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New Jersey Institute of Technology

College of Science and Liberal Arts

Department of Physics

The Earth in Space

Phys 203

Fall 2024

First Examination lecture notes

Introduction to Earth Science

A system is a collection of seemingly separate parts that are actually interrelated to form a common whole. For example, the human body has a nervous system, which includes the brain, the spinal column, and nerves. The brain, the spinal column, and nerves are not separate. They are all interrelated and form a common whole: the nervous system. As another example, the human body has a circulatory system (cardiovascular system), which includes the heart, arteries, veins, and capillaries. The heart, arteries, veins, and capillaries are not separate. They are all interrelated and form a common whole: the circulatory system (the cardiovascular system). As yet another example, the Solar System includes the Sun, planets, and moons. The Sun, planets, and moons are not separate. They are all interrelated and form a common whole: the Solar System.

The planet we call Earth is a system. The Earth’s geosphere is the solid part of the Earth. The Earth’s hydrosphere is the totality of all water on Earth. The Earth’s atmosphere is the totality of all air on Earth. The Earth’s biosphere is the totality of all life on Earth. The geosphere, the hydrosphere, the atmosphere, and the biosphere are not separate. These spheres are all interrelated and form a common whole: the system we call planet Earth. The topic of this entire course is Earth Science, which is the study of the system we call planet Earth. In other words, Earth Science is the combination of at least five sciences: geology (the study of the Earth’s geosphere), oceanography (the study of the Earth’s hydrosphere), meteorology (the study of the Earth’s atmosphere), biology (the study of the Earth’s biosphere), and even astronomy (the study of the Earth’s surroundings, primarily the Sun and the Moon but also the other planets).

An open system is a system that exchanges both matter and energy with its surroundings. At the opposite extreme, an isolated system is a system that does not exchange matter and does not exchange energy with its surroundings. In between these two extremes is a closed system, which is a system that exchanges energy with its surroundings without exchanging matter with its surroundings. Note that it is impossible for a system to exchange matter with its surroundings without exchanging energy with its surroundings. In the strictest sense, planet Earth is an open system, since the Earth exchanges both matter and energy with its surroundings. However, the matter that the Earth exchanges with its surroundings can be ignored for most practical applications. Therefore, planet Earth can be assumed to be a closed system as an excellent approximation for most intents and purposes.

When we say planet Earth exchanges energy with its surroundings, we mean that the Earth both receives energy from its surroundings and radiates energy into its surroundings. The Earth even has an internal energy source, which we will call geothermal energy. By far, the most important external energy source of planet Earth is the Sun. Fascinatingly, these two energy sources (the Sun and the geothermal energy) feed or drive different spheres of planet Earth. In particular, the Earth’s external energy source (the Sun) feeds the hydrosphere and the atmosphere, whereas the Earth’s internal energy source (the geothermal energy) feeds the geosphere. In other words, if God were to turn off the Sun, oceanographic processes and meteorological processes would end but geological processes would continue. Conversely, if God were to turn off the geothermal energy, geological processes would end but oceanographic processes and meteorological processes would continue. The biosphere is mostly fed by or driven by the Sun, but remarkably a small part of the biosphere is driven by the geothermal energy, as we will discuss later in the course.

The Geographic Coordinate System

A sphere is a geometrical shape with an equatorial radius and a polar radius that are equal to each other. An oblate spheroid is a geometrical shape with an equatorial radius that is larger than its polar radius; in other words, an oblate spheroid has a polar radius that is smaller than its equatorial radius. A prolate spheroid is a geometrical shape with an equatorial radius that is smaller than its polar radius; in other words, a prolate spheroid has a polar radius that is larger than its equatorial radius. The true shape of the Earth is not a sphere because of its rotation. The Earth is rotating or turning or spinning around an imaginary line called the Earth’s rotational axis or axis of rotation. This rotation causes a centrifugal force that causes the Earth’s Equator to bulge outward. Thus, the true shape of the Earth is an oblate spheroid. Indeed, every planet, moon, and star in the universe is rotating which causes a centrifugal force that causes its equator to bulge outward. Thus, the true shape of every planet, moon, and star in the universe is actually an oblate spheroid. Since the true shape of the Earth is an oblate spheroid, we are actually further from the center of the Earth if we are standing at the Equator, and we are actually closer to the center of the Earth if we are standing at either the North Pole or the South Pole. Nevertheless, the Earth’s centrifugal force is actually quite weak. In other words, the bulging of the Earth’s Equator is very small. Therefore, although the true shape of the Earth is an oblate spheroid, planet Earth can be assumed to be a sphere as an excellent approximation for most practical applications. Indeed, we will assume that the Earth is a sphere for the rest of this course.

There are three possible intersections of a sphere and a plane. The intersection of a sphere and a plane that cuts the center of the sphere is called a great circle. A great circle is the largest possible circle that we can draw on a sphere; the radius of a great circle is equal to the radius of the entire sphere. The intersection of a sphere and a tangent plane is a point, the point where the tangent plane touches the sphere. A point is actually a circle with a radius equal to zero. In between these two extremes is a small circle, the intersection of a sphere and a plane between a center-cutting plane and a tangent plane.

