially molten.  A large terrestrial planet would have a long geologic lifetime, since it would have more mass and therefore more radioactive atoms and hence a greater supply of internal energy.  A small terrestrial planet would have a short geologic lifetime, since it would have less mass and therefore less radioactive atoms and hence a smaller supply of internal energy.  Over billions of years, more and more radioactive atoms composing a terrestrial planet decay, leaving a smaller and smaller supply of internal energy.  The interior of the planet cools, resulting in more and more of the interior of the planet becoming more and more rigid, resulting in less and less geologic activity.  Eventually, most of the radioactive atoms of the terrestrial planet will have decayed.  With very little radioactive atoms remaining to provide internal energy, the interior of the terrestrial planet becomes nearly entirely solid.  Geologic activity ends, and the terrestrial planet becomes geologically dead.  Since a large terrestrial planet has a long geologic lifetime, there is abundant geologic activity to cover or eradicate craters caused by asteroid impacts and comet impacts.  Hence, large terrestrial planets do not have heavily cratered surfaces.  Since a small terrestrial planet has a short geologic lifetime, there is no geologic activity for most of its history to cover or eradicate craters caused by asteroid impacts and comet impacts.  Hence, small terrestrial planets have heavily cratered surfaces.

 

A terrestrial planet generates a magnetic field from circulating currents of molten metal in its core caused by the rotation of the planet.  Therefore, the two equally important variables that create a terrestrial planet’s magnetic field is a metallic core that is at least partially molten and reasonably rapid rotation.  Again, internal energy from radioactive decay is responsible for heating the interior of the terrestrial planet, causing part of the metallic core to be molten.  A large terrestrial planet will maintain its magnetic field over its long geologic lifetime assuming it has reasonably rapid rotation, while a small terrestrial planet can only maintain its magnetic field over its short geologic lifetime assuming it even has reasonably rapid rotation.  Eventually, most of the radioactive atoms of the terrestrial planet will have decayed.  With very little radioactive atoms remaining to provide internal energy, the interior of the terrestrial planet becomes nearly entirely solid.  As the metallic core gradually solidifies, the terrestrial planet’s magnetic field weakens and ultimately dies, even if the planet has reasonably rapid rotation.

 

An atmosphere is a thin layer of gas gravitationally held to a moon, a planet, or a star.  Although terrestrial planets are born with primary atmospheres composed of almost entirely hydrogen gas and helium gas, the gravitational attraction of a terrestrial planet is too weak to retain this primary atmosphere.  A terrestrial planet’s secondary atmosphere is composed of an abundance of water vapor and nitrogen gas and carbon dioxide gas.  These gases come from volcanic outgassing.  Since terrestrial planets are born almost entirely molten, the volcanic eruptions everywhere on the surface of the planet eject not just lava but gases as well, thus forming the secondary atmosphere.  Note that water vapor and carbon dioxide are greenhouse gases.  Thus, a terrestrial planet’s secondary atmosphere causes the planet to become warmer than it would have been otherwise, based on its particular distance from the Sun.

 

As we discussed, the geologic history of a terrestrial planet is determined by its size.  Similarly, the atmospheric history of a terrestrial planet is strongly, but not exclusively, determined by its size.  A small terrestrial planet has less mass and therefore weak gravity, insufficient to retain even its secondary atmosphere.  In addition, a small terrestrial planet has a short geologic lifetime; thus, a small terrestrial planet cannot maintain its secondary atmosphere, since there is no ongoing geologic activity that would result in volcanic outgassing.  Moreover, a small terrestrial planet can only maintain its magnetic field over its short geologic lifetime, assuming it even has reasonably rapid rotation.  After its magnetic field dies, a small terrestrial planet can no longer protect its atmosphere from the Sun’s solar wind, which will substantially ionize any weak atmosphere that the small terrestrial planet may have.  After only a few hundred million years, a small terrestrial planet is left with virtually no atmosphere.  At best, there will be an exosphere that begins at the surface of the small terrestrial planet that smoothly transitions into the very cold temperatures of the surrounding outer space.  A large terrestrial planet has more mass and therefore strong gravity, sufficient to retain its secondary atmosphere.  In addition, a large terrestrial planet has a long geologic lifetime; thus, a large terrestrial planet can maintain its secondary atmosphere, since there is ongoing geologic activity that results in volcanic outgassing.  Moreover, a large terrestrial planet can maintain its magnetic field over its long geologic lifetime, although this assumes the planet has reasonably rapid rotation.  The large terrestrial planet’s magnetic field will protect its atmosphere from significant ionization from the Sun’s solar wind.  In summary, a large terrestrial planet will have a substantial atmosphere over its long geologic lifetime.  The lowest atmospheric layer of a large terrestrial planet is the troposphere, which becomes cooler with increasing elevation, since we are further and further from the surface of the planet and thus further and further from the heat radiated from its surface.  Since there may be significant convection (circulation) of air in the troposphere and since the large terrestrial planet’s gravity pulls most of its atmosphere down into its troposphere, the vast majority of all meteorological phenomena (weather) on the planet occurs within its troposphere, the lowest layer of its atmosphere, although this generalization may be altered by the rotation of the planet.  The next atmospheric layer of most large terrestrial planets is the thermosphere, which becomes warmer with increasing elevation, since we are closer and closer to the ionosphere, the layer within the upper thermosphere composed of various atoms and molecules that have absorbed X-rays from the Sun, thus shielding the surface of the large terrestrial planet from the Sun’s X-rays.  There is no convection (circulation) of air within a planet’s thermosphere, since the air in the thermosphere remains layered based on temperature.  Beyond the planet’s thermosphere is the exosphere, where the air becomes cooler and cooler, smoothly transitioning into the very cold temperatures of the surrounding outer space.  Note that planet Earth is an extraordinary exception to this generalization.  Due to the presence of life on Earth, there is an abundance of oxygen in the Earth’s atmosphere, which absorbs far ultraviolet from the Sun forming an ozonosphere, which not only shields the surface of the Earth from the Sun’s far ultraviolet but is also responsible for two additional layers of its atmosphere: the stratosphere and the mesosphere both sandwiched between the troposphere and the thermosphere.  No other terrestrial planet has an abundance of oxygen in its atmosphere; therefore, no other terrestrial planet’s atmosphere shields the planet from the Sun’s far ultraviolet, nor does any other terrestrial planet’s atmosphere have a stratosphere or a mesosphere.

 

In addition to its size, the atmospheric history of a terrestrial planet is strongly determined by its distance from the Sun.  If a large terrestrial planet is sufficiently far from the Sun, the planet will be sufficiently cool that the water vapor of its secondary atmosphere may freeze to solid water (ice), subtracting this important greenhouse gas from the atmosphere, making the planet even cooler.  If a large terrestrial planet is sufficiently close to the Sun, the planet will be sufficiently warm that the water vapor of its secondary atmosphere will remain in the gaseous state, leaving this important greenhouse gas in the atmosphere, making the planet even warmer.  If a large terrestrial planet is at an intermediate distance from the Sun, the planet may be at the ideal temperature for some water vapor to freeze into solid water (ice), for some water vapor to condense into liquid water, and for the remaining water vapor to remain in the gaseous state.  As a result, the terrestrial planet remains at an intermediate temperature where water can exist in all three of its physical states: solid water (ice), liquid water, and water vapor.  Note that the distance from the Sun would be a less important variable for the atmospheric history of a small terrestrial planet, since the short geologic lifetime of such a planet would prevent it from maintaining a substantial atmosphere for longer than a few hundred million years.  Even a large terrestrial planet would deviate from this analysis if it had slow rotation resulting in a weak magnetic field, which would expose the planet’s atmosphere to substantial ionization from the Sun’s solar wind.

 

The first terrestrial (inner) planet is Mercury, the closest planet to the Sun.  The orbital period of Mercury around the Sun is roughly three months.  Mercury is the smallest of the eight planets.  Because of its small size, Mercury presumably had very little radioactive atoms to provide internal energy.  Therefore, Mercury was geologically alive for only a brief amount of time, perhaps a few hundred million years.  For most of its history, Mercury has been a geologically dead planet.  Also due to its small size and small mass, Mercury’s gravity is sufficiently weak that it cannot retain an atmosphere.  Without geologic activity for most of its history to provide volcanic outgassing to replenish a lost atmosphere, Mercury has had virtually no atmosphere for most of its lifetime.  At best, there is an exosphere that begins at the surface of Mercury that smoothly transitions into the very cold temperatures of the surrounding outer space.  Since Mercury has been geologically dead for most of its lifetime, there has been no geologic activity for most of its history to cover or eradicate craters caused by asteroid impacts and comet impacts.  Hence, the surface of Mercury is much more cratered as compared with the surface of the Earth.  Much of what we have described about planet Mercury is similar to the Earth’s Moon.  In fact, Mercury’s actual appearance is also similar to the appearance of the Earth’s Moon.

 

Whereas the Earth’s Moon has an unusually small metallic core as compared with its overall size, Mercury has an unusually large metallic core as compared with its overall size.  This usually large metallic core may explain why Mercury generates a modest magnetic field.  The dominant theory to explain Mercury’s unusually large metallic core is as follows.  Mercury was actually born a somewhat larger terrestrial planet, roughly the size of Mars but not as large as Venus or Earth.  This would make Mercury’s metallic core more reasonably proportioned as compared with its original larger size.  While the young Mars-sized Mercury was still geologically alive, a violent collision with a large planetesimal stripped off its outer layers, making the entire planet smaller and leaving it with a disproportionately large metallic core.  As we discussed, a violent collision between the young Earth and a large planetesimal ripped huge chunks of molten rock from the outer layers of the Earth.  In the case of the Earth however, these chunks of molten rock did not have enough energy to escape from the Earth’s gravitational attraction.  Thus, these chunks of molten rock remained in orbit around the Earth, eventually forming the Earth’s Moon.  The young Mercury was already Mars-sized before it suffered from its own violent collision.  Hence, Mercury was already smaller than the Earth, and so Mercury already had less mass and therefore weaker gravitational attraction as compared with the Earth.  Immediately after the violent collision, Mercury lost a significant fraction of its mass, making its gravitational attraction even weaker.  Therefore, the chunks of molten rock ripped from Mercury’s outer layers were able to escape its very weak gravitational attraction.  Therefore, this violent collision did not form a Mercurian moon.  Since Mercury lost a large fraction of its mass from this violent collision, it also lost a large fraction of its radioactive atoms to supply it with internal energy to keep it geologically alive.  Therefore, Mercury suffered from sudden internal cooling, as it abruptly transformed from a geologically alive terrestrial planet to a geologically dead terrestrial planet.  Most substances contract when they cool.  If this theory is correct, the already smaller Mercury would have suddenly contracted to an even smaller size, not only giving it an even more disproportionately large metallic core but also resulting in Mercury becoming the smallest of the eight planets of the Solar System.  This sudden contraction would have fractured (broken) Mercury’s outer layers.  Indeed, there are scarps (steep cliffs) throughout the surface of planet Mercury, which geophysicists believe are actually fractures (breaks) caused when Mercury suffered from this sudden thermal contraction as it transformed from a geologically alive terrestrial planet to a geologically dead terrestrial planet.  In summary, a violent collision between a young Mars-sized Mercury with a large planetesimal explains why Mercury is the smallest of the eight planets of the Solar System, explains why Mercury has an unusually large metallic core as compared with its present overall size, explains why Mercury has no moons despite suffering from a violent collision, and explains the abundance of scarps (steep cliffs) throughout the surface of Mercury.

 

It is a common misconception that Mercury is the hottest planet in the Solar System, since it is the closest planet to the Sun.  This is false.  As we will discuss shortly, Venus is the hottest planet in the Solar System.  Of course, Mercury’s daytime side (facing toward the Sun) is very hot.  However, Mercury has virtually no atmosphere and has no liquid water to regulate the temperature between its daytime side and its nighttime side, as is the case with planet Earth.  Therefore, the nighttime side of Mercury (facing away from the Sun) is very cold.  Indeed, Mercury is one of the hottest planets and one of the coldest planets at the same time!  The poles of Mercury receive very little sunlight, and some regions near the poles are in permanent darkness due to shadows cast by nearby landforms.  As a result, these shadowed regions remain perpetually near absolute zero temperature, on the closest planet to the Sun!

 

The second terrestrial (inner) planet is Venus, the second planet from the Sun.  The orbital period of Venus around the Sun is roughly seven months.  Venus is almost exactly the same size as the Earth, and Venus has almost exactly the same mass as the Earth.  With almost the same size and mass, Venus therefore has almost exactly the same density and gravity as the Earth.  For all these reasons, Venus is sometimes considered Earth’s twin sister planet.  However, the similarities with the Earth end here.  Venus has no moons, unlike the Earth.  Venus has an incredibly thick atmosphere that completely covers the planet.  The thick atmosphere of Venus reflects so much sunlight that Venus appears to be the brightest object in the Earth’s sky, aside from the Sun and the Moon of course.  Since Venus is closer to the Sun than the Earth, Venus always appears near the Sun in the Earth’s sky.  Since the Sun is in the sky in the daytime, our only hope of observing Venus in the Earth’s sky is in the west shortly after sunset or in the east shortly before sunrise.  Venus appears so bright in the west shortly after sunset that it is often called the evening star, and Venus appears so bright in the east shortly before sunrise that it is often called the morning star.  Again, the evening star and the morning star are not stars; they are actually the planet Venus.  The atmosphere of Venus so thoroughly covers the planet that we cannot observe Venusian surface features through our telescopes.  We knew nothing about the topography of Venus until we sent artificial satellites to orbit Venus.  These probes used radar to penetrate the thick Venusian atmosphere.  Thus, we have successfully mapped the topography of Venus using radar from the satellites that we have sent to orbit Venus.

