The Tides

It may seem that on Earth we should feel the same gravitational force from the Sun anywhere on Earth, but in fact at noon we are 13,000 km closer to the Sun than near midnight when we are on the other side of the Earth.  This 13,000 km may seem a small difference compared to the 150 million km distance from the Sun, but even so the difference has consequences. These differences in the force experienced within a body lead to tidal bulges, as shown in Figure 2, below.

Figure 2:  Differential (tidal) forces on a body relative to the primary (left), and relative to its
own center (right).  The forces relative to its center stretch the body along the line joining the
body and the primary, and compress the body along the perpendicular directions, to form a
football shape (prolate spheroid).

The figure on the left shows the forces relative to the Sun, and the figure on the right (obtained by subtracting the central force on the left from all of them) shows the forces relative to the center of the body.  These relative forces tend to stretch the body laterally, and compress the body in the perpendicular direction, to form a football shape. In the case of Earth, the liquid oceans are easily disorted into the above shape, so that the oceans become slightly deeper in the direction both toward and away from the Sun--about 1 meter in the deep oceans. However, the Earth is rotating under these tidal bulges, and the water can slosh much higher in some areas such as the St. Lawrence Seaway. As the Earth rotates, the continents pass through these tidal bulges once a day, causing the diurnal tides every 12 hours.

Both the Moon and the Sun exert tidal forces on the Earth.  Although the Moon is much smaller than the Sun, it is also much closer. In fact, the Sun's influence is only 5/16 of the total, while the Moon causes 11/16 of the total influence. So the Moon exerts more than twice the influence as the Sun, but the Sun-produced tides are still significant. When the Sun and the Moon line up (near new or full Moon), the forces add together and cause very high spring tides (the word spring is not related to the season!).  When the Sun is 90 degrees from the Moon (near first and third quarter), the high and low tides are not as great--these are called neap tides.

Spring Tide	Neap Tide

Consequences of Tidal Friction

The ocean tides are not the only effect of these tidal forces.  The solid body of the Earth also bulges slightly in this way.  The daily flexing of the Earth (both solid body and sloshing of the oceans) cause loss of energy of the Earth's rotation, due to friction.  This energy goes into heat, increasing the Earth's internal temperature.  The loss of rotational energy means that the Earth is slowing down in its rotation rate, currently by about 0.002 seconds per century.

As you might imagine, the Earth also exerts tidal forces on the Moon.  In fact, the tidal forces of Earth on the Moon are about 20 times larger than those from the Moon on the Earth.  Note what happens when a rotating body is tidally distorted.  The line of distortion is continually being rotated away from the line between the two bodies, causing the bulges to lead slightly.  There is then a net torque opposing the direction of rotation, thus slowing down both bodies.  This torque exists until the slowing rotation causes the body's orbital period to equal its rotational period.  Once this happens, the body is said to be tidally locked, and the torque and dissipation by tidal forces ceases.  At this moment in time, the Moon is tidally locked with the Earth, but the Earth is not tidally locked with the Moon.  That is why the Moon keeps the same face to the Earth.  In the distant future, the slowing Earth will eventually become tidally locked with the Moon, and no further evolution of the system will occur.

When this occurs, what will the Earth/Moon system look like?  The leading bulge of the Earth also exerts an extra pull on the Moon in its orbit, giving a slight acceleration along the orbit, and increases its orbital velocity.  This means the Moon is slowly spiraling away from the Earth.

Lecture Quiz #1

Atmospheres

The atmosphere is the layer of gas that surrounds some planets. As you may know, heating a gas causes it to expand (the pressure increases). A massive planet like Jupiter has such a strong gravity that it can hold down its gases, and they cannot escape into space. Earth can hold on to heavier gases, like oxygen and carbon dioxide, but not the lightest gases such as hydrogen and helium. Any body has an escape speed, which is how fast an object has to move in order to escape. The escape speed at Earth's surface is 11.2 km/s. When a gas is heated, its particles move faster, so whether a gas will be kept in Earth's atmosphere depends on how hot it is, and whether the molecules are moving faster than the escape speed. But not all gas molecules move at the same speed. We talk about the average speed, which depends on the temperature, but even when most molecules are moving at a lower average speed, a few of the fastest will still exceed the escape speed and drift off into space. The closer the average speed is to the escape speed, the more molecules are lost, and the faster the atmosphere will escape.