The geographical coordinate system labels every point on the surface of planet Earth with two numbers: a latitude and a longitude. A line of latitude is defined as the intersection of the Earth and a plane that is perpendicular to the Earth’s rotational axis. All lines of latitude are parallel to one another. For this reason, lines of latitude are also called parallels. Most lines of latitude are small circles, but there are three exceptions: the Equator, the North Pole, and the South Pole. The Equator is the only line of latitude that is a great circle. The Equator divides planet Earth into two hemispheres: the northern hemisphere and the southern hemisphere. Lines of latitude in the northern hemisphere are measured in degrees north, and lines of latitude in the southern hemisphere measured in degrees south. The Equator itself is zero degrees latitude. The North Pole and the South Pole are the only lines of latitude that are points. These poles are the only two points where planet Earth intersects its own rotational axis. The North Pole is ninety degrees north latitude, and the South Pole is ninety degrees south latitude. There are four other lines of latitude that have special names. The Tropic of Cancer is roughly 23½ degrees north latitude, and the Tropic of Capricorn is roughly 23½ degrees south latitude. The Arctic Circle is roughly 66½ degrees north latitude, and the Antarctic Circle is roughly 66½ degrees south latitude. We will discuss the importance of these special lines of latitude later in the course. The latitudes between the Tropic of Cancer and the Tropic of Capricorn are commonly called the tropical latitudes or simply the tropics, but in this course we will refer to these latitudes as the equatorial latitudes since they are at and near the Equator. We will refer to the latitudes north of the Arctic Circle as well as the latitudes south of the Antarctic Circle as the polar latitudes, since they are at and near the poles. We will refer to the latitudes between the Tropic of Cancer and the Arctic Circle as well as the latitudes between the Tropic of Capricorn and the Antarctic Circle as the midlatitudes, since they are between the equatorial latitudes and the polar latitudes.

A line of longitude is defined as the intersection of the Earth and a plane that cuts the center of the Earth and is perpendicular to the lines of latitude. By this definition, all lines of longitude are great circles. This is the first significant difference between lines of latitude and lines of longitude. Whereas most lines of latitude are small circles, all lines of longitude are great circles. Another significant difference is that lines of longitude are measured in degrees east or west, whereas lines of latitude are measured in degrees north or south. If we regard north as up and south as down, then east will be to the right and west will be to the left. Yet another significant difference between lines of latitude and lines of longitude is that lines of longitude are not parallel to one another, whereas lines of latitude are parallel to one another. Lines of longitude are not parallel to one another because they all begin together at the North Pole, they spread apart from one another until they are furthest apart from one another at the Equator, and they all converge back together at the South Pole. Whereas lines of latitude are also called parallels, lines of longitude are also called meridians. There are some similarities between lines of latitude and lines of longitude however. Just as zero degrees latitude divides planet Earth into two hemispheres, zero degrees longitude also divides planet Earth into two hemispheres. Zero degrees latitude is called the Equator, which divides planet Earth into the northern hemisphere and the southern hemisphere. Similarly, zero degrees longitude is called the Prime Meridian, which divides planet Earth into the eastern hemisphere and the western hemisphere. However, this reveals yet another difference between lines of latitude and lines of longitude. Lines of latitude range from zero degrees to ninety degrees in each hemisphere (north and south), but lines of longitude range from zero degrees to one hundred and eighty degrees in each hemisphere (east and west).

The most important difference between lines of latitude and lines of longitude is that different lines of longitude are at different times. During the daytime, the Sun appears to rise in the eastern horizon and set in the western horizon. During the nighttime, the stars and galaxies also appear to rise in the eastern horizon and set in the western horizon. In other words, everything in the universe appears to rise in the eastern horizon and set in the western horizon. This is because the Earth is actually rotating or turning or spinning in the other direction, from west to east. It takes planet Earth one day or twenty-four hours to complete one full rotation around its rotational axis. Suppose that it is noon at our location on planet Earth. Noon is when the Sun appears highest in the sky. However, another person who is west of our location is at a time before noon, since that person must wait for planet Earth to rotate from the west to our location where the Sun appears to be highest in the sky. Conversely, yet another person who is east of our location is at a time after noon, since planet Earth has already rotated that person past our location. We conclude that lines of longitude to the west are at earlier times, and lines of longitude to the east are at later times. If we divide three hundred and sixty degrees (the number of degrees around the entire planet Earth or any full circle) by twenty-four hours, the result is a simple whole number: fifteen degrees of longitude per hour of time. In other words, for every fifteen degrees of longitude we move to the west, we are one hour earlier in time, and for every fifteen degrees of longitude we move to the east, we are one hour later in time. Indeed, humans have divided the entire surface of the Earth into twenty-four time zones, each of which is fifteen degrees of longitude wide. The time at the Prime Meridian is called universal time. In other words, the Prime Meridian is the only line of longitude where the local time is equal to the universal time. Every line of longitude in the western hemisphere has a local time that is earlier than universal time, and every line of longitude in the eastern hemisphere has a local time that is later than universal time.