 

Since Venus is almost the same size as the Earth, it has roughly the same amount of radioactive atoms and thus roughly the same supply of internal energy as the Earth.  Therefore, Venus has a geologic lifetime similar to the Earth.  Indeed, Venus is still geologically alive, as is the Earth.  For example, there is evidence of both igneous activity and seismic activity on Venus.  There are also mountains on Venus.  The tallest mountain on Venus is Maxwell Montes.  Although Venus is still geologically alive, the Theory of Plate Tectonics is not the correct theory to explain the geologic activity on Venus, and geophysicists have not yet come to an agreement on the correct theory to explain the geologic activity of Venus.  Although Venus is still geologically alive and therefore has a partially molten metallic core, Venus also has very slow rotation.  Hence, Venus has a very weak magnetic field.  As a result, the Venusian atmosphere is substantially ionized by the Sun’s solar wind.  As we would expect, the Venusian atmosphere begins with a troposphere that cools with increasing elevation followed by a thermosphere that warms with increasing elevation as we approach the ionosphere in the upper thermosphere.  Beyond the thermosphere is the exosphere, where the temperature smoothly transitions into the very cold temperatures of the surrounding outer space.  Without life to provide oxygen, the Venusian atmosphere has no ozonosphere and therefore no stratosphere and mesosphere sandwiched between the troposphere and the thermosphere.  Without an ozonosphere, the surface of Venus is not shielded from far ultraviolet from the Sun.

 

Since it is almost the same size as the Earth, Venus should have outgassed a secondary atmosphere similar to the Earth’s secondary atmosphere.  However, since Venus is closer to the Sun than the Earth, hotter temperatures caused more water vapor and carbon dioxide to be extracted from Venusian volcanic activity.  Since both water vapor and carbon dioxide are greenhouse gases, this caused the Venusian atmosphere to trap more heat, making the planet even hotter.  This caused even more water vapor and carbon dioxide to be extracted from Venusian volcanic activity, causing the Venusian atmosphere to trap even more heat, making the planet hotter still, and so on and so forth.  The result was a runaway greenhouse effect, causing Venus to become the hottest planet in the Solar System, even though it is the second planet from the Sun.  This also explains the incredibly thick atmosphere of Venus.  The Venusian atmosphere is so thick that the air pressure on the surface of Venus is enormous as compared with the Earth’s air pressure.  Note however that very little water vapor remains in the Venusian atmosphere.  Since Venus does not have a magnetic field to shield its atmosphere from the Sun’s solar wind, most of the outgassed water vapor was attacked by the Sun’s solar wind, stripping hydrogen atoms off of the water molecules.  The hydrogen atoms then escaped from the gravitational attraction of Venus.  There are clouds within the Venusian atmosphere, but these are not like clouds in the Earth’s atmosphere.  Clouds in the Earth’s atmosphere are composed of and precipitate (rain) liquid water.  However, the clouds within the Venusian atmosphere are composed of and precipitate (rain) sulfuric acid, which is poisonous.  It is so hot on Venus that most of the sulfuric acid rain evaporates before reaching the ground, although there may be gaseous sulfuric acid near the surface of Venus.  If we were to stand on the surface of Venus, we would be crushed by the air pressure, poisoned by the sulfuric acid, burned to a crisp by the greenhouse effect, and irradiated by the far ultraviolet from the Sun all at the same time!  A lack of oxygen thus causing suffocation would be the least of our worries!

 

The third terrestrial planet is the Earth-Moon system, the third planet from the Sun.  However, we have already discussed this third planet in tremendous detail.  Therefore, we now discuss the fourth and last of the terrestrial (inner) planets: Mars, the fourth planet from the Sun.  The orbital period of Mars around the Sun is roughly two Earth years.  Since Mars is smaller than the Earth, it has less mass and thus weak gravity as compared with the Earth.  Hence, Mars is less severely differentiated as compared with the Earth, resulting in a greater abundance of metals such as iron on the surface of Mars as compared with the Earth.  The abundance of iron on the surface of Mars has reacted with oxygen forming iron oxide (rust), which has a reddish color.  This is why Mars is red.  In fact, the nickname of Mars is the Red Planet.  Mars even appears red to the naked eye (without the aid of a telescope or even binoculars) as seen in the Earth’s sky.  Mars has an obliquity (axial tilt) similar to the Earth, causing seasons on Mars similar to the seasons on Earth.  Mars has polar ice caps similar to the Earth’s polar ice caps.  Mars also rotates once in roughly twenty-four hours, just like the Earth.  For all of these reasons, Mars is sometimes regarded as being Earth’s twin brother planet.  However, the similarities with the Earth end here.  Mars is smaller than the Earth and Venus, but Mars is not as small as Mercury or the Earth’s Moon.  Therefore, Mars had more radioactive atoms and thus a greater supply of internal energy than Mercury and the Earth’s Moon, giving Mars a longer geologic lifetime than Mercury or the Earth’s Moon.  However, Mars did not have as much radioactive atoms and thus did not have as great a supply of internal energy as the Earth or Venus, giving Mars a shorter geologic lifetime than the Earth or Venus.  Mars was probably geologically alive for a couple billion years, and Mars has probably been geologically dead for a couple billion years.  In other words, Mars is the only terrestrial (inner) planet that has been both geologically alive for a significant duration of time and geologically dead for a significant duration of time.  Therefore, studying Mars may offer insight into what Earth will become billions of years from now after it has exhausted its own geothermal energy.  This would imply that Mars may have been similar to the Earth in the distant past.

 

While it was still geologically alive, Mars outgassed a secondary atmosphere similar to the Earth’s secondary atmosphere, composed primarily of water vapor, nitrogen gas, and carbon dioxide gas.  Also while Mars was still geologically alive, it still had a partially molten metallic core.  Together with a rotation rate that is roughly equal to Earth’s rotation rate, ancient Mars generated a substantial magnetic field while it was geologically alive.  This magnetic field shielded the ancient Martian atmosphere from substantial ionization from the Sun’s solar wind.  Since water vapor and carbon dioxide are greenhouse gases, the ancient Martian atmosphere caused Mars to become warmer than it would have been otherwise, based on its distance from the Sun.  The temperature of ancient Mars may have permitted water to exist in all three of its physical states: solid water (ice), liquid water, and water vapor.  Hence, some of the water vapor in the ancient Martian atmosphere could condense into liquid water, precipitating (raining) onto the planet.  Indeed, there is evidence that there were rivers of running water, lakes of water, and perhaps even an ocean of water on ancient Mars.  Although the condensation of water vapor into liquid water subtracted this greenhouse gas from the ancient Martian atmosphere, the abundance of carbon dioxide remaining in the ancient Martian atmosphere still maintained a warm ancient Martian temperature, based on its distance from the Sun.  Also, the continuing geologic activity caused volcanic outgassing, replenishing the atmosphere with both water vapor and carbon dioxide, both greenhouse gases that helped to maintain the warm ancient Martian temperature.  Ancient Mars was indeed similar to the Earth, both geologically and atmospherically.  To our knowledge however, there was never life on Mars.  Therefore, the Martian atmosphere (both ancient and present) begins with a troposphere that cools with increasing elevation followed by a thermosphere that warms with increasing elevation as we approach the ionosphere in the upper thermosphere.  Beyond the thermosphere is the exosphere, where the temperature smoothly transitions into the very cold temperatures of the surrounding outer space.  Without life to provide oxygen, the Martian atmosphere (both ancient and present) has no ozonosphere and therefore no stratosphere and mesosphere sandwiched between the troposphere and the thermosphere.  Without an ozonosphere, the surface of Mars (ancient and present) is not shielded from far ultraviolet from the Sun.

 

Since Mars is smaller than Earth and Venus, it had fewer radioactive atoms and thus did not have as great a supply of internal energy as Earth or Venus, giving Mars a shorter geologic lifetime than Earth or Venus.  The Earth-like conditions we have described on ancient Mars could only be maintained for a couple billion years.  As Mars exhausted its supply of internal energy, its interior cooled, resulting in more and more of the interior of the planet becoming more and more rigid, resulting in less and less geologic activity and a weaker and weaker magnetic field.  With less and less geologic activity, there was less and less volcanic outgassing to replenish the Martian atmosphere.  With a weaker and weaker magnetic field, Mars could no longer shield its atmosphere from substantial ionization from the Sun’s solar wind.  Also since Mars is smaller than Earth and Venus, it has less mass and therefore weaker gravity, insufficient to retain its dwindling atmosphere.  As the Martian atmosphere became thinner and thinner, its greenhouse effect became weaker and weaker, making the planet colder and colder.  Eventually, Mars became so cold that water could no longer exist in the liquid state.  Most of the water froze into solid water (ice) at the Martian poles, forming the Martian ice caps.  Although the present Martian atmosphere is composed mostly of carbon dioxide which is a greenhouse gas, the present Martian atmosphere is too thin to cause a significant greenhouse effect.  Therefore, Mars is presently significantly colder than the Earth, which is appropriate since Mars is further from the Sun than the Earth.  Also as a result of the weakening Martian magnetic field, any remaining water vapor in the Martian atmosphere was attacked by the Sun’s solar wind, stripping hydrogen atoms off of the water molecules.  The hydrogen atoms then escaped from the gravitational attraction of Mars.  The remaining oxygen atoms bonded with each other to form molecular oxygen, which then reacted with the abundance of iron on the surface of Mars to form iron oxide (rust), giving the surface of Mars is famously red color.  Over the past couple billion years, Mars has had no geologic activity to cover or eradicate craters caused by asteroid impacts and comet impacts.  Hence, the surface of Mars is more cratered as compared with the surfaces of Earth or Venus.  However, the surface of Mars is not as cratered as the surface of Mercury or the Earth’s Moon, since those terrestrial planets have been geologically dead for much longer than Mars.  In terms of size, mass, gravity, geologic lifetime, atmospheric pressure, and impact cratering, Mars is intermediate between two extremes.  At one extreme, Earth and Venus have larger sizes, are more massive, have stronger gravity, have long geologic lifetimes, have substantial atmospheric pressure, and have fewer impact craters.  At the other extreme, Mercury and the Earth’s Moon have smaller sizes, are less massive, have weaker gravity, have short geologic lifetimes, have virtually zero atmospheric pressure, and have an abundance of impact craters.  Between these two extremes, Mars has intermediate size, is intermediate in mass, has intermediate gravity, has an intermediate geologic lifetime, has intermediate (thin but appreciable) atmospheric pressure, and has an intermediate number of impact craters.

 

While the young Mars was still geologically alive, it built the largest geologic features in the entire Solar System.  For example, Olympus Mons is not only the largest, tallest mountain on Mars, Olympus Mons is also the largest, tallest mountain in the entire Solar System.  It is much larger and much taller than Mount Everest on Earth for example.  Olympus Mons is actually an extinct volcano that formed from igneous activity when the young Mars was still geologically alive.  Valles Marineris is not only the longest, widest, deepest canyon on Mars, Valles Marineris is also the longest, widest, deepest canyon in the entire Solar System.  It is much longer, wider, and deeper than the Grand Canyon on Earth for example.  Canyons on Earth form from rivers of running water; the Grand Canyon was carved by the Colorado River for example.  Although we discussed that there were rivers of running water on ancient Mars, Valles Marineris is too enormous to have been carved by a river.  Valles Marineris probably formed from an enormous seismic disruption of the Martian crust when the young Mars was still geologically alive.  Utopia Planitia is not only the largest impact basin on Mars, Utopia Planitia is also the largest impact basin in the entire Solar System.  Utopia Planitia is so enormous that astronomers formerly believed that it was simply a plain, which is why it was named Utopia Planitia.

 

Mars has two moons: Phobos and Deimos.  Both of these moons are very small.  They were probably asteroids in the asteroid belt that Jupiter’s gravity ripped out of the asteroid belt, as we will discuss shortly.  Since the orbit of Mars is right next to the asteroid belt, it would be somewhat likely for the gravity of Mars to capture an asteroid that Jupiter’s gravity ripped from out of the asteroid belt.  Both Phobos and Deimos are tidally locked to Mars, meaning that their rotational periods are equal to their orbital periods around Mars.  Hence, both of these moons always face the same side toward Mars as they orbit Mars.