Moon

Does the Moon have an atmosphere?  To find out, we compare the escape speed of the Moon with the speed of the gas particles making up its atmosphere.  Unless the gas particles are moving a lot (a factor of 10) slower than the escape speed, the particles will seep out of the atmosphere over time.  The Moon's escape speed is only 2.32 km/s, and the speed of oxygen (0₂) at the Moon's surface is 0.78 km/s. So the escape speed is only 3 times the average speed.  The Moon will lose any oxygen that might be produced, after only a few hundred years.

Any atoms lingering around the Moon, produced due to outgassing or spalation from rocks, lasts only for a short time and must be continually replenished.  The atmosphere of the Moon is an amazingly good vacuum, only 10^-14 atm.

Earth

When the Earth was first formed, its atmosphere would have started out to be mostly H and He, but lost it due to the speed of these particles allowing them to escape over time.  A new, heavier atmosphere of H₂O, O₂, N₂, and CO₂ was outgassed from volcanism, or brought here by comets.

The pressure of the Earth's atmosphere (and all atmospheres) fall with height, so by far most of the atmosphere is at the lowest heights. The temperature also falls with height, at least near the surface. That is why it gets so cold and there is so little air at the top of a mountain.  This same general behavior is true for all atmospheres, even the atmospheres of stars! But notice what happens in the figure below, which shows a plot of the change of temperature with height in the Earth's atmosphere.

Atmospheric temperature structure:

Why does the temperature of the atmosphere drop to a height of about 10 km, then start to rise again in the Stratosphere?  This is due to absorption of ultraviolet (UV) light from the Sun, which deposits energy in this region of the atmosphere, and heats it.  This region is called the Stratosphere because it is stable to upward motions (an inversion layer), which means that clouds do not rise in columns, but spread out in thin layers, like strata.  The region of maximum heating by UV light (the Stratopause) is also the location of the ozone layer, O3, which is largely responsible for absorbing the UV and protecting us from the harmful radiation.

Up to the Mesopause, the temperature again declines, but then rises again in the Thermosphere due to absorption of X-rays from the Sun.  This "atmosphere" is only slightly below the height of low Earth orbiting satellites such as the Space Shuttle, which orbits about 200 km up, and this part of the atmosphere is so thin that it is a nearly perfect vacuum.

The Earth's atmosphere is about 1/5 O₂, and 4/5 N₂, with trace amounts of other gases such as carbon dioxide (CO₂) and water (H₂O). However, the amount of CO₂ has risen significantly in the last 200 years, partly as a result of human activity (burning fossil fuels, etc.). Carbon dioxide is a greenhouse gas, so-called because it acts like a greenhouse in keeping the Earth warm. How does the greenhouse effect work? Radiation from the Sun passes through the atmosphere in the visible range of the spectrum, and heats up the ground, which then reradiates the energy out into space, but now in the infrared part of the spectrum. Greenhouse gases block the escape of the heat by absorbing the infrared radiation. As a result, there are alarming indications that the Earth's climate is getting warmer. The Earth's climate has gotten colder and warmer at intervals over time, causing glacial periods and interglacial periods, so it is impossible yet to tell whether humans are mainly to blame for the climate warming. Nevertheless, we can help to keep the problem under control by reducing greenhouse gas emissions.

Lecture Question #2

Interiors

The Earth is the one planet that we can study in great detail.  We know a lot about the structure of the interior of the Earth, but we must remember that other planets may be different in fundamental ways.  We must take what we learn about Earth and compare and contrast it with the other planets.