If we begin at the Prime Meridian and move one hundred and eighty degrees to the west, we are twelve hours earlier, since one hundred and eighty degrees is half of a full circle and half of twenty-four hours is twelve hours. Note also that one hundred and eighty degrees divided by fifteen degrees per hour is indeed twelve hours. However, if we begin at the Prime Meridian again but instead move one hundred and eighty degrees to the east, we are twelve hours later. Suppose the local time at the Prime Meridian (the universal time) is any time whatsoever, such as 03:14 p.m. Twelve hours earlier than 03:14 p.m. is 03:14 a.m., but twelve hours later than 03:14 p.m. is also 03:14 a.m., but the following morning! Therefore, one hundred and eighty degrees longitude is the only line of longitude where the clock time does not change upon crossing it; the day changes instead! This special line of longitude is called the International Date Line. When we cross the International Date Line from the eastern hemisphere to the western hemisphere, we cross into the earlier day but remain at the same clock time. When we cross the International Date Line from the western hemisphere to the eastern hemisphere, we cross into the next day but remain at the same clock time. The International Prime Meridian Conference was held in the United States in Washington, D.C., in the year 1884. At this conference, the major powers of the world met to agree upon where to draw the Prime Meridian. Whichever choice they would have made for the Prime Meridian (zero degrees longitude) would have forced the International Date Line (one hundred and eighty degrees longitude) to end up on the opposite side of planet Earth from their choice of the Prime Meridian. During that time in human history, the United Kingdom was the most powerful empire in the world. Therefore, the British representatives at the conference pressured the other world powers to agree to draw the Prime Meridian through Greenwich, England. Although this was partly a politically-motivated choice, the world powers at the time realized that this was also a logical choice, since drawing the Prime Meridian through England forces the International Date Line to run through the middle of the Pacific Ocean. If instead the date line were to run through a continent, everyone who crosses that date line by foot or by horse or by train (or by car today) would need to remember that they are now in a different day. This would be too confusing. If the International Date Line runs through an ocean, the only persons who would need to remember that they are now in a different day would be persons in a ship who are crossing that ocean, which took months of time regardless. Therefore, the major powers of the world have agreed since the year 1884 to draw the Prime Meridian (zero degrees longitude) through Greenwich, England. This choice forces the International Date Line (one hundred and eighty degrees longitude) to run through the middle of the Pacific Ocean. Today, anyone who flies by jet aircraft across the Pacific Ocean in a matter of a few hours must remember that they are in a different day when they land at their destination.

A geodesic is the shortest possible distance between two points on the surface of planet Earth. This is not a straight line, since we cannot draw a straight line on planet Earth without drilling a tunnel straight through the planet! The geometrical question of what is the shortest distance between two points on a sphere is difficult to prove mathematically. Nevertheless, the answer to this geometrical question is simple: the shortest distance between two points on a sphere is an arc of a great circle. Therefore, a geodesic (the shortest distance between two points on the surface of planet Earth) is an arc of a great circle, which can be constructed by intersecting planet Earth with a plane that cuts the center of planet Earth (and the two points of interest, of course). In some cases, the geodesic between two locations on Earth is intuitive, but in other cases the geodesic between two locations on Earth is counterintuitive. For example, consider two cities on the same line of longitude. What is the shortest distance between these two cities? Since a geodesic is an arc of a great circle, we must construct a great circle connecting these two cities on this line of longitude, but every line of longitude is a great circle, as we discussed. Therefore, the shortest distance between two cities on the same line of longitude is an arc of that line of longitude. As another example, consider two cities on the Equator. What is the shortest distance between these two cities? Since a geodesic is an arc of a great circle, we must construct a great circle connecting these two cities on the Equator, but the Equator is a great circle, as we discussed. Therefore, the shortest distance between two cities on the Equator is an arc of the Equator. As yet another example, consider two cities on the same line of latitude other than the Equator. What is the shortest distance between these two cities? Since a geodesic is an arc of a great circle, we must construct a great circle connecting these two cities that are on this line of latitude, but lines of latitude (other than the Equator) are not great circles, as we discussed. Therefore, the shortest distance between two cities on the same line of latitude (other than the Equator) is not an arc of that line of latitude. In particular, consider two cities on the same midlatitude in the northern hemisphere. To construct the geodesic between these two cities, we must construct an arc of a great circle between these two cities. To do this, we intersect a plane with the center of the Earth (and the two cities, of course). If these two cities are on the same midlatitude in the northern hemisphere, then we must incline that plane so that it intersects with the center of the Earth. The result is that the geodesic (the arc of the great circle) between these two cities curves to the north of the line of latitude connecting them. To travel from the eastern city to the western city in the shortest distance, we follow the geodesic to the northwest and then to the southwest before finally arriving at the western city. To travel from the western city to the eastern city in the shortest distance, we follow the geodesic to the northeast and then to the southeast before finally arriving at the eastern city. As an extreme example of this construction, consider two cities on the same midlatitude in the northern hemisphere that happen to be located on opposite sides of planet Earth. To construct the geodesic between these two cities, we must construct an arc of a great circle between these two cities. We again intersect a plane with the center of the Earth (and the two cities, of course). If these two cities are on the same midlatitude in the northern hemisphere and happen to be located on opposite sides of planet Earth, then we must incline the plane vertically (intersecting the North Pole and the South Pole) so that the plane intersects with the center of the Earth. The result is that the geodesic (the arc of the great circle) between these two cities is along the lines of longitude connecting each city with the North Pole, not along their common midlatitude. To travel from either city to the other city in the shortest distance, we follow the line of longitude directly to the north over the North Pole and then continue along a line of longitude directly to the south before finally arriving at the other city.

Cartography

Another word for a map is a projection, and cartography is the study of maps (or projections). A map (or a projection) is defined as a flat representation of a part of the Earth (or perhaps the entire Earth). The most important part of this definition is the word flat. Since a map (or a projection) is a flat representation of a part of the Earth (or perhaps the entire Earth), this means that a map (or a projection) is not a true representation of whichever part of the Earth the map is attempting to represent, since the Earth is not flat! In other words, there will always be something wrong with every possible map (or projection).

A conformal projection is a map that preserves shapes (or angles). In other words, the shapes of continents, oceans, islands, lakes, and so on and so forth are all correct on a conformal projection. An equivalent projection is a map that preserves relative sizes (or relative areas). In other words, the relative sizes of continents, oceans, islands, lakes, and so on and so forth are all correct on an equivalent projection. There is a mathematical theorem from advanced geometry which states that it is impossible for a map to be both conformal and equivalent. In other words, it is impossible for a map to have shapes and sizes both correct at the same time. A map can be entirely conformal, but then it will not be equivalent. A map can be entirely equivalent, but then it will not be conformal. A map can be mostly conformal, but then it will only be a little equivalent. A map can be mostly equivalent, but then it will only be a little conformal. In other words, this mathematical theorem from advanced geometry states that the more conformal a map is, the less equivalent it will be. Conversely, the more equivalent a map is, the less conformal it will be. Two variables that behave this way are called incompatible. In other words, this mathematical theorem from advanced geometry states that conformality and equivalence are incompatible variables.