 

 

The Jovian, Gas-Giant Planets, their Moons, and their Rings

 

During the formation of the Solar System, the frost line was the precise distance from the Sun beyond which volatile ices were able to condense in addition to metal and rock.  Volatile ices are hydrogen compounds, such as methane CH4, ammonia NH3, and water H2O.  Closer to the Sun than the frost line, the protoplanetary disk was sufficiently warmed by the Sun that only materials with hot melting temperatures were able to condense, such as metal and rock.  Further from the Sun than the frost line, the protoplanetary disk was sufficiently cool that volatile ices with cooler melting temperatures were able to condense in addition to metal and rock.  As we will discuss later in the course, the very early universe was composed entirely of hydrogen and helium, and stars later synthesized small amounts of carbon, nitrogen, and oxygen and even smaller amounts of silicon, iron, and nickel.  As a result, even later generations of star systems, such as our own Solar System, were born from a nebula that was mostly hydrogen and helium with small amounts of volatile ices and even smaller amounts of metal and rock.  Only metal and rock were able to condense in the warmer inner parts of the protoplanetary disk, but metal and rock only accounted for tiny fractions of the composition of the Solar System.  This is why the terrestrial (inner) planets are small as compared with the jovian, gas-giant (outer) planets.  Volatile ices, which are more abundant than metal and rock, were able to condense in the cooler, outer parts of the protoplanetary disk in addition to metal and rock.  Therefore, large planetesimals composed of volatile ices in addition to metal and rock condensed in the outer Solar System.  These large planetesimals grew even larger through accretion, eventually becoming large enough with sufficient self-gravity to force themselves into spherical shapes.  These planetesimals began to differentiate themselves, with the most dense metals sinking toward their centers, the least dense volatile ices rising toward their surfaces, and moderately dense rock settling in the intermediate layer between the metallic core and the icy outer layers.  As these planetesimals continued to grow through accretion, they eventually became so massive that they began to gravitationally attract the surrounding hydrogen and helium, which accounted for the vast majority of the mass of the protoplanetary disk.  Consequently, these outer planets grew to enormous sizes as compared with the terrestrial (inner) planets.  These outer planets ultimately became gas-giant planets, but note that this term is misleading.  Although the outer layers of these so-called gas-giant planets are indeed mostly hydrogen gas and helium gas, these so-called gas-giant planets have sufficiently strong gravity to compress these gases to exotic densities in deep (interior) layers.  Beneath the hydrogen gas and helium gas are layers of dense liquid hydrogen, at even deeper layers are higher density electrically conducting hydrogen (commonly known as metallic hydrogen), and at deeper layers still are even higher density volatiles ices.  Beneath the volatile ices, we would find a very high-density layer of rock before we would finally encounter the most dense metallic core of a so-called gas-giant planet.  In summary, small terrestrial planets formed in the protoplanetary disk closer to the Sun than the frost line, while large jovian planets formed in the protoplanetary disk further from the Sun than the frost line.  The frost line was obviously somewhere between the orbit of Mars and the orbit of Jupiter.  More precisely, the frost line was somewhere between the asteroid belt and the orbit of Jupiter.  We will discuss the asteroid belt shortly.

 

As we discussed, the final stage of formation of these jovian, gas-giant planets was the gravitational attraction of large amounts of hydrogen gas and helium gas that fell onto the forming planet.  The collapsing material rotated faster, ensuring that the angular momentum of the gas remained conserved (remained constant).  This explains why the jovian, gas-giant (outer) planets have fast rotations as compared with the terrestrial (inner) planets.  The fast rotations have caused each of the jovian, gas-giant (outer) planets to be severely oblate: bulged out at the equator and pushed in at the poles.  The terrestrial (inner) planets also rotate, causing their shapes to be oblate as well.  However, the terrestrial (inner) planets rotate slowly as compared with the jovian, gas-giant (outer) planets.  Hence, the oblateness of each of the terrestrial (inner) planets is very small.  To the naked eye, the shape of the four terrestrial (inner) planets seems to be perfectly spherical.  The jovian, gas-giant (outer) planets rotate sufficiently fast that they are so severely oblate that they are noticeably oblate in photographs or when observed through telescopes.  The fast rotations of the gas-giant (outer) planets also cause circulating currents of electrically conducting hydrogen (metallic hydrogen) in deeper layers of the planet.  These circulating currents of electrically conducting hydrogen (metallic hydrogen) in turn create extraordinarily powerful magnetic fields.  Indeed, the magnetic fields of all the jovian, gas-giant (outer) planets are much stronger than even Earth’s magnetic field, which is the strongest magnetic field among the terrestrial (inner) planets of the Solar System.

 

The material that fell toward young forming jovian, gas-giant (outer) planets was sufficiently abundant that the final stages of formation of each of these planets was a microcosm of the formation of the entire Solar System.  Most of the material collapsed to form the outer layers of the planet.  As the rest of the material collapsed, collisions between particles within the collapsing cloud became more frequent, since the gravitational collapse brought the particles closer together.  These collisions tended to be sticky, with colliding particles merging into larger masses.  By the law of conservation of translational (linear) momentum, the resulting larger masses had less motion along the direction of the axis defined by the total angular momentum of the collapsing cloud, since the collisions averaged out their more random motions in this direction.  By the law of conservation of energy, the resulting larger masses were heated, since much of the kinetic energy (moving energy) of the colliding particles was converted to thermal energy (heat energy).  By the law of conservation of angular momentum, the resulting larger masses had more circular orbits, since the collisions averaged out their more random orbits, many of which were more elliptical.  In summary, the laws of physics together caused the gravitationally collapsing material to flatten into a circular, rotating disk perpendicular to the axis of the total angular momentum of the forming jovian, gas-giant planet.  This disk is a microcosm of the protoplanetary disk that formed the planets orbiting the Sun.  We will call this smaller disk around a forming jovian, gas-giant planet a protolunar disk, since large-sized moons and even medium-sized moons would eventually form from this flat, circular, rotating disk.  First, small-sized baby moons condensed from the protolunar disk.  As these baby moons orbited the forming planet, they grew larger through accretion, the gaining of mass through sticky collisions.  As the baby moons orbited the forming planet, they collided with material along their orbits, which stuck to the baby moons.  Thus, the baby moons grew larger and larger through accretion until they became so large that their self-gravity became strong enough to force themselves into spherical shapes, thus becoming medium-sized moons and even large-sized moons.  This explains why most of the large-sized and medium-sized moons of the jovian, gas-giant (outer) planets orbit their mother planet in nearly the same plane with roughly circular (but nevertheless slightly elliptical) orbits in the same direction around the planet.  This is also enough to explain why these planets have many moons.  In addition, these jovian, gas-giant (outer) planets are so massive that they can gravitationally capture asteroids that Jupiter rips out of the asteroid belt, as we will discuss shortly.  These captured asteroids become small-sized moons of the planet, explaining why these jovian, gas-giant (outer) planets have dozens of small-sized moons.  The medium-sized moons and certainly the large-sized moons that formed around the jovian planets had sufficient mass and hence sufficiently strong self-gravity to differentiate themselves as they formed, with the most dense metals sinking toward their centers surrounded by a layer of less dense rock.  Most of these large-sized moons and medium-sized moons have icy outer layers that surround the rocky layers.

 

The first of the jovian, gas-giant (outer) planets is Jupiter, the fifth planet from the Sun.  The orbital period of Jupiter around the Sun is roughly twelve Earth years.  Jupiter is the largest planet in the Solar System.  Jupiter is also the most massive planet in the Solar System.  In fact, Jupiter is more massive than the rest of the material in the Solar System combined, excluding the Sun of course.  The Sun is itself one thousand times Jupiter’s mass.  In other words, Jupiter is more massive than the rest of the planets and their moons and the asteroids and the meteoroids and the comets and the dust all combined together.  Stated another way, roughly 99.9% of the mass of the Solar System is the Sun, the remaining 0.1% of the mass of the Solar System is Jupiter, and the rest of the material in the Solar System is insignificant by comparison.  Since Jupiter has tremendous mass, Jupiter exerts tremendous gravity.  Caution: since Jupiter’s mass is one-thousandth of the Sun’s mass, Jupiter’s gravity is still weak as compared with the Sun’s gravity.  The Sun’s gravitational attraction is the one and only one thing that holds the Solar System together.  Nevertheless, Jupiter’s gravity is very strong as compared with the other planets.  Hence, Jupiter exerts sufficiently strong gravity that nearly all perturbative (small but noticeable) gravitational effects in the Solar System are the result of Jupiter’s influence.  For example, Jupiter’s gravity perturbs the orbits of the other planets, causing their orbits to alternate from more elliptical to less elliptical and back again.  In particular, Jupiter’s gravity causes the Earth’s orbit to alternate in eccentricity once every roughly one hundred thousand years causing major glacial periods of the Earth’s Current Ice Age, as we discussed.  Jupiter’s gravity also causes the elliptical orbits of the other planets to turn very slowly.  The slow turning of an elliptical orbit is called orbital precession, which we will discuss again later in the course.  Jupiter’s gravity can also change the orbit of a comet that passes close enough to Jupiter.  Astronomers witnessed a spectacular example of this in the year 1992 when Jupiter’s gravity not only changed the orbit of comet Shoemaker-Levy but also ripped that comet apart into more than twenty comet fragments.  These comet fragments did not have enough energy to escape Jupiter’s gravity.  Thus, all of these comet fragments collided with Jupiter in the year 1994.  Jupiter’s gravity also rips asteroids out of the asteroid belt.  We will discuss the asteroids and the asteroid belt in detail shortly.  For now, most asteroids orbit the Sun in the asteroid belt, which is between the orbit of Mars and the orbit of Jupiter.  Since these asteroids in the asteroid belt are closer to the Sun than Jupiter, their orbital periods around the Sun are shorter than Jupiter’s orbital period around the Sun.  Suppose an asteroid in the asteroid belt has an orbital period around the Sun commensurate with Jupiter’s orbital period, meaning that the ratio of the asteroid’s orbital period to Jupiter’s orbital period is a simple ratio (a simple fraction), such as one-to-two or two-to-five or four-to-seven.  In this case, the asteroid would come near Jupiter at regular intervals.  With each encounter, Jupiter’s gravity would pull on the asteroid.  After many such periodic tugs, Jupiter’s gravity would eventually succeed in ripping the asteroid out of the asteroid belt.  The jovian, gas-giant (outer) planets have sufficiently strong gravity to capture these asteroids that Jupiter rips out of the asteroid belt.  The captured asteroids would thus become small-sized moons of these planets.  This explains why all of the jovian, gas-giant (outer) planets have many small-sized moons.  The terrestrial (inner) planets by contrast have insufficient gravity to capture asteroids that Jupiter rips out of the asteroid belt.  This explains why the terrestrial (inner) planets should have no moons.  Mars is an exception since its orbit is right next to the asteroid belt; this gives Mars a somewhat higher probability of capturing asteroids that Jupiter has ripped out of the asteroid belt.  We have already discussed that the Earth’s Moon is also an exception, since it formed from a violent collision between a planetesimal and the young forming Earth.  If we graph the number of asteroids in the asteroid belt as a function of their orbital periods around the Sun, we see gaps in the graph at the orbital periods where there are no asteroids in the asteroid belt.  Indeed, these gaps in this graph are at orbital periods that are commensurate (simple ratios) with Jupiter’s orbital period.  These gaps are called the Kirkwood gaps, named for the American astronomer Daniel Kirkwood who discovered and correctly explained the origin of these gaps.  There is however a peak in this graph at one simple fraction, the ratio of one-to-one.  If the ratio is one-to-one, these asteroids have the same orbital period around the Sun as Jupiter’s orbital period around the Sun, but this implies that these asteroids orbit the Sun on Jupiter’s own orbit around the Sun.  Indeed, there are two groups of asteroids orbiting the Sun on Jupiter’s own orbit.  These are the Trojan asteroids.  One group of Trojan asteroids orbits the Sun sixty degrees ahead of Jupiter, and the other group of Trojan asteroids orbits the Sun sixty degrees behind Jupiter.  More technically, the Trojan asteroids are locked orbiting the Sun at the fourth and fifth Lagrangian points of the combined gravitational fields of the Sun and Jupiter.

 

Jupiter is the fastest rotating planet in the Solar System, rotating more than twice as fast as planet Earth.  This rapid rotation has caused Jupiter to be severely oblate, as is the case with all the jovian, gas-giant (outer) planets.  Jupiter’s fast rotation also generates a strong magnetic field, as is the case with all the jovian, gas-giant (outer) planets.  In fact, among all the planets, Jupiter generates the strongest magnetic field in the entire Solar System.  Jupiter’s rapid rotation has also divided its atmosphere into many prevailing winds, which appear as cloud bands.  There is a giant storm in Jupiter’s southern hemisphere called the Great Red Spot.  The Great Red Spot is enormous; it is roughly two Earth diameters across and roughly one Earth diameter wide!  The Great Red Spot was discovered through powerful telescopes in the year 1830, but there is evidence that it may have been discovered by smaller telescopes more than a century earlier.  The Great Red Spot seems to have existed for at least as long as telescopes have been powerful enough to observe it, for at least two or perhaps three centuries.  This suggests that giant storms are long-lived phenomena on jovian, gas-giant planets.