The mean or bulk density of a planet is an easily measured quantity that can tell us a great deal about what the planet is made of.  Earth's bulk density is 5520 kg/m³ (compare with the density of water, 1000 kg/m³).  But the density of the Earth's surface (density of silicate rocks) is only 2800 kg/m³, so the interior must be much more dense than the surface.  The structure of the interior of the Earth has been pieced together from a number of clues, such as what the surface is made of, what we see coming to the surface in volcanoes, and most of all what we learn from earthquakes.

The earthquakes, adjustments of the Earth's crust due to internal stresses, launch two types of seismic waves, longitudinal compression (P) waves (sound waves), and transverse distortion (S) waves.  The P waves travel faster, and so the letter P could stand for Pressure or Prompt waves.  The slower S waves arrive later, and so the letter S could stand for Secondary, or Slow waves.  An important difference between longitudinal and transverse waves is that longitudinal waves can travel through liquid, but transverse waves cannot.  Both kinds of waves refract due to density gradients in the Earth's interior.  Due to the refraction of both kinds of waves, and the lack of propagation of S waves, we learn that the interior has a liquid layer, and also can measure such quantities as temperature and density as a function of depth.  See this web page to see some drawings of the interior of the Earth.  If you ever wondered how Earthquake epicenters and magnitudes are determined, take this short virtual earthquake lesson.

The Moon's interior is quite different from the Earth's. From seismic experiments left from the Moon landings, we know that the Moon appears to be made entirely of the crustal material of the same sort as Earth's surface.  It is strange that it does not have metals in its core.  It is thought that late in the formation of the Earth, a giant impactor (planetesimal) struck the Earth.  Such a collision would have destroyed the impactor, the metals of the impactor would sink to the center of the Earth, and much of the outer crust of the Earth could have been torn off to later come together to form the Moon.  This may explain the unusually thin crust of the Earth's oceans.  Without the impact, the Earth might not have plate tectonics, as we discuss in the next section.

Lecture Quiz #3

Surfaces

Earth

The surface of the Earth is dominated by plate tectonics. The idea of plate tectonics explains the shape of the continents, the locations of earthquake zones and volcanoes, the locations of mountains and ocean trenches, the presence of hotspots such as Hawaii and Yellowstone, and many other phenomena. For many years the subject was hotly debated, but in the 1970's it was finally widely accepted and has revolutionized our understanding of the Earth's surface.

• Plate Tectonics
• Subduction Zones
• Magnetic Striping
• Earthquake Zones
• Hotspots

The other great factor in shaping the Earth's surface, of course, is weathering by water, ice, wind, and the action of plants and animals. Over geologic time, mountains are worn down and craters are obliterated, even while new ones are created through continental drift and asteroid strikes.

Moon

The surface of the Moon, on the other hand is dominated by craters, highlands (mountainous areas), and maria (low-lying lava-filled depressions). Like many other planets, the Moon is heavily cratered. However, most craters are more than 4 billion years old, indicating that the heavy bombardment by asteroids and planetesimals ceased by about then. The Earth must also have been similarly pocked by craters, but weathering obliterated them. The oldest rock on Earth's surface is now only about 3.5 billion years.

Some time after the bombardment ceased, lava welled up into the lower basins to create the maria (latin for seas, although they have nothing to do with water). Since the Moon keeps the same face to Earth, humankind did not know what the other side of the Moon looked like until space probes were launched to orbit the Moon in the 1960's. What we found is that the far side of the Moon is not like the near side.

• Clementine Image Browser

Lecture Quiz #4

Earth's Magnetic Fields (Magnetosphere)

The rotating liquid metallic core of the Earth generates magnetic fields that, at the surface, look like a dipole (a North and South magnetic pole).  At the surface of the Earth, the magnetic field strength is about 0.4 gauss.  This is the magnetic field that allows a compass to point north. The magnetic fields reach far out into space, and surround the Earth in a protective region called the magnetosphere. Some other planets have a magnetosphere also, especially Jupiter.

• Magnetosphere
• Radiation Belts
• Particle Motions

Disturbances of the magnetosphere by the Sun cause the aurorae, or northern (and southern) lights, as well as many other effects.  We will talk more about this when we discuss solar activity.