Maps are often constructed by touching a flat paper to planet Earth and projecting a part of the Earth (or perhaps the entire Earth) onto that flat paper. This flat paper often touches the Earth along a circle on planet Earth. This circle is called the circle of tangency. We can construct three different types of maps based upon the three different possible circles of tangency: cylindrical projections, conical projections, and planar projections.

A cylindrical projection is a map that projects the Earth onto a cylinder that touches planet Earth at a great circle. In other words, a cylindrical projection has a great circle as the circle of tangency. This great circle is often the Equator, but not necessarily. Cylindrical projections are useful for mapping the entire world. Indeed, maps of the entire world are almost always cylindrical projections. Here is the most important question we must ask about a cylindrical projection: is it conformal or is it equivalent? The answer is either (our choice). However, if it is conformal, then it is not equivalent, and if it is equivalent, then it is not conformal, by the mathematical theorem from advanced geometry. For example, consider the Mercator projection, named for the Belgian-German cartographer Gerardus Mercator. The Mercator projection is a cylindrical projection that is conformal, which means that it is not equivalent. In other words, shapes of continents, oceans, islands, lakes, and so on and so forth are all correct on a Mercator projection, but relative sizes of continents, oceans, islands, lakes, and so on and so forth are incorrect on a Mercator projection. As another example, consider the Gall-Peters projection, named for the Scottish cartographer James Gall and the German historian Arno Peters. The Gall-Peters projection is a cylindrical projection that is equivalent, which means that it is not conformal. In other words, relative sizes of continents, oceans, islands, lakes, and so on and so forth are all correct on a Gall-Peters projection, but shapes of continents, oceans, islands, lakes, and so on and so forth are incorrect on a Gall-Peters projection.

A conical projection is a map that projects the Earth onto a cone that touches planet Earth at a small circle. In other words, a conical projection has a small circle as the circle of tangency. This small circle is often a line of latitude, but not necessarily. Conical projections are useful for mapping the midlatitude regions of the world. For example, maps of the contiguous United States are almost always conical projections. Here is the most important question we must ask about a conical projection: is it conformal or is it equivalent? The answer is either (our choice). However, if it is conformal, then it is not equivalent, and if it is equivalent, then it is not conformal, by the mathematical theorem from advanced geometry. For example, consider the Lambert projection, named for the Swiss-French mathematician and physicist Johann Heinrich Lambert. The Lambert projection is a conical projection that is conformal, which means that it is not equivalent. In other words, shapes of continents, oceans, islands, lakes, and so on and so forth are all correct on a Lambert projection, but relative sizes of continents, oceans, islands, lakes, and so on and so forth are incorrect on a Lambert projection. As another example, consider the Albers projection, named for the German cartographer Heinrich Albers. The Albers projection is a conical projection that is equivalent, which means that it is not conformal. In other words, relative sizes of continents, oceans, islands, lakes, and so on and so forth are all correct on an Albers projection, but shapes of continents, oceans, islands, lakes, and so on and so forth are incorrect on an Albers projection.

A planar projection is a map that projects the Earth onto a tangent plane that touches planet Earth at a point. In other words, a planar projection has a point as the circle of tangency. This point is often the North Pole or the South Pole, but not necessarily. Planar projections are useful for mapping the polar regions of the world. In particular, maps of the Arctic Ocean (at the North Pole) or the continent Antarctica (at the South Pole) are almost always planar projections. Here is the most important question we must ask about a planar projection: is it conformal or is it equivalent? The answer is either (our choice). However, if it is conformal, then it is not equivalent, and if it is equivalent, then it is not conformal, by the mathematical theorem from advanced geometry. For example, the stereographic projection is a planar projection that is conformal, which means that it is not equivalent. In other words, shapes of continents, oceans, islands, lakes, and so on and so forth are all correct on a stereographic projection, but relative sizes of continents, oceans, islands, lakes, and so on and so forth are incorrect on a stereographic projection. As another example, the gnomonic projection is a planar projection that is equivalent, which means that it is not conformal. In other words, relative sizes of continents, oceans, islands, lakes, and so on and so forth are all correct on a gnomonic projection, but shapes of continents, oceans, islands, lakes, and so on and so forth are incorrect on a gnomonic projection.

Whereas a conformal projection is not equivalent, the equivalence is at least partially preserved near the circle of tangency. As we move further and further from the circle of tangency, the equivalence becomes worse and worse, becoming most severely distorted far from the circle of tangency. Similarly, whereas an equivalent projection is not conformal, the conformality is at least partially preserved near the circle of tangency. As we move further and further from the circle of tangency, the conformality becomes worse and worse, becoming most severely distorted far from the circle of tangency.