 

Jupiter has a weak ring system.  Since its ring system is weak, we will defer a discussion of rings until we discuss Saturn, which has a spectacular ring system.  Jupiter has roughly one hundred moons, but most of them are small-sized moons.  They may have been asteroids that Jupiter itself ripped out of the asteroid belt, and then Jupiter itself captured them gravitationally.  However, four of Jupiter’s moons are enormous as compared with the other one hundred.  These four moons are so enormous that Galileo Galilei discovered them through his primitive telescope more than four hundred years ago.  Hence, they are called the Galilean moons in his honor.  The correct order to list the moons of any planet is from closest to the mother planet to furthest from the mother planet, just as the correct order to list the planets is from closest to the Sun to furthest from the Sun.  The four Galilean moons in the correct order from closest to Jupiter are Io, Europa, Ganymede, and Callisto furthest from Jupiter.  These four Galilean moons are named for various lovers of the ancient mythological god Jupiter (Zeus).  All four of these moons are tidally locked to Jupiter, meaning that their rotational periods are equal to their orbital periods.  Hence, they always face the same side towards Jupiter as they orbit Jupiter.  All four of these moons have sufficient mass and therefore sufficiently strong self-gravity to have differentiated themselves when they formed.  Hence, all four of these moons have a metallic core surrounded by less dense rock.  Most of them, with Io being the exception, have even less dense icy outer layers surrounding the rocky layers.  All four of these moons orbit Jupiter in nearly the same plane.  All four of these moons orbit Jupiter in the same direction, counterclockwise if observed from above the plane of the Solar System.  All four of these moons rotate in that same direction as they orbit Jupiter in that same direction.  Jupiter itself rotates in that same direction.  We see that the Jovian System is a microcosm of the entire Solar System.  In this analogy, Jupiter itself is analogous to the Sun, and Jupiter’s large-sized moons are analogous to the planets.  As we discussed, this is because these four moons formed from a protolunar disk around Jupiter while Jupiter was first forming, just as the planets formed from a protoplanetary disk around the Sun while the Sun was first forming.  This analogy between the Jovian System and the entire Solar System is even stronger than this however.  Io and Europa are similar to each other, Ganymede and Callisto are similar to each other, and these two subsets of moons are somewhat opposite to each other in character.  This is remarkable; it is as if there are two different categories of moons.  Both inner moons (Io and Europa) are of one category, and both outer moons (Ganymede and Callisto) are of the other category, just as there are two different categories of planets, with all four inner planets (Mercury, Venus, Earth, and Mars) of one category and all four outer planets (Jupiter, Saturn, Uranus, and Neptune) of the other category.  This analogy between the Jovian System and the Solar System is not perfect however.  The four inner planets are similar to one another because they were more subject to the Sun’s intense heat as they were forming, while the four outer planets are similar to one another because they were less subject to the Sun’s intense heat as they were forming.  The key variable that resulted in two different categories of the Galilean moons is not Jupiter’s intense heat but Jupiter’s intense gravity.  The two inner moons (Io and Europa) are similar to each other because they formed closer to Jupiter and hence were more subject to Jupiter’s intense gravity, while the two outer moons (Ganymede and Callisto) are similar to one another because they formed further from Jupiter and hence were less subject to Jupiter’s intense gravity.

 

The large-sized inner moon Io orbits so close to Jupiter that Jupiter’s intense gravity continuously tries to rip Io apart.  Io is large enough with sufficient mass and therefore sufficient self-gravity to hold itself together in a spherical shape however.  Nevertheless, Jupiter’s gravity melts rocks on Io, pulls this molten rock into the interior of Io, and pulls this molten rock out of the interior of Io again.  As a result, Io is the most volcanically active world in the entire Solar System.  There is continuous igneous activity such as lava extrusions and even volcanic eruptions nearly everywhere upon the surface of Io.  There are no impact craters visible anywhere on the surface of Io.  Although asteroids and comets do collide with Io and these impacts do form craters, frequent lava eruptions almost immediately cover these craters.  The mechanism to explain the geologic activity on Io is obviously not plate tectonics; it is the strong gravitational tidal forces from Jupiter.  We will call this mechanism strong tidal heating.  The large-sized inner moon Europa is also more subject to Jupiter’s intense gravity as compared with the outer moons.  However, Europa is somewhat further from Jupiter than Io.  Therefore, Europa is less subject to Jupiter’s gravity as compared with Io, making Europa nowhere nearly as geologically active as Io.  Nevertheless, Jupiter’s gravity has succeeded in fracturing (cracking) the ice that covers Europa.  Some astrophysicists speculate that Jupiter’s gravity has melted some of the ice into liquid water beneath the fractured (cracked) ice that covers Europa.  Moreover, there is evidence that Jupiter’s gravity pushes large slabs of ice that float upon this deeper layer of liquid water, rather like Earth’s moving tectonic plates that float upon the deeper asthenosphere.  There is even evidence of cryovolcanoes on Europa that erupt ice instead of molten rock.  In other words, the Theory of Plate Tectonics may apply to Europa but for giant slabs of floating ice instead of giant slabs of floating rock!  We will use the term weak tidal heating for the mechanism to explain the fractured (cracked) ice that covers Europa, the possible liquid water beneath that fractured (cracked) ice, the possible moving tectonic ice plates floating upon that deeper layer of liquid water, and the possible cryovolcanism on Europa.  If there is liquid water beneath the fractured (cracked) ice that covers Europa, there might be very primitive lifeforms, such as unicellular microorganisms, within that deep liquid water.  This however is unlikely, since Europa is far enough from the Sun that it should be too cold for life to exist.  Nevertheless, if weak tidal heating from Jupiter can provide sufficient heat to melt ice, that weak tidal heating may also provide enough heat to maintain a sufficiently warm temperature for life to exist.

 

The large-sized outer moon Ganymede is much less subject to Jupiter’s gravity as compared with the inner moons.  Hence, Ganymede is geologically dead, rather like planet Mercury and the Earth’s Moon.  Since Ganymede is geologically dead, there is very little geologic activity to remove or cover impact craters resulting from collisions from asteroids and comets.  Hence, Ganymede is heavily cratered, again rather like planet Mercury and the Earth’s Moon.  Ganymede is Jupiter’s largest moon.  In fact, Ganymede is the largest moon in the entire Solar System.  Ganymede is so enormous that it is even larger than planet Mercury!  Hence, it is possible for the moon of one planet to be larger than an entire other planet.  Note however that the mass of Ganymede is significantly less than the mass of planet Mercury.  A larger size and a significantly smaller mass together make Ganymede much less dense than planet Mercury.  Nevertheless, Ganymede is sufficiently large with sufficient mass that it was born with a sufficient amount of radioactive atoms to provide itself with internal energy for geologic processes for a few hundred million years, just like planet Mercury and the Earth’s Moon.  After most of the radioactive atoms decayed and with insufficient tidal heating from Jupiter due to Ganymede’s far distance from Jupiter, Ganymede has been geologically dead for most of its history.  Much of what we have described about Ganymede is similar to planet Mercury and the Earth’s Moon.  In fact, Ganymede actually has an appearance similar to planet Mercury and the Earth’s Moon.  Ganymede has heavily cratered older regions, just like the Earth’s Moon, and Ganymede has sparsely cratered younger regions, just like the Earth’s Moon.  However, unlike planet Mercury and the Earth’s Moon, Ganymede has icy outer layers that surround a deeper layer of rock surrounding a metallic core.  It is these icy outer layers that are heavily cratered.  It is also these icy outer layers that give Ganymede a significantly lower density than planet Mercury.  The large-sized outer moon Callisto is the furthest of the four Galilean moons.  Hence, Callisto is the least subject to Jupiter’s gravity among these four Galilean moons, making Callisto even more geologically dead than Ganymede.  Therefore, Callisto is even more heavily cratered than Ganymede.  Nearly every square kilometer of Callisto is covered with impact craters.  In fact, Callisto is the most heavily cratered world in the entire Solar System.  Callisto has icy outer layers surrounding a deeper layer of rock surrounding a metallic core, similar to Europa and Ganymede.  It is Callisto’s icy outer layers that are heavily cratered, as is the case with Ganymede.

 

The second of the jovian, gas-giant (outer) planets is Saturn, the sixth planet from the Sun.  The orbital period of Saturn around the Sun is roughly thirty Earth years.  Saturn is the second largest planet in the Solar System, second only to Jupiter.  Saturn is the second most massive planet in the Solar System, second only to Jupiter.  Saturn is tenuous (low density) since it is composed of hydrogen gas and helium gas surrounding a deeper layer of volatiles ices surrounding an even deeper layer of rock surrounding a metallic core, as are all of the jovian, gas-giant (outer) planets.  In fact, Saturn is the most tenuous (least dense) planet in the entire Solar System.  The density of Saturn is actually less than the density of liquid water.  Saturn would float in water if we had a bathtub large enough to hold that much water!  Note that the most dense planet in the Solar System happens to be planet Earth.  Saturn suffers from fast rotation, causing Saturn to be severely oblate, as is the case with all the jovian, gas-giant (outer) planets.  Saturn’s fast rotation also generates a strong magnetic field, as is the case with all the jovian, gas-giant (outer) planets.  In fact, among all the planets, Saturn generates the second strongest magnetic field in the entire Solar System, second only to Jupiter.  Saturn’s fast rotation has also divided its atmosphere into many prevailing winds that appear as cloud bands.  Saturn has more than one hundred moons, but these are mostly small-sized moons.  They may have been asteroids that Jupiter’s gravity ripped out of the asteroid belt.  Saturn’s gravity is sufficiently strong that it could have captured these asteroids after Jupiter’s gravity ripped them out of the asteroid belt.  Saturn does have one large-sized moon named Titan and six medium-sized moons.  These seven moons listed in the correct order from closest to Saturn are Mimas, Enceladus, Tethys, Dione, Rhea, Titan, and Iapetus furthest from Saturn.  Again, Titan is the only large-sized moon, while the other six moons are medium-sized moons.  All seven of these moons are tidally-locked to Saturn.  All seven of these moons have sufficient mass and therefore sufficiently strong self-gravity to have differentiated themselves when they formed.  Hence, all seven of these moons have a metallic core surrounded by less dense rock surrounded by even less dense icy outer layers.  All seven of these moons orbit Saturn in nearly the same plane.  All seven of these moons orbit Saturn in the same direction.  All seven of these moons rotate in that same direction as they orbit Saturn in that same direction.  Saturn itself also rotates in this same direction.  We see that the Saturnian System is a microcosm of the entire Solar System, with Saturn itself being analogous to the Sun and Saturn’s moons being analogous to the planets.  As we discussed, this is because these seven moons formed from a protolunar disk around Saturn while Saturn was first forming, just as the planets formed from a protoplanetary disk around the Sun while the Sun was first forming.

 

Mimas and Enceladus are medium-sized inner moons of Saturn.  Therefore, these moons are more subject to Saturn’s gravity as compared with the outer moons of Saturn.  In particular, Saturn’s gravity has fractured (cracked) the ice that covers Enceladus.  There is also evidence that Saturn’s gravity has melted some of the ice into liquid water beneath the fractured (cracked) ice that covers Enceladus.  Moreover, there are cryovolcanoes on Enceladus that erupt ice instead of molten rock.  In summary, weak tidal heating from Saturn explains the fractured (cracked) ice that covers Enceladus, the possible liquid water beneath that fractured (cracked) ice, and the cryovolcanism on Enceladus, just as weak tidal heating from Jupiter is responsible for similar processes on Jupiter’s moon Europa.  If there is liquid water beneath the fractured (cracked) ice that covers Enceladus, there might be very primitive lifeforms, such as unicellular microorganisms, within that deep liquid water.  This however is unlikely, since Enceladus is far enough from the Sun that it should be too cold for life to exist.  Nevertheless, if weak tidal heating from Saturn can provide sufficient heat to melt ice, that weak tidal heating may also provide enough heat to maintain a sufficiently warm temperature for life to exist.  Again, we see that Saturn’s moon Enceladus is very much similar to Jupiter’s moon Europa.  The icy outer layers of Enceladus surround a deeper layer of rock surrounding a metallic core, again similar to Europa.  Since Mimas is even closer to Saturn than Enceladus, we expect Mimas to suffer from strong tidal heating from Saturn, making Mimas similar to Jupiter’s moon Io.  However, this is not the case.  Firstly, Mimas has icy outer layers that surround deeper layers of rock surrounding a metallic core, while Io lacks icy outer layers.  Moreover, the ice that covers Mimas is heavily cratered similar to an outer moon, which implies that Mimas is geologically dead as an outer moon should be, not an inner moon.  Astrophysicists continue to debate why Mimas is geologically dead even though it is the innermost medium-sized moon of Saturn.  Mimas has an enormous crater called the Herschel crater, named for the British astronomer William Herschel who discovered Mimas.  The Herschel crater is nearly the size of the entire moon Mimas.  Whatever object collided with Mimas to form the Herschel crater would have completely obliterated this moon if that object had been moving just a little bit faster or if that object had been somewhat more massive.  Therefore, the Herschel crater on Mimas reveals that collisions can occur in the Solar System that are powerful enough to obliterate medium-sized moons and certainly small-sized moons.  The Herschel crater gives Mimas the appearance of the Death Star from the Star Wars mythology.  Mimas is also roughly the size of the Death Star from the Star Wars mythology.  Therefore, the nickname of Mimas is the Death Star Moon, and the nickname of the Herschel crater is Darth Crater, a fanciful name based upon one of the most popular characters from the Star Wars mythology, Darth Vader.

 

Tethys, Dione, and Rhea are medium-sized outer moons of Saturn.  Therefore, these moons are less subject to Saturn’s gravity as compared with Mimas and Enceladus, making Tethys, Dione, and Rhea geologically dead moons.  Hence, there is very little geologic activity on these moons to remove or cover impact craters resulting from collisions from asteroids and comets.  Therefore, Tethys, Dione, and Rhea are heavily cratered.  In fact, Tethys has an enormous crater called the Odysseus crater that is nearly the size of the entire moon Tethys.  Whatever object collided with Tethys to form the Odysseus crater may have completely obliterated this moon if that object had been moving just a little bit faster or if that object had been somewhat more massive.  Just as the Herschel crater on Mimas reveals that collisions can occur in the Solar System that are powerful enough to obliterate medium-sized moons and certainly small-sized moons, the Odysseus crater on Tethys is further evidence that collisions can occur in the Solar System that are powerful enough to obliterate medium-sized moons and small-sized moons.  Tethys, Dione, and Rhea have icy outer layers that surround a deeper layer of rock surrounding a metallic core.  It is these icy outer layers that are heavily cratered.

 

Titan is Saturn’s only large-sized moon.  This is an appropriate name for Saturn’s largest moon, since the ancient mythological figure Saturn (Kronos) was the youngest of the mythical titans.  Titan is the second-largest moon in the entire Solar System, second only to Ganymede (Jupiter’s largest moon).  In fact, Titan is so enormous that it is even larger than planet Mercury!  Again, we see that the moon of one planet can be even larger than an entire other planet.  Note however that the mass of Titan is significantly less than the mass of planet Mercury.  A larger size and a significantly smaller mass together make Titan much less dense than planet Mercury.  Titan has the most substantial atmosphere out of all the moons in the entire Solar System, but Titan’s atmosphere is not habitable for life.  Although Titan’s atmosphere is mostly nitrogen like Earth’s atmosphere, Titan’s atmosphere also has an abundance of volatile ices and virtually no oxygen.  Also, Titan is so distant from the Sun that the temperature is too cold to sustain life.  Titan’s atmosphere surrounds its icy surface which surrounds a deeper layer of rock surrounding a metallic core.

 

Iapetus is the outermost medium-sized moon of Saturn.  Therefore, Iapetus is much less subject to Saturn’s gravity as compared with inner moons, making Iapetus a geologically dead moon.  Hence, there is very little geologic activity on Iapetus to remove or cover impact craters resulting from asteroid impacts and comet impacts.  Therefore, Iapetus is heavily cratered.  Iapetus has icy outer layers surrounding a deeper layer of rock surrounding a metallic core.  It is the icy outer layers of Iapetus that are heavily cratered.  Iapetus has the most severe difference in color between its two hemispheres than any other object in the Solar System.  In particular, the near side of Iapetus (the hemisphere that always faces toward Saturn) is very dark in color, while the far side of Iapetus (the hemisphere that always faces away from Saturn) is very light in color.  Moreover, Iapetus has a steep ridge along its equator.  Astrophysicists continue to debate why Iapetus has such an extreme difference in color between its two hemispheres and why it has such a steep ridge along its equator.

 

All four of the jovian, gas-giant (outer) planets, Jupiter, Saturn, Uranus, and Neptune, have rings.  However only Saturn has a spectacular ring system.  Jupiter, Uranus, and Neptune have weak ring systems.  Through a small telescope, Saturn’s rings appear to be solid.  However, through a more powerful telescope, a large gap is visible in the rings called the Cassini division.  Using an even more powerful telescope, we discover more gaps within the rings, such as the Colombo gap, the Maxwell gap, the Huygens gap, the Encke gap, and the Keeler gap.  Through an even more powerful telescope, we see so many gaps that we realize that the rings are not solid at all.  Saturn’s rings are actually composed of thousands of individual ringlets.  The ringlets themselves are not solid.  The entire ring system is actually billions of individual chunks of metal, rock, and volatile ices, and each chunk is on its own orbit around Saturn in accord with Kepler’s laws.  The light from all these billions of chunks of metal, rock, and volatile ices blends together, causing the rings to appear to be solid from the Earth through a small telescope.  If we interpret each of these chunks of metal, rock, and volatile ices as a moon (they orbit Saturn after all), then Saturn actually has billions of moons!  The rings are thousands of kilometers across, but the rings are also extremely thin, less than one kilometer thick!  Saturn’s rings are so thin that they seem to disappear when we happen to be looking at the rings edge on.  The rings of all the jovian, gas-giant planets are caused by their own intense gravity.  When any object such as an asteroid or a comet or even one of its own moons ventures too close to the planet, the planet’s gravity rips the object apart into many small fragments.  The fragments remain in orbit around the planet, becoming rings.  Indeed, Saturn’s rings are closer to Saturn than any of its seven medium-to-large-sized moons, implying that if an object of such size were to approach Saturn closer, the object would be ripped apart by Saturn’s gravity and become part of Saturn’s ring system.  The closest distance that a small object of a given size can approach a large gravitating object before being torn apart by the gravity of the large object is called the Roche limit, named for the French astrophysicist Édouard Roche who first performed this calculation.  Saturn’s rings are closer to Saturn than the Roche limit of medium-to-large-sized moons.  This also explains why all the jovian, gas-giant (outer) planets have rings, while none of the terrestrial (inner) planets have rings.  The jovian, gas-giant (outer) planets are large with more mass and therefore strong gravity as compared with the terrestrial (inner) planets.  Therefore, jovian, gas-giant planets can capture objects that they can rip apart to form rings.  The terrestrial (inner) planets are small with less mass and therefore weak gravity as compared with the jovian, gas-giant (outer) planets.  Therefore, terrestrial planets are much less likely to capture objects that they would be able to rip apart to form rings.  The rings of gas-giant planets are thin and circular for the same reason the protoplanetary disk and protolunar disks are thin and circular.  Various laws of physics together caused orbiting material to flatten into a thin, circular, rotating disk perpendicular to the axis of the total angular momentum of the planet.  Over time, fragments within rings continue to collide with each other.  The collisions cause the fragments to lose orbital speed.  This in turn causes the fragments to approach the planet and to eventually collide with the planet.  As a result, a spectacular ring system such as Saturn’s rings only lasts a few hundred million years.  All of the jovian, gas-giant planets have had weak rings for most of the history of the Solar System, including Saturn.  On rare occasions, a jovian, gas-giant planet happens to capture and rip apart a large number of asteroids and comets over a period of a few hundred million years, resulting in a spectacular ring system.  During some eras in the history of the Solar System, perhaps Jupiter had a spectacular ring system while the other three gas-giant planets, including Saturn, had weak ring systems.  During other eras in the history of the Solar System, perhaps Uranus had a spectacular ring system while the other three gas-giant planets, including Saturn, had weak ring systems.  We happen to be alive when Saturn happens to have a spectacular ring system, while the other three gas-giant planets have weak ring systems.  As we will discuss shortly, Neptune will have a spectacular ring system a few hundred million years from now, while the other three gas-giant planets, including Saturn, will have weak ring systems.  Although it is possible for more than one gas-giant planet in the Solar System to have spectacular ring systems at the same time, this is sufficiently improbable that it most likely never occurred.

 

What causes the gaps within Saturn’s rings?  If we use Kepler’s third law to determine the orbital period around Saturn of a hypothetical object in the Cassini division, we calculate that the object would have an orbital period around Saturn exactly half the orbital period of Mimas, one of Saturn’s medium-sized moons.  Before the Cassini division existed, certain chunks of metal, rock, and volatile ices within Saturn’s rings encountered Mimas at regular intervals.  The gravity of Mimas tugged on these bodies regularly with each encounter.  Eventually, the gravity of Mimas ripped these bodies out of the ring system, leaving the Cassini division within the rings.  The other ring gaps formed similarly, from gravitational encounters from other moons of Saturn.  This is precisely the same mechanism that caused the Kirkwood gaps within the asteroid belt.  This mechanism is important enough to deserve a name: orbital resonance.  The Kirkwood gaps are caused by orbital resonances with Jupiter, the Cassini division is caused by orbital resonances with Mimas, and the other gaps within Saturn’s rings are caused by orbital resonances with other moons of Saturn.  If the Saturnian System is analogous to the entire Solar System, then Saturn’s rings would be analogous to the asteroid belt, and all of the ring gaps would be analogous to the Kirkwood gaps.

 

The two small-sized moons Telesto and Calypso orbit Saturn on the same orbit as the medium-sized moon Tethys.  Telesto orbits Saturn sixty degrees ahead of Tethys, while Calypso orbits Saturn sixty degrees behind Tethys.  Telesto and Calypso are locked orbiting Saturn at the fourth and fifth Lagrangian points of the combined gravitational fields of Saturn and Tethys.  The two small-sized moons Helene and Polydeuces orbit Saturn on the same orbit as the medium-sized moon Dione.  Helene orbits Saturn sixty degrees ahead of Dione, while Polydeuces orbits Saturn sixty degrees behind Dione.  Helene and Polydeuces are locked orbiting Saturn at the fourth and fifth Lagrangian points of the combined gravitational fields of Saturn and Dione.  These small-sized moons are beautifully analogous to the Trojan asteroids orbiting the Sun on Jupiter’s own orbit.  Therefore, we will call the small-sized moons Telesto, Calypso, Helene, and Polydeuces the Trojan moons of Saturn.  To summarize, the Saturnian System is a microcosm of the entire Solar System.  In this analogy, Saturn itself is analogous to the Sun, Saturn’s moons are analogous to the planets, Saturn’s rings are analogous to the asteroid belt, the ring gaps are analogous to the Kirkwood gaps, and the Trojan moons of Saturn are analogous to the Trojan asteroids.

 

All four of the jovian, gas-giant (outer) planets, Jupiter, Saturn, Uranus, and Neptune, all share several physical properties.  They are all large as compared with the terrestrial (inner) planets.  They are all tenuous, being composed of hydrogen gas and helium gas surrounding a deeper layer of volatiles ices surrounding an even deeper layer of rock surrounding a metallic core.  They all have many moons.  They all have rings.  They all suffer from fast rotation, generating strong magnetic fields and causing them to be severely oblate.  However, there are significant differences among these planets, compelling us to subdivide the jovian, gas-giant planet category into two subcategories.  Jupiter and Saturn are in one subcategory, while Uranus and Neptune are in the other subcategory.  Uranus and Neptune are composed of significantly less outer layers of hydrogen gas and helium gas as compared with Jupiter and Saturn.  As a result, deeper layers of volatile ices are more exposed with Uranus and Neptune as compared with Jupiter and Saturn.  The exposed volatile ices give Uranus and Neptune exotic colors: greenish for Uranus and bluish for Neptune.  Some astrophysicists go so far as to claim that only Jupiter and Saturn are truly gas-giant planets.  These astrophysicists place Uranus and Neptune in a different category: ice-giant planets.  We will not adopt this extreme interpretation.  We will regard all four of the outer planets as gas-giant planets.  We will regard Jupiter and Saturn as one type of gas-giant planet, and we will regard Uranus and Neptune as another type of gas-giant planet.  Astrophysicists continue to debate why Uranus and Neptune are composed of significantly less outer layers of hydrogen gas and helium gas as compared with Jupiter and Saturn.

 

The third of the jovian, gas-giant (outer) planets is Uranus, the seventh planet from the Sun.  The orbital period of Uranus around the Sun is roughly eighty-four Earth years.  Uranus is tenuous (low density), being composed of hydrogen gas and helium gas surrounding a deeper layer of volatiles ices surrounding an even deeper layer of rock surrounding a metallic core.  However, Uranus has less outer layers of hydrogen gas and helium gas as compared with Jupiter and Saturn.  As a result, deeper layers of volatile ices are exposed, giving Uranus a greenish color.  Although Uranus is slightly larger in size than Neptune, the mass of Uranus is slightly less than the mass of Neptune.  A slightly larger size and a slightly smaller mass together make Uranus noticeably less dense than Neptune.  Uranus has a weak ring system and more than two dozen moons.  Most of the moons of Uranus are small-sized moons.  They may have been asteroids that Jupiter’s gravity ripped out of the asteroid belt.  Uranus has sufficient gravity to capture them after Jupiter ripped them out of the asteroid belt.  Although Uranus does not have any large-sized moons, Uranus does have five medium-sized moons.  All five of these moons are tidally locked to Uranus.  All five of these moons have sufficient mass and therefore sufficiently strong self-gravity to have differentiated themselves when they formed.  Hence, all five of these moons have a metallic core surrounded by less dense rock surrounded by even less dense icy outer layers.  All five of these moons orbit Uranus in nearly the same plane.  All five of these moons orbit Uranus in the same direction and rotate in that same direction as they orbit Uranus.  Uranus itself rotates in that same direction.  We see that the Uranian System is a microcosm of the entire Solar System, with Uranus itself being analogous to the Sun, the moons of Uranus being analogous to the planets, and the rings of Uranus being analogous to the asteroid belt.  As we discussed, this is because these five moons formed from a protolunar disk around Uranus while Uranus was first forming, just as the planets formed from a protoplanetary disk around the Sun while the Sun was first forming.  These five moons listed in the correct order from closest to Uranus are Miranda, Ariel, Umbriel, Titania, and Oberon furthest from Uranus.  The largest of these five moons is Titania, although Titania is still a medium-sized moon.  Most of the moons of Uranus, both medium-sized and small-sized, are named for fictional characters from the plays of William Shakespeare, the greatest writer of the English language.