We emphasize again this mathematical theorem from advanced geometry: conformality and equivalence are incompatible variables, meaning that it is impossible for a map to be both conformal and equivalent. Although this geometrical theorem is difficult to prove mathematically, the essential reason for this incompatibility is simple to understand. A map is a flat representation of a part of the Earth (or perhaps the entire Earth), but the Earth is not flat. Therefore, something is certain to go wrong if we try to flatten the Earth. On the other hand, most humans believed that the Earth is flat for thousands of years. Humans believed that the Earth is flat because the curvature of a sphere is unmistakable if it is small, but the curvature becomes smaller and smaller as the sphere becomes larger and larger. More precisely, the curvature of a sphere is inversely related to its radius (its size). A small sphere has a large curvature, while a large sphere has a small curvature. More plainly, a sphere appears to be more and more flat as it becomes larger and larger. The Earth is so enormous compared with humans (in other words humans are so tiny compared with planet Earth) that the Earth appears to be flat to humans. We conclude that a tiny patch of planet Earth must be approximately flat to an excellent approximation. Therefore, a map of a tiny patch of the Earth (perhaps a city) will be both conformal and equivalent to an excellent (but still imperfect) approximation. As we attempt to construct a map of a larger and larger part of the Earth, conformality and equivalence become more and more noticeably incompatible. In the limit of attempting to map the entire world, this mathematical theorem shows its full teeth.

Physical Geography

The Earth is mostly covered with oceans. A relatively small fraction of planet Earth is covered with seven continents: North America, South America, Africa, Europe, Asia, Australia, and Antarctica. There are four oceans: the Atlantic Ocean, the Pacific Ocean, the Indian Ocean, and the Arctic Ocean.

There is a major mountain range near the west coast of North America: the Rocky Mountains. The tallest mountain in North America is in the Rocky Mountains: Mount McKinley (Denali), which is in Alaska. Immediately to the east of the Rocky Mountains is the Great Plains. A plain is an area of land with low elevation and shallow relief, whereas a plateau is an area of land with high elevation and shallow relief. There is a modest mountain range near the east coast of North America: the Appalachian Mountains. Historically, the longest river in North America was the Mississippi River, the mouth of which is at the Gulf of Mexico. However, the United States Army Corps of Engineers has shortened the Mississippi River through channelization to such a degree over the past two centuries that the Mississippi River is now the second longest river in North America. The longest river in North America is currently the Missouri River, the mouth of which is at the Mississippi River. The Rio Grande is a river in North America that serves as part of the border between the United States and Mexico. The mouth of the Rio Grande is at the Gulf of Mexico. The Saint Lawrence River in North America serves as part of the border between the United States and Canada. The mouth of the Saint Lawrence River is at the Atlantic Ocean. The five lakes Lake Superior, Lake Michigan, Lake Huron, Lake Erie, and Lake Ontario are together called the Great Lakes, which also serve as part of the border between the United States and Canada. Lake Superior is not only the largest of the Great Lakes, but it is also the largest lake in North America. A peninsula is a body of land that sticks out into a body of water and is therefore surrounded on three sides by water. Florida is an important peninsula in North America. The Yucatán (in Mexico) is another important peninsula in North America. Baja California is yet another important peninsula in North America. The Sea of Cortez is between Baja California and Mexico. The Aleutian Peninsula in Alaska is another important peninsula in North America. An archipelago is a group or a chain of islands. The Aleutian Islands is an archipelago that can be interpreted as a continuation of the Aleutian Peninsula, since the Aleutian Islands begin where the Aleutian Peninsula ends. Another important archipelago is the West Indies to the southeast of North America. The West Indies is itself a collection of several archipelagoes, including the Greater Antilles (composed of the four islands Cuba, Hispaniola, Puerto Rico, and Jamaica), the Lesser Antilles, the Bahamas, and the Bermuda Islands. The Caribbean Sea is to the south of the West Indies, between the West Indies and South America. The largest coastal inlet in North America is Hudson Bay. Greenland is a body of land to the northeast of North America that is too large to be considered an island but is too small to be considered a continent. A body of land that is intermediate in size between an island and a continent is called a microcontinent. Greenland is not only a microcontinent; Greenland is the second largest microcontinent in the world. We will reveal the largest microcontinent in the world shortly. There is a collection of deserts in southwestern United States and northwestern Mexico that we will collectively call the Basin and Range. The deserts that together form the Basin and Range include the Mojave Desert, the Sonoran Desert, and the Chihuahuan Desert. A strait is a narrow strip of water connecting two enormous bodies of water. The Bering Strait is between Alaska (United States) and Chukotka (Russia) and connects the Bering Sea with the Arctic Ocean. If a strait is a narrow strip of water connecting two enormous bodies of water, then the opposite of a strait would be a narrow strip of land connecting two enormous bodies of land. This is called an isthmus. An excellent example of an isthmus is Panama, a narrow strip of land that connects North America and South America.

There is a major mountain range near the west coast of South America: the Andes Mountains. The tallest mountain in South America is in the Andes Mountains: Mount Aconcagua, which is in Argentina. There is a tropical rainforest in northern South America: the Amazon rainforest, which is mostly in Brazil. There is a desert in southern South America: the Patagonian Desert, which is mostly in Argentina. The most arid (most dry) desert in the entire world is in South America: the Atacama Desert, which is mostly in Chile. The longest river in South America is the Amazon River, which cuts through the Amazon rainforest. The mouth of the Amazon River is at the Atlantic Ocean. The largest lake in South America is Lake Titicaca, which serves as part of the border between Peru and Bolivia. The Galápagos Islands is an archipelago in the Pacific Ocean off the coast of northwestern South America. The Falkland Islands is an archipelago in the Atlantic Ocean off the coast of southeastern South America. Tierra del Fuego is an archipelago off the southern tip of South America. The Strait of Magellan is between the southern tip of South America and Tierra del Fuego. The Strait of Magellan is named for the Portuguese explorer Ferdinand Magellan who led the first mission to successfully circumnavigate the entire world in the early sixteenth century (the early 1500s). South America is the closest continent to Antarctica, since it is only roughly one thousand kilometers between Tierra del Fuego and the northern tip of the Antarctic Peninsula. The Drake Passage is between Tierra del Fuego and the Antarctic Peninsula. The Drake Passage is named for the British explorer Francis Drake, the first Englishman to circumnavigate the entire world. Both the Drake Passage and the Strait of Magellan connect the Atlantic Ocean with the Pacific Ocean.

There is a major mountain range in northwestern Africa: the Atlas Mountains. The tallest mountain in Africa is not in northwestern Africa in the Atlas Mountains; the tallest mountain in Africa is in southeastern Africa in the African Rift Valleys: Mount Kilimanjaro. The second tallest mountain in Africa is also in southeastern Africa in the African Rift Valleys: Mount Kenya. Madagascar is a large island off the coast of southeastern Africa. Madagascar is so large that it may be regarded as a microcontinent. The Mozambique Channel is between Madagascar and Africa. The largest lake in Africa is Lake Victoria, which serves as part of the border among Uganda, Kenya, and Tanzania. The largest hot desert in the world is in northern Africa: the Sahara. There is also a desert in southern Africa: the Kalahari. There is a tropical rainforest in central Africa: the Congo rainforest. The Congo River, which cuts through the Congo rainforest, is the second longest river in Africa. The mouth of the Congo River is at the Atlantic Ocean. The longest river in Africa is the Nile River, which is also the longest river in the entire world. The mouth of the Nile River is at the Mediterranean Sea, a large body of water between Africa and Europe. The Mediterranean Sea is actually a collection of many small seas, including the Aegean Sea, the Adriatic Sea, the Ionian Sea, and the Tyrrhenian Sea. There are several large islands in the Mediterranean Sea, including Cyprus, Crete, Sicily, Sardinia, and Corsica. The Strait of Gibraltar is between Spain (in Europe) and Morocco (in Africa) that connects the Mediterranean Sea with the Atlantic Ocean. The Canary Islands is an archipelago in the Atlantic Ocean off the coast of Morocco.

Iberia is the westernmost part of Europe and includes the countries Spain and Portugal. Iberia may be regarded as a peninsula. Another important peninsula in Europe is Scandinavia, which includes the countries Norway, Sweden, and Finland. To the east of Scandinavia is the Baltic Sea. To the west of Scandinavia is the Norwegian Sea. To the southwest of Scandinavia is the North Sea. To the west of the North Sea is the island Great Britain, which includes England, Wales, and Scotland. The English Channel separates Great Britain from France on mainland Europe. To the west of Great Britain is the island Ireland. The Irish Sea separates Ireland from Great Britain. Further west of Ireland is the island Iceland. Another important peninsula in Europe is Italy. The Alps is a major mountain range that separates Italy from the rest of Europe. The second tallest mountain in Europe is in the Alps: Mont Blanc. The tallest mountain in Europe is Mount Elbrus in the Caucasus Mountains, which are between the Black Sea and the Caspian Sea. The Caspian Sea is the largest land-enclosed body of water in the world. The Caucasus Mountains are one set of mountains that separate Europe from Asia. Another mountain range that separates Europe from Asia is the Ural Mountains, which separate European Russia from Asian Russia. The longest river in Europe is the Volga, the mouth of which is at the Caspian Sea. The second longest river in Europe is the Danube, the mouth of which is at the Black Sea.

The largest continent in the world is Asia. Arabia is a part of the Asian continent and is separated from Africa by the Red Sea. There is a collection of deserts in Arabia that we will collectively call the Arabian Desert. India is a part of the Asian continent. The island Sri Lanka is off the southern coast of India. The Indian Ocean is to the south of India. The Arabian Sea is to the west of India. The Bay of Bengal is to the east of India. India is separated from the rest of Asia by an enormous mountain range: the Himalayas. The tallest mountain in the Himalayas is also the tallest mountain in Asia and the tallest mountain in the entire world: Mount Everest. To the north of the Himalayas is an enormous plateau: Tibet. To the north of Tibet is a large desert in China and Mongolia: the Gobi. The longest river in Asia is the Yangtze River, the mouth of which is at the East China Sea. Japan is an archipelago off the east coast of Asia. The Sea of Japan separates Japan from mainland Asia. The Philippines is an archipelago off the southeastern coast of Asia. The South China Sea separates the Philippines from mainland Asia. Taiwan is a large island between Japan and the Philippines. The Taiwan Strait separates Taiwan from mainland Asia. Indonesia is a major archipelago between Asia and Australia.

The smallest continent in the world is Australia. There is a collection of deserts in Australia that we will collectively call the Great Australian Desert. The deserts that together form the Great Australian Desert include the Great Victoria Desert, the Great Sandy Desert, the Tanami Desert, the Simpson Desert, and the Gibson Desert. There is a major mountain range along the east coast of Australia: the Great Dividing Range. The tallest mountain in Australia is in the Great Dividing Range: Mount Kosciuszko. The longest river in Australia is the Murray River, the mouth of which is at the Indian Ocean. New Zealand appears to be two islands to the east of Australia, but the New Zealand islands are actually a part of the largest microcontinent in the world: Zealandia. The Tasman Sea is between Zealandia and Australia. Tasmania is an island to the south of eastern Australia. The Bass Strait separates Tasmania from Australia.

There happens to be an ocean at the North Pole: the Arctic Ocean. There happens to be a continent at the South Pole: Antarctica. The tallest mountain in Antarctica is Mount Vinson. The longest river in Antarctica is the Onyx River. The closest continent to Antarctica is South America, since it is only roughly one thousand kilometers between the northern tip of the Antarctic Peninsula and Tierra del Fuego, an archipelago off the southern tip of South America. The Drake Passage is between the Antarctic Peninsula and Tierra del Fuego. The Drake Passage connects the Atlantic Ocean with the Pacific Ocean.