 

Miranda and Ariel are medium-sized inner moons of Uranus.  Therefore, these two moons are more subject to the gravity of Uranus as compared with the outer moons of Uranus.  Since Miranda is the innermost medium-sized moon of Uranus, Miranda is therefore the most subject to the gravity of Uranus as compared with the other medium-sized moons of Uranus.  The gravitational forces from Uranus are so strong that the icy outer layers of Miranda are severely fractured with countless canyons, scarps (steep cliffs), and ridges.  In fact, the tallest cliff in the entire Solar System, named Verona Rupes, is on Miranda.  Verona Rupes is roughly twenty kilometers high!  If a cliff of this height were on Earth, it would take roughly one minute to fall from the top to the bottom of that cliff, hitting the ground at more than two thousand kilometers per hour.  However, since Miranda is only a medium-sized moon, its surface gravity is more than one hundred times weaker than the Earth’s surface gravity.  As a result, it would take roughly twelve minutes to fall from the top to the bottom of Verona Rupes, hitting the icy surface of Miranda at only two hundred kilometers per hour!  The severe fracturing of the icy outer layers of Miranda is also caused by cryovolcanism, which is itself also caused by the strong gravitational forces from Uranus.  In summary, strong tidal heating from Uranus is responsible for the severe fracturing of the icy outer layers of Miranda and the cryovolcanism on Miranda.  The fracturing of the icy outer layers of Miranda is so severe that astronomers formerly believed that a violent collision shattered Miranda into many pieces which then accreted back together to recreate Miranda.  However, this violent collision model has been replaced by the modern strong tidal heating model to explain the severe fracturing of the icy outer layers of Miranda.  The medium-sized inner moon Ariel is also more subject to the gravity of Uranus as compared with the outer moons of Uranus.  However, Ariel is somewhat further from Uranus than Miranda.  Therefore, Ariel is less subject to the gravity of Uranus as compared with Miranda, making the surface of Ariel nowhere nearly as fractured as the surface of Miranda.  Nevertheless, the gravity of Uranus has succeeded in fracturing the icy outer layers of Ariel.  There is an abundance of canyons, scarps (steep cliffs), and ridges throughout the icy outer layers of Ariel.  There is even evidence of cryovolcanism on Ariel.  In summary, weak tidal heating from Uranus causes the fracturing of the icy outer layers of Ariel and the cryovolcanism on Ariel, just as the large-sized moon Europa suffers from weak tidal heating from Jupiter and the medium-sized moon Enceladus suffers from weak tidal heating from Saturn.

 

Umbriel, Titania, and Oberon are medium-sized outer moons of Uranus.  Therefore, these three moons are less subject to the gravity of Uranus as compared with Miranda and Ariel, making Umbriel, Titania, and Oberon geologically dead moons.  Hence, there is very little geologic activity on these three moons to remove or cover impact craters resulting from collisions from asteroids and comets.  Therefore, the icy outer layers of Umbriel, Titania, and Oberon are heavily cratered.  As we would expect, we find little fracturing of the icy outer layers of these three moons that would have been caused by tidal heating from Uranus.  Hence, we find few canyons, few scarps (steep cliffs), and few ridges within the icy outer layers of Umbriel, Titania, and Oberon.  As we would also expect, we find little evidence of cryovolcanism on these three moons.  Since Oberon is the outermost medium-sized moon of Uranus, Oberon is therefore the least subject to the gravity of Uranus as compared with the other medium-sized moons of Uranus, making Oberon the most geologically dead medium-sized moon of Uranus.  As we would expect, Oberon is the most heavily cratered moon of Uranus with the least amount of cryovolcanism and the least number of canyons, scarps (steep cliffs), and ridges.

 

Uranus has an obliquity (axial tilt) that is slightly greater than ninety degrees.  If the obliquity were ninety degrees, we would say that Uranus rotates on its side.  Since the obliquity is slightly greater than ninety degrees, Uranus rotates mostly on its side and in the opposite direction from its orbital motion around the Sun.  Uranus and Venus are the only two planets in the Solar System that rotate in the opposite direction of the planet’s orbital motion around the Sun.  Warning: all eight planets, including Venus and Uranus, orbit the Sun in the same direction.  More plainly, Venus and Uranus orbit the Sun in the same direction as all the other planets while rotating in the opposite direction of their orbital motion around the Sun.  Since Uranus rotates mostly on its side, its northern hemisphere and its southern hemisphere are mostly within its orbital plane instead of mostly above and below its orbital plane, as is the case with all the other planets in the Solar System.  Consequently, Uranus experiences the most extreme seasonal variations among all the planets in the Solar System.  For roughly forty-two Earth years (half of its orbital period around the Sun), Uranus’s northern hemisphere experiences nearly continuous daytime while Uranus’s southern hemisphere experiences nearly continuous nighttime.  During the other half of its orbit (also roughly forty-two Earth years), Uranus’s northern hemisphere experiences nearly continuous nighttime while Uranus’s southern hemisphere experiences nearly continuous daytime.  The strange obliquity of Uranus may have been caused by a violent impact.  Presumably, Uranus had a more reasonable obliquity before the violent impact, but the impact was so violent that the rotational axis of Uranus was tipped sideways.  Further evidence that this severe obliquity was caused by a violent impact is Uranus’s strange magnetic field.  Uranus suffers from fast rotation, generating a strong magnetic field, as is the case with all the jovian, gas-giant (outer) planets.  However, the magnetic poles of Uranus are severely displaced from its rotational poles.  The magnetic center of Uranus is also severely displaced from its gravitational center.  Presumably, Uranus generated a more reasonable magnetic field before the violent impact, with magnetic poles that were reasonably close to its rotational poles and a magnetic center reasonably close to its gravitational center.  The violent impact gave Uranus a mostly sideward rotation, rotational poles severely displaced from its magnetic poles, and a gravitational center severely displaced from its magnetic center.

 

It seems that nearly every unexpected deviation from dominant patterns in the Solar System was caused by a violent collision.  For example, a violent collision explains why Mercury is the smallest of the eight planets of the Solar System, explains why Mercury has an unusually large metallic core as compared with its present overall size, and explains the abundance of scarps (steep cliffs) throughout the surface of Mercury.  As another example, a violent collision explains the existence of the Earth’s unusually large Moon, explains why the composition of the Earth’s Moon is similar to the composition of the outer layers of the Earth, and explains why the Earth’s Moon has an unusually small metallic core as compared with its overall size.  As yet another example, a violent collision explains the enormous Herschel crater on the Saturnian moon Mimas and the enormous Odysseus crater on the Saturnian moon Tethys, thus revealing that collisions can occur in the Solar System that are powerful enough to obliterate medium-sized moons and certainly small-sized moons.  As a fourth example, a violent collision gave Uranus a mostly sideward rotation, gave Uranus rotational poles severely displaced from its magnetic poles, and gave Uranus a gravitational center severely displaced from its magnetic center.

 

The fourth and last of the jovian, gas-giant (outer) planets is Neptune, the eighth and final planet from the Sun.  The orbital period of Neptune around the Sun is roughly one hundred and sixty-five Earth years.  Neptune is tenuous (low density), being composed of hydrogen gas and helium gas surrounding a deeper layer of volatiles ices surrounding an even deeper layer of rock surrounding a metallic core.  With less outer layers of hydrogen gas and helium gas, deeper layers of volatile ices are exposed, giving Neptune a bluish color.  Although Neptune is slightly smaller in size than Uranus, the mass of Neptune is slightly greater than the mass of Uranus.  A slightly smaller size and a slightly greater mass together make Neptune noticeably more dense than Uranus.  Neptune suffers from fast rotation, causing it to be severely oblate, as is the case with all the jovian, gas-giant (outer) planets.  Neptune’s fast rotation also generates a strong magnetic field, as is the case with all the jovian, gas-giant (outer) planets.  Neptune’s fast rotation has also divided its atmosphere into many prevailing winds that appear as cloud bands.

 

Neptune has a weak ring system and more than one dozen moons.  Most of the moons of Neptune are small-sized moons, but Neptune does have one large-sized moon named Triton and two medium-sized moons.  These three moons listed in the correct order from closest to Neptune are Proteus, Triton, and Nereid furthest from Neptune.  Again, Triton is the only large-sized moon, while the other two moons are medium-sized moons.  Since Proteus is a medium-sized moon, it should have sufficient mass and therefore sufficient self-gravity to force itself into a spherical shape.  However, Proteus is highly non-spherical in shape.  In fact, Proteus is the largest non-spherical object in the entire Solar System.  Triton is the only large-sized moon of Neptune.  Triton is the only large-sized moon in the entire Solar System that orbits its mother planet in the opposite direction as its mother planet’s rotation.  This implies that Triton could be a captured moon.  Perhaps Triton was formerly a short-period comet orbiting the Sun within the neighboring Kuiper belt, which we will discuss shortly.  Perhaps Triton’s previous orbit around the Sun brought it too close to Neptune on one occasion.  Since Neptune is a jovian, gas-giant planet, it had sufficient gravity to capture Triton, turning Triton from a short-period comet orbiting the Sun within the Kuiper belt to Neptune’s only large-sized moon.  The medium-sized moon Nereid has the most severely elliptical orbit among all the medium-to-large-sized moons in the entire Solar System.  Also, Nereid is the only medium-sized moon in the Solar System that is not tidally locked to its mother planet.  In other words, the rotational period of Nereid is not equal to its orbital period around Neptune.  Both Proteus and Triton are tidally locked to Neptune however.  Just as the Earth’s Moon is slowing down the Earth’s rotation, Triton is slowing down Neptune’s rotation.  This lost rotational angular momentum is transferred back to Triton, just as the Earth’s lost rotational angular momentum is transferred back to the Earth’s Moon.  The angular momentum transfer from the Earth to its Moon causes its Moon to drift further and further from the Earth, as we discussed.  There is also an angular momentum transfer from Neptune to Triton.  However, Triton orbits Neptune in the opposite direction as Neptune’s rotation.  Thus, instead of drifting away from Neptune, Triton is instead drifting toward Neptune.  In a few hundred million years, Triton will approach its Roche limit from Neptune, and hence Neptune’s gravity will rip Triton apart into billions of individual chunks of metal, rock, and volatile ices.  Triton is sufficiently large that when it is eventually ripped apart, Neptune will have a spectacular ring system like Saturn’s rings.  A few hundred million years from now, it will be Neptune with a spectacular ring system while the other three gas-giant planets, including Saturn, will have weak ring systems.

 

In the 1970s, NASA launched two probes to study the jovian, gas-giant (outer) planets.  These probes were named Voyager 1 and Voyager 2.  These probes revolutionized our understanding of the jovian, gas-giant (outer) planets.  For example, these two probes discovered dozens of moons around all four of these planets and discovered the weak ring systems around Jupiter, Uranus, and Neptune.  The Voyager 2 probe flew by Neptune in the year 1989 and discovered a giant storm storm on Neptune beautifully analogous to the Great Red Spot on Jupiter.  Astronomers named this giant storm on Neptune the Great Dark Spot.  Many astrophysicists believed that the Great Dark Spot served as strong evidence that giant storms are long-lived phenomena on jovian, gas-giant planets.  However, recent telescopic observations of Neptune have not found the Great Dark Spot.  This giant storm seems to have ended.  Therefore, the Great Dark Spot seems to serve as evidence that giant storms on jovian, gas-giant planets are temporary, not long-lived.  Astrophysicists continue to debate the nature of giant storms on jovian, gas-giant planets, with the Great Red Spot on Jupiter being evidence in favor of their longevity and with the Great Dark Spot formerly on Neptune being evidence against their longevity.

 

 

The Minor Objects of the Solar System

 

By far, the most important member of the Solar System is the Sun, but during this survey of the Solar System we are for the most part ignoring the Sun.  We will study the Sun in tremendous detail, but in the context of it being a star, not in the context of it being a member of the Solar System.  If we are for the most part ignoring the Sun and if we have completed a discussion of the eight planets and their moons and rings, then what remains to be discussed is the minor objects of the Solar System.  The minor objects of the Solar System are the asteroids, the meteoroids, the comets, and the dust.  Most of these minor objects are not spherically shaped.  At sizes larger than roughly four hundred kilometers in diameter, most objects have enough mass and therefore strong enough self-gravity to force themselves into spherical shapes.  This is why the Sun, all eight planets, all the large-sized moons of the Solar System, and most of the medium-sized moons of the Solar System are nearly spherically shaped.  However, small-sized moons, most asteroids, all meteoroids, and most comets are smaller than roughly four hundred kilometers in diameter.  Thus, small-sized moons, most asteroids, all meteoroids, and most comets are irregularly shaped.  This argument also applies to even smaller objects, such as mountains, houses, cars, tables, chairs, and mobile telephones.  These objects are so small with so little mass that they have insufficient self-gravity to force themselves into spherical shapes.  (Although baseballs and some humans are spherically shaped, they are spherical for reasons different from self-gravity.)  Dust particles, molecules, and atoms have such minuscule self-gravity that they are not spherical as well.