The Pacific Ocean is the largest ocean in the world. Hawaii is an important archipelago in the middle of the Pacific Ocean. Three other archipelagoes in the Pacific Ocean are Micronesia, Melanesia, and Polynesia.

Atoms, Chemical Bonding, and States of Matter

All materials in the universe (such as solids, liquids, and gases) are composed of atoms. Atoms are composed of even smaller particles. The center of the atom is called the nucleus, since the center of anything is often called its nucleus. For example, the center of a biological cell is called the cellular nucleus, and the center of an entire galaxy is called the galactic nucleus. The center of an atom is more properly called the atomic nucleus, but we will often simply refer to it as the nucleus. Surrounding the atomic nucleus are electrons. The atomic nucleus is positively charged, and electrons are negatively charged. Like charges repel, and unlike charges attract. In other words, positive and positive repel, negative and negative repel, and positive and negative attract. It is the attraction between the positive nucleus and the surrounding negative electrons that holds the atom together. The atomic nucleus is composed of even smaller particles: protons and neutrons. Protons are positively charged. In fact, it is because of the protons that the entire atomic nucleus has a positive charge. Neutrons have zero electrical charge. In other words, neutrons are neutral. This is why they are called neutrons!

The number of protons in the nucleus is the single most important number of the atom. The number of protons in the nucleus is so important that it is called the atomic number. The atomic number, which is always the number of protons in the nucleus, is so important that an atom is named solely based on its atomic number. For example, every atom in the universe with twelve protons in its nucleus is considered to be a magnesium atom. As another example, every atom in the universe with seven protons in its nucleus is considered to be a nitrogen atom. We are not saying that the number of neutrons is irrelevant, nor are we saying that the number of electrons is irrelevant. The neutrons and the electrons are quite important. We are saying that the atomic number is always the number of protons, and the name of an atom is based only upon its atomic number, the number of protons.

Consider an atom where the number of electrons balances the number of protons. Since protons are positive and electrons are negative, the atom is neutral overall. Now suppose we add extra electrons to the atom. Since electrons are negative, the atom will no longer be neutral overall; the atom will now be negative overall. Suppose instead that we removed electrons from the atom in the first place. Now the atom will be positive overall. A charged atom is called an ion. Therefore, changing the number of electrons results in ions. For example, consider the sodium atom with the symbol Na. The atomic number of sodium is eleven, meaning that every sodium atom in the universe has eleven protons. We will make this clear with a subscript before the atom’s symbol as follows: ₁₁Na. If the sodium atom were neutral, it would have eleven electrons as well, but suppose we add three more electrons. Since electrons are negative, we now have an ion with a charge of negative three. We write the charge as a superscript after the symbol of the atom as follows: ₁₁Na^3–. Even though the charge is read negative three, the superscript is written in the strange way 3–. As another example, consider the aluminum atom with the symbol Al. The atomic number of aluminum is thirteen, meaning that every aluminum atom in the universe has thirteen protons. We make this clear with a subscript before the atom’s symbol as follows: ₁₃Al. If the aluminum atom were neutral, it would have thirteen electrons as well, but suppose we remove two of its electrons. We now have an ion with a charge of positive two. We write the charge as a superscript after the symbol of the atom as follows: ₁₃Al²⁺. Even though the charge is read positive two, the superscript is written in the strange way 2+. A positive ion is called a cation, and a negative ion is called an anion. In other words, an anion (a negative ion) has extra electrons, while a cation (a positive ion) is deficient (has lost) electrons.

If we change the number of neutrons, we do not get ions, since neutrons are neutral. So, adding or removing neutrons does not change the charge at all. If we change the number of neutrons, what we are changing is the mass of the atom. The atomic mass of an atom is the number of protons plus the number of neutrons. We do not include the electrons when calculating the mass of the atom because an electron is almost two thousand times less massive than a proton or a neutron. Thus, electrons contribute a minuscule amount to the mass of an atom. A proton and a neutron have roughly equal amounts of mass, which is why we count them equally. When we change the number of neutrons, we are changing the atomic mass of the atom. Two atoms with the same atomic number but different atomic mass are called isotopes. Therefore, changing the number of neutrons results in isotopes. For example, consider the carbon atom with the symbol C. The atomic number of carbon is six, meaning that every carbon atom in the universe has six protons. We make this clear with a subscript before the symbol of the atom as follows: ₆C. However, carbon has three isotopes: carbon-twelve, carbon-thirteen, and carbon-fourteen. An isotope is named based on its atomic mass. Thus, the numbers twelve, thirteen, and fourteen are the atomic masses of these isotopes of carbon. We make this clear with a superscript before the symbol of the atom as follows: for carbon-twelve, for carbon-thirteen, and for carbon-fourteen. Notice that carbon always has six protons, but the carbon-fourteen isotope has eight neutrons, since six plus eight equals fourteen. The carbon-thirteen isotope has seven neutrons, since six plus seven equals thirteen. The carbon-twelve isotope has six neutrons, since six plus six equals twelve. As another example, consider the oxygen atom with the symbol O. The atomic number of oxygen is eight, meaning that every oxygen atom in the universe has eight protons. We make this clear with a subscript before the symbol of the atom as follows: ₈O. However, oxygen has three isotopes: oxygen-sixteen, oxygen-seventeen, and oxygen-eighteen. An isotope is named based on its atomic mass. Thus, the numbers sixteen, seventeen, and eighteen are the atomic masses of these isotopes of oxygen. We make this clear with a superscript before the symbol of the atom as follows: for oxygen-sixteen, for oxygen-seventeen, and for oxygen-eighteen. Notice that oxygen always has eight protons, but the oxygen-eighteen isotope has ten neutrons, since eight plus ten equals eighteen. The oxygen-seventeen isotope has nine neutrons, since eight plus nine equals seventeen. The oxygen-sixteen isotope has eight neutrons, since eight plus eight equals sixteen.

Let us apply everything we have discussed about atoms to the following examples. Consider the neon atom with the symbol Ne. Now suppose we write ^2–. This neon atom has ten protons, eleven neutrons, twelve electrons, an atomic number of ten, an atomic mass of twenty-one, and a charge of negative two. As another example, consider the boron atom with the symbol B. (There are borons in this class!) Now suppose we write ³⁺. This boron atom has five protons, four neutrons, two electrons, an atomic number of five, an atomic mass of nine, and a charge of positive three.

Atoms form chemical bonds with one another. Although there are several types of weak chemical bonds, there are only three types of strong chemical bonds: the ionic bond, the covalent bond, and the metallic bond. First, we discuss the ionic bond. Consider a neutral atom that surrenders (loses) one or more of its electrons. This would turn the atom into a positive ion (a cation). Now suppose another neutral atom accepts or receives the electron or electrons that the first atom surrendered. This would turn the second atom into a negative ion (an anion). Since unlike charges attract each other, the cation (the positive ion) and the anion (the negative ion) will attract each other. This attraction between two oppositely charged ions is called an ionic bond. A collection of atoms chemically bonded to each other is called a molecule, and there are many examples of molecules built from ionic bonding. For example, a neutral sodium atom almost always surrenders one of its electrons to become the sodium cation Na¹⁺. A neutral chlorine atom almost always accepts one electron to become the chlorine anion Cl^1–. If a sodium cation and a chlorine anion attract each other, they together become the sodium chloride molecule, which we write as NaCl. The sodium chloride molecule has a common name: ordinary table salt. In other words, the salt that we cook with and that we put on our food is sodium chloride, which is built from ionic bonding. As another example, a neutral magnesium atom almost always surrenders two of its electrons to become the magnesium cation Mg²⁺. A neutral chlorine atom can accept one of these electrons to become the chlorine anion Cl^1–, and another neutral chlorine atom can accept the other electron to become another chlorine anion Cl^1–. If a magnesium cation attracts two chlorine anions, they together become the magnesium chloride molecule, which we write as MgCl₂. Hence, magnesium chloride is another example of a molecule built from ionic bonding.

An ionic bond results when electrons are transferred from one atom to another, but electrons can also be shared more or less equally between two atoms. This sharing of electrons between two atoms is called a covalent bond, and there are many examples of molecules built from covalent bonding. For example, an oxygen atom may share a pair of electrons with a hydrogen atom. If such an oxygen atom shares another pair of electrons with another hydrogen atom, then we have a molecule with one oxygen atom sharing electrons with two hydrogen atoms. This is a molecule built from covalent bonding. This molecule is written H₂O and has a common name: water. In other words, the water we drink and the water that composes most of the human body is built from covalent bonding. Under ordinary temperatures and pressures, the oxygen atom will never remain by itself; it will almost always covalently bond with other atoms. The oxygen atom will even covalently bond with another oxygen atom. Two oxygen atoms covalently bonded with each other is called the oxygen molecule, which is written O₂. This oxygen molecule O₂ is the form of oxygen that all humans and all animals must inhale to survive. All humans and all animals must exhale carbon dioxide to survive. Carbon dioxide is another molecule built from covalent bonding and is written CO₂. The carbon atom often covalently bonds with four atoms at the same time with a tetrahedral geometry, since the geometrical shape of the resulting molecule is called a tetrahedron. Remarkably, the silicon atom often covalently bonds with four atoms at the same time with a tetrahedral geometry as well.

The metallic bond is the sharing of an enormous number of delocalized electrons among an enormous number of atoms. This type of bond is called a metallic bond since it is usually how the atoms of a metal are held together, such as the atoms that compose a sample of pure aluminum, pure iron, pure nickel, pure copper, pure zinc, pure silver, pure tin, pure platinum, pure gold, or pure lead. Whereas ionic bonding and covalent bonding both result in molecules, metallic bonding does not result in molecules. A sample of pure gold for example is composed of an enormous number of gold atoms all sharing an enormous number of delocalized electrons among them. Although the gold sample is composed of an enormous number of atoms as are all materials in the universe, the gold sample is not composed of molecules. Again, atoms form molecules through ionic bonding or covalent bonding, but atoms do not form molecules through metallic bonding.

Under which circumstances do we expect ionic bonding, covalent bonding, or metallic bonding? As a gross simplification, all the atoms in the Periodic Table of Elements can be divided into three categories: metals, reactive nonmetals, and noble gases. Generally but not strictly, reactive nonmetals bond with one another covalently, metals bond with one another metallically, and metals and reactive nonmetals bond with one another ionically. Generally but not strictly, the noble gases do not participate in any chemical bonding, which is why the noble gases are also called the inert gases. Caution: this discussion is a gross simplification. For example, there is a fourth category of atoms called the metalloids, which have properties intermediate between the properties of metals and reactive nonmetals.

The three states of matter are the solid phase, the liquid phase, and the gas phase. A solid is the state of matter at relatively cold temperatures where the atoms have the least amount of energy. The atoms of a solid have such little energy that they remain at particular locations within a rigid chemical structure. Although the atoms can vibrate, they nevertheless cannot move away from their particular locations. As a result, a solid has a definite volume and a definite shape. A liquid is the state of matter at relatively intermediate temperatures where the atoms