 

Our provisional definition of an asteroid is a small chunk of metal and rock orbiting the Sun.  However, this definition is not satisfactory.  Aren’t the inner planets small chunks of metal and rock orbiting the Sun?  By this definition, Mercury, Venus, Earth, and Mars would be considered asteroids.  We could refine our provisional definition by claiming that an asteroid is a very small chunk of metal and rock orbiting the Sun.  Although this is a better definition, we will reveal the true definition of an asteroid shortly.  Most asteroids are irregularly shaped, since they are small with insufficient mass and hence insufficient self-gravity to force themselves into spherical shapes.  Most asteroids orbit the Sun within the asteroid belt between the orbit of Mars and the orbit of Jupiter.  The asteroid belt should have been the orbit of a fifth terrestrial planet after Mars.  However, Jupiter is so massive with such intense gravity that it perturbed the metallic and rocky planetesimals at that orbit, ripping many planetesimals out of that orbit and even preventing the remaining planetesimals from accreting together to form a fifth terrestrial planet.  This reveals the true definition of an asteroid.  An asteroid is defined as a metallic and rocky planetesimal leftover from the formation of the Solar System.  Presumably, the total mass of the asteroid belt was once equal to that of a terrestrial planet, but Jupiter’s gravity has ripped the overwhelming majority of the planetesimals out of the original asteroid belt.  Today, the total mass of all the asteroids in the asteroid belt combined together is barely equal to that of a single large-sized moon.  Many asteroids that Jupiter ripped out the asteroid belt collided with forming planets during the heavy bombardment period of the young Solar System.  Jupiter’s gravity continues to rip asteroids out of the asteroid belt today through orbital resonances, as we discussed.  Many of these asteroids have been captured by the jovian, gas-giant (outer) planets and in addition Mars to become small-sized moons.  Some asteroids are actually orbiting the Sun on Jupiter’s orbit; these are the Trojan asteroids.  Some asteroids orbit the Sun on random orbits outside of the asteroid belt.  Some of the orbits of these asteroids intersect the Earth’s orbit around the Sun.  Therefore, an asteroid could collide with the Earth.  If an asteroid were to collide with the Earth, the collision would unleash roughly one thousand times the combined nuclear arsenal of the entire world!  This much liberated energy would completely obliterate all life at and near the point of impact.  In addition, this much energy would shatter the asteroid into innumerable extremely hot fragments that would shoot outward from the point of impact and then rain back downward, igniting global forest fires and heating most of the Earth’s atmosphere to inhospitable temperatures, eradicating life over an even larger area.  Most significantly, this much energy would pulverize rock at the point of impact into dust and ash, and the force of the collision would eject that dust and ash into the atmosphere, surrounding the entire planet and blocking most sunlight for several months, perhaps even a couple of years.  Without sunlight, most plants would die, since plants require the energy of sunlight to synthesize their own food (photosynthesis).  Most herbivorous animals would then die, since herbivores eat plants.  Most carnivorous animals would then die, since carnivores eat herbivores.  The result is an extinction level event, when most of the organisms across the entire planet suddenly become extinct.  The most recent extinction level event was roughly sixty-six million years ago when most of the organisms on planet Earth suddenly became extinct, including the dinosaurs.  In the 1970s, a crater was discovered in Yucatán in Mexico, named the Chicxulub crater.  This crater is roughly the correct size that would be caused by an asteroid impact.  The Chicxulub crater is also the correct age, having formed at the rock layer that is roughly sixty-six million years old.  Finally, this rock layer is rich in dense elemental metals such as iridium and osmium that are less abundant on the surface of the Earth but more abundant in asteroids.  Therefore, the extinction level event that occurred roughly sixty-six million years ago that caused most life on Earth to suddenly become extinct, including the dinosaurs, was definitely caused by an asteroid impact in Yucatán in modern-day Mexico.

 

A meteoroid is an extremely small chunk of metal and rock orbiting the Sun.  Meteoroids come from asteroids.  When two asteroids happen to collide with each other, they chip pieces off of each other.  These chipped pieces of asteroids are meteoroids.  These meteoroids fill the entire Solar System, and countless meteoroids continuously fall toward all planets and moons.  Millions of meteoroids fall toward planet Earth every day.  Most of them completely burn up in Earth’s atmosphere as they fall toward Earth.  While the chunk of metal and rock is in outer space, it is called a meteoroid, but while burning in Earth’s atmosphere, the chunk of metal and rock is called a meteor.  It is also called a falling star or a shooting star, since it appears to be as bright as a star while falling from the sky.  We can see some meteors (falling stars or shooting stars) every day of the year.  On any given night that is not cloudy, we can see meteors (falling stars or shooting stars) if we stare continuously up at the night sky over the course of a few hours.  A large number of meteors (falling stars or shooting stars) over the course of a few nights is called a meteor shower, which we will discuss shortly.  If the original meteoroid was large enough, it may survive the burning as a meteor (falling star or shooting star) and then crash into the Earth.  This is called a meteorite.  Meteorites crash into the Earth rather often, but most fall into the ocean since the Earth is mostly covered with water.  Although houses and cars have been damaged by meteorites falling from the sky, no human being has ever been killed by a meteorite falling from the sky.  The largest meteorite in captivity in the entire world is at the American Museum of Natural History in New York City.  To summarize, an extremely small chunk of metal and rock in outer space is called a meteoroid, while it burns in the Earth’s atmosphere as it falls toward the Earth it is called a meteor (or falling star or shooting star), and if it crashes into the Earth it is called a meteorite.  Why should we use three different terms for the same chunk of metal and rock?  In fact, different names are often used for the same thing in colloquial languages.  While they are living animals, chickens, turkeys, and ducks are called fowl, but after they have been slaughtered and prepared as food they are called poultry.  While they are living animals, bulls and cows are called cattle, but after they have been slaughtered and prepared as food they are called beef.  While they are living animals, pigs are called swine, but after they have been slaughtered and prepared as food they are called pork.  While they are living animals, deer, elk, moose, and reindeer are called cervids, but after they have been slaughtered and prepared as food they are called venison.  The Spanish word for living fish is pez, but the Spanish word for fish that is slaughtered and prepared as food is pescado.  There are countless other examples in colloquial languages.  As a technical example, molten rock deep within the Earth is called magma, but molten rock that has extruded out of the Earth is called lava.

 

As we discussed, volatile ices in addition to metal and rock were able to condense beyond the frost line of the protoplanetary disk of the young Solar System.  These planetesimals differentiated themselves, with the most dense metals sinking toward their centers, the least dense volatile ices rising toward their surfaces, and moderately dense rock settling in the intermediate layer between the metallic core and the icy outer layers.  Many of these icy planetesimals accreted together to form the four jovian, gas-giant planets Jupiter, Saturn, Uranus, and Neptune.  These planets are so massive with such intense gravity that they perturbed all the remaining icy planetesimals in the outer Solar System that had not yet accreted together.  In many cases, the gas-giant planets, particularly Jupiter, flung icy planetesimals in random directions out to enormous distances from the Sun, almost ejecting them entirely from the Solar System.  In other cases, the gas-giant planets, particularly Jupiter, prevented the remaining icy planetesimals from accreting together to form a fifth jovian planet.  In either case, there remains to the present day millions of these icy planetesimals orbiting the Sun.  These are comets, icy planetesimals leftover from the formation of the Solar System.  Note however that it is the outer layers of a comet that are volatile ices.  Beneath these volatile ices is higher density rock, and the core of a comet is very dense metal.  As a result, most comets are larger than most asteroids, since asteroids are metallic and rocky planetesimals leftover from the formation of the Solar System that formed closer to the Sun than the frost line where volatile ices could not condense.  Although most comets are larger than most asteroids, most comets are nevertheless not spherically shaped, since they have such little mass and therefore such weak self-gravity that they cannot force themselves into spherical shapes.  Hence, most comets are irregularly shaped, just as most asteroids are irregularly shaped.

 

We divide comets into two categories: short-period comets and long-period comets.  Short-period comets take a short amount of time to orbit the Sun, between a few decades and a few centuries.  The most famous comet, the Halley comet, is certainly a short-period comet since it has an orbital period around the Sun of seventy-six years.  The orbits of short-period comets are more or less within the plane of the Solar System, although the orbits of some short-period comets have somewhat significant inclinations with the plane of the Solar System.  Most short-period comets orbit the Sun in the Kuiper belt, a belt of comets mostly in the plane of the Solar System just beyond Neptune’s orbit.  The Kuiper belt is named for the Dutch astronomer Gerard Kuiper who theorized that there should be comets orbiting the Sun beyond Neptune’s orbit.  The Kuiper belt is beautifully analogous to the asteroid belt.  This is further evidence that comets are icy planetesimals leftover from the formation of the Solar System, just as asteroids are metallic and rocky planetesimals leftover from the formation of the Solar System.  Just as the asteroid belt should have become a fifth terrestrial planet, the Kuiper belt should have become a fifth jovian, gas-giant planet with less hydrogen and helium outer layers thus exposing volatile ices, similar to Uranus and Neptune.  The total mass of the Kuiper belt was once roughly equal to the mass of Uranus or Neptune, but the gas-giant planets, particularly Jupiter, have ripped the overwhelming majority of the icy planetesimals out of the original Kuiper belt.  Today, the total mass of all the short-period comets in the Kuiper belt combined together is barely equal to that of a single large-sized moon.  Many short-period comets that Jupiter ripped out the Kuiper belt collided with forming planets during the heavy bombardment period of the young Solar System.  Gravitational perturbations from Jupiter continue to rip short-period comets out of the Kuiper belt.  Therefore, not all short-period comets orbit the Sun from within the Kuiper belt.  There are short-period comets orbiting the Sun on random orbits.  The Halley comet is an example of a short-period comet that orbits the Sun but not from within the Kuiper belt.  Some short-period comets intersect the Earth’s orbit.  Therefore, a comet could collide with the Earth.  The result of such a collision would be an extinction level event similar to an extinction level event caused by an asteroid impact.

 

Long-period comets take such a long period of time to orbit the Sun that astronomers are not certain of their orbital periods.  Perhaps their orbital periods are several million years.  Perhaps some of them are on unbound orbits (parabolic orbits or hyperbolic orbits), meaning that they will never return after passing by the Sun once.  The orbits of long-period comets are not confined to the plane of the Solar System.  A long-period comet may come from above the plane of the Solar System or from below the plane of the Solar System, pass around the Sun once, and then move away from the Sun, possibly never to return.  The source of the long-period comets is the Oort cloud, an enormous spherical cloud of comets around the entire Solar System, possibly one light-year in size.  The Oort cloud is named for the Dutch astronomer Jan Oort who theorized its existence.  Oort cloud comets are so distant from the Sun that they are barely held by the Sun’s gravitational attraction.  Gravitational attractions from other stars in other star systems can perturb the orbit of a long-period comet, causing it to fall to the inner Solar System.  Caution: the inner Solar System relative to the Oort cloud would include the four inner planets, the asteroid belt, the four outer planets, and even the Kuiper belt of short-period comets.  The Oort cloud must be spherically shaped, since the orbits of long-period comets are not confined to the plane of the Solar System.  The Oort cloud formed when the jovian, gas-giant planets, particularly Jupiter, flung most of the icy planetesimals of the young Solar System in random directions out to enormous distances from the Sun, almost ejecting them entirely from the Solar System.

 

As any comet (short-period or long-period) approaches the Sun, the Sun’s heat will melt its volatile ices.  Actually, the very low pressures of outer space causes the volatile ices to turn from the solid state (ice) directly into the gaseous state, skipping the liquid state.  In other words, the Sun’s heat does not melt the volatile ices; the Sun’s heat sublimes the volatile ices.  As the volatile ices sublime, dust particles that were trapped within the ice are liberated.  The result is a halo of sublimed volatile ices and dust particles around the comet.  This is the coma of the comet, which is rather like an atmosphere around the comet.  The nucleus of the comet is the volatile ices that remain in the solid state around the core of metal and rock.  The coma forms just where we would expect: at the frost line between the orbit of Mars and the orbit of Jupiter.  After passing around the Sun and then moving away from the Sun, the coma condenses back into solid ice when the comet again crosses the frost line as it returns to the outer Solar System.  Throughout the comet’s orbit, the Sun’s light will push the liberated dust particles away from the Sun.  The force that light exerts is called radiation pressure, which is so weak that we do not notice it in our daily lives.  Although the radiation pressure of the Sun’s light does push planets and asteroids and comets away from the Sun, this radiation pressure is so weak that it can be completely ignored as compared with the gravitational attraction of the Sun keeping all of these bodies in their orbits.  However, a tiny dust particle is so small with such a minuscule mass that the gravitational attraction it feels from the Sun is so weak that the radiation pressure of the Sun’s light may balance or even exceed the Sun’s gravitational attraction.  Thus, the tiny dust particles liberated from comets are pushed away from the Sun by the radiation pressure of the Sun’s light.  Hence, the comet grows a dust tail that points away from the Sun.  Actually, the comet grows two tails that both point away from the Sun.  The dust tail is caused by the radiation pressure of the Sun’s light.  The ion tail (or the plasma tail) is caused by the Sun’s solar wind.  Although both comet tails point away from the Sun, the dust tail is curved while the ion tail (plasma tail) is straight, pointing directly away from the Sun.  These two tails always point away from the Sun, whether the comet is moving toward the Sun or moving away from the Sun.  When the comet is moving toward the Sun, the comet’s two tails point behind it.  When the comet is moving away from the Sun, the comet’s two tails are ahead of it, preceding its own motion.  It is theoretically possible to build a spacecraft that would be propelled by the radiation pressure of the Sun’s light and the Sun’s solar wind.  Although these forces are relatively weak, an enormous panel attached to a spacecraft would suffer a significant force from the radiation pressure of the Sun’s light and from the Sun’s solar wind as both continuously bombard the panel’s large surface area.  If the spacecraft together with the enormous panel had a sufficiently small mass, the spacecraft together with its enormous panel would suffer a significant acceleration away from the Sun as the radiation pressure of the Sun’s light and the Sun’s solar wind both push the enormous panel attached to the spacecraft.  This theoretical enormous panel is called a solar sail, since it is rather like the sail of a sailboat that propels the sailboat as the Earth’s atmospheric winds push upon the sail.

 

Each time a short-period comet approaches the Sun closer than the frost line between the orbit of Mars and the orbit of Jupiter, some of its volatile ices will sublime.  Although some of these sublimed ices will condense back into solid ice when the comet moves away from the Sun further than the frost line, some of the sublimed ices completely escape the weak gravitational attraction of the comet.  Therefore, a short-period comet that has part of its orbit closer to the Sun than the frost line will continually lose more and more of its volatile ices with each orbit.  Ultimately, the short-period comet may lose its entire outer layer of volatile ices, leaving only its core of metal and rock.  This is a dead comet.  The comet Phaethon is an example of a dead comet.  Moreover, each time a short-period comet approaches the Sun closer than the frost line, dust particles will be liberated whenever the comet’s ice sublimes.  Since short-period comets orbit the Sun cyclically (over and over again) on roughly the same orbit, the orbit of a short-period comet that periodically approaches the Sun closer than the frost line is littered with dust particles that were liberated by the Sun’s heat each time the short-period comet approached the Sun.  Although Jupiter’s gravity perturbs the orbits of planets and asteroids and comets, these perturbations are small.  Therefore, planets and asteroids and short-period comets orbit the Sun cyclically (over and over again) on roughly the same orbit.  If the orbit of a short-period comet intersects Earth’s orbit, then the Earth will pass through the orbit of that comet at roughly the same time every year.  As a result, all of the dust particles at that part of the comet’s orbit will fall toward the Earth, burning within the Earth’s atmosphere and appearing as falling stars or shooting stars.  This is called a meteor shower.  A meteor shower is named for a particular constellation in the sky, but not because the meteors only appear within that constellation.  The meteors (falling stars or shooting stars) actually appear everywhere throughout the entire sky.  A meteor shower is named for a particular constellation because that particular constellation appears to be the extrapolated source of all the meteors throughout the entire sky.  In actuality, the Earth is moving toward that particular constellation as the Earth moves through a particular location within the comet’s orbit, causing that constellation to appear to be the extrapolated source of all the meteors throughout the entire sky.  This is similar to driving into a snowstorm.  The snowflakes appear to diverge away from the point in front of us, the point in the direction toward which we are driving.  Similarly, the meteors during a meteor shower appear to diverge away from the constellation in the direction toward which the Earth is moving.  Examples of meteor showers include the Lyrids named for the constellation Lyra (the harp) and occurring in late April every year, the Perseids named for the constellation Perseus (the hero) and occurring in mid-August every year, the Draconids named for the constellation Draco (the dragon) and occurring in early October every year, the Orionids named for the constellation Orion (the hunter) and occurring in late October every year, the Leonids named for the constellation Leo (the lion) and occurring in mid-November every year, and the Geminids named for the constellation Gemini (the twins) and occurring in mid-December every year.

 

The entire plane of the Solar System is filled with dust.  We can see this dust from the Earth, although barely.  At extremely dark locations, far from any city lights and other light pollution, we can see a faint glow along the zodiac constellations.  This is called zodiac light.  In actuality, zodiac light is sunlight reflected off of the dust that fills the plane of the Solar System.  As we discussed earlier in the course, the zodiac constellations are along the ecliptic, which is the apparent path of the Sun around the sky.  In actuality, the Earth orbits the Sun in a plane called the ecliptic plane.  The ecliptic is actually the projection of the ecliptic plane onto the Earth’s sky.  Hence, the zodiac constellations are also in the ecliptic plane, but the stars within constellations are far beyond our Solar System.  Although, the stars within constellations are still within our Milky Way Galaxy.  The galaxies within constellations are far beyond the stars within our Milky Way Galaxy.

 

Pluto is the final object in the Solar System that we must discuss.  The orbital period of Pluto around the Sun is roughly two hundred and fifty Earth years.  Pluto should not be considered a planet for several reasons.  Firstly, Pluto’s orbit around the Sun is moderately inclined to the plane of the Solar System, while the eight planets all have orbits around the Sun nearly in the plane of the Solar System.  Secondly, Pluto’s orbit around the Sun is significantly elliptical, while the eight planets all have orbits around the Sun that are roughly circular (but nevertheless slightly elliptical).  More correctly, the eight planets all have orbits around the Sun that are ellipses with small eccentricities, while Pluto has an orbit around the Sun with a significant eccentricity.  Thirdly, Pluto’s orbit around the Sun intersects Neptune’s orbit around the Sun, while the eight planets all have orbits that do not intersect each other.  Although Pluto’s orbit intersects Neptune’s orbit, Pluto will not collide with Neptune.  The gravity of Neptune has adjusted Pluto’s orbital motion around the Sun using orbital resonance to ensure that Pluto will never collide with Neptune.  Since Pluto’s orbit intersects Neptune’s orbit, sometimes Pluto is closer to the Sun than Neptune.  Fourthly, Pluto’s orbit is mostly just beyond Neptune’s orbit.  If Pluto were a planet, then it should be a jovian, gas-giant planet, since it is in the outer Solar System.  However, Pluto is smaller than Mercury, the smallest of the eight planets!  Also, Pluto was not a terrestrial planet that was accidentally ejected from the inner Solar System to the outer Solar System.  If this were the case, Pluto would be composed of metal and rock.  Although Pluto probably does have a core composed of metal and rock, Pluto is primarily composed of volatile ices surrounding that metallic and rocky core.  For all of these reasons, Pluto should not be regarded as a planet.  After discussing at length that Pluto is not a planet, we must now explain what Pluto actually is.  Since Pluto is a chunk of volatile ices (with a metallic-rocky core) orbiting the Sun just beyond Neptune’s orbit, would this not make Pluto a short-period comet?  The answer is yes: Pluto is actually a short-period comet in the Kuiper belt.  Pluto’s largest moon Charon is practically the same size as Pluto itself.  Charon is so large that it should not even be regarded as a moon of Pluto.  The Pluto-Charon system should be regarded as a short-period, double comet system orbiting the Sun within the Kuiper belt.

 

Many students are offended that Pluto is no longer considered a planet.  These students argue that Pluto was considered the ninth planet from the Sun for more than seventy-five years, from its discovery in the year 1930 until the year 2006.  These students argue that we cannot demote Pluto from a planet to a Kuiper belt short-period comet after it was considered to be a planet for more than three-quarters of a century.  However, this type of demotion has occurred before.  In the year 1801, an object was discovered orbiting the Sun between the orbit of Mars and the orbit of Jupiter.  This object was named Ceres after the ancient Roman mythological goddess of agriculture (Demeter in ancient Greek mythology).  The ancient Roman mythological goddess Ceres (Demeter) is depicted on the flag and the great seal of the State of New Jersey, representing prosperity.  When the astronomical body Ceres was discovered in the year 1801, it was declared to be the fifth planet.  Ceres was even given the astronomical symbol ⚳ that astronomers continue to use to the present day, just as the other planets each have their own astronomical symbol, as we discussed.  Notice Ceres was even named for an ancient mythological Roman figure, as any planet should be named.  Jupiter was then reclassified as the sixth planet, Saturn was reclassified as the seventh planet, and Uranus was reclassified as the eighth planet.  Note that Neptune was not yet discovered.  However, Pallas was then discovered in the year 1802 orbiting the Sun between the orbit of Mars and the orbit of Jupiter.  Juno was then discovered in the year 1804 orbiting the Sun between the orbit of Mars and the orbit of Jupiter.  Vesta was then discovered in the year 1807 orbiting the Sun between the orbit of Mars and the orbit of Jupiter.  Hygiea was discovered in the year 1849 orbiting the Sun between the orbit of Mars and the orbit of Jupiter.  As telescopes became more and more powerful, more and more of these objects were discovered orbiting the Sun between the orbit of Mars and the orbit of Jupiter.  Also, more powerful telescopes began to reveal that these objects were much, much smaller than the other planets.  Several decades later, astronomers realized that none of these objects should be regarded as planets.  After roughly fifty years of regarding Ceres as a planet, Ceres and Pallas and Juno and Vesta and Hygiea and all these other objects were demoted to minor planets.  The term minor planet was used to appease millions of people who considered Ceres to be a planet for decades.  After this demotion, Jupiter was then restored as the fifth planet, Saturn was restored as the sixth planet, and Uranus was restored as the seventh planet.  After several more decades, there was no one left alive who remembered that Ceres was ever regarded as a planet.  At that point, Ceres and Pallas and Juno and Vesta and Hygiea and all these other objects were renamed as asteroids.  The historical classification of Pluto nearly perfectly parallels the historical classification of Ceres.  In the year 1930, Pluto was discovered just beyond Neptune’s orbit, and Pluto was regarded as the ninth planet for decades.  Pluto was even given the astronomical symbol ♇ that astronomers continue to use to the present day, just as the other planets each have their own astronomical symbol, as we discussed.  Notice Pluto was even named for an ancient mythological Roman figure, as any planet should be named.  However, Varuna was discovered in the year 2000 orbiting the Sun just beyond Neptune’s orbit.  Ixion was then discovered in the year 2001 orbiting the Sun just beyond Neptune’s orbit.  Quaoar and its moon Weywot were discovered in the years 2002 and 2007, respectively, orbiting the Sun just beyond Neptune’s orbit.  Sedna was discovered in the year 2003 orbiting the Sun just beyond Neptune’s orbit.  Orcus and its moon Vanth were discovered in the years 2004 and 2005, respectively, orbiting the Sun just beyond Neptune’s orbit.  As telescopes became more and more powerful, more and more of these objects were discovered orbiting the Sun just beyond Neptune’s orbit.  Also, more powerful telescopes began to reveal that these objects were much, much smaller than the other planets.  In particular, Pluto is not only smaller than planet Mercury (the smallest of the eight planets), but Pluto is even smaller than all seven of the large-sized moons in the Solar System (Ganymede, Titan, Callisto, Io, Earth’s Moon, Europa, and Triton).  Eris and its moon Dysnomia were discovered in the year 2005 orbiting the Sun just beyond Neptune’s orbit, and Eris is roughly the same size and roughly the same mass as Pluto.  If we were to regard Pluto as a planet, shouldn’t we regard Eris as a planet as well?  Suppose dozens of more objects are someday discovered just beyond Neptune’s orbit that are slightly larger and slightly more massive than Pluto.  Should all these dozens of objects be regarded as planets?  After more than seventy-five years of regarding Pluto as a planet, Pluto-Charon and Varuna and Ixion and Quaoar-Weywot and Sedna and Orcus-Vanth and Eris-Dysnomia and all these other objects were demoted to dwarf planets.  The term dwarf planet was used to appease millions of people who considered Pluto to be a planet for decades.  After several more decades, there will be no one left alive who will remember that Pluto was ever regarded as a planet.  At that point, everyone will agree that Pluto-Charon and Varuna and Ixion and Quaoar-Weywot and Sedna and Orcus-Vanth and Eris-Dysnomia and all these other objects are short-period comets orbiting the Sun within the Kuiper belt.  Just as astronomers eventually realized that Ceres is not a planet but instead was the first asteroid of the asteroid belt that was ever discovered, astronomers have now realized that Pluto is not a planet but instead was the first short-period comet of the Kuiper belt that was ever discovered.

 

 

 

Links

 

Libarid A. Maljian homepage at the Department of Physics at CSLA at NJIT

Libarid A. Maljian profile at the Department of Physics at CSLA at NJIT

Department of Physics at CSLA at NJIT

College of Science and Liberal Arts at NJIT

New Jersey Institute of Technology

 

 

 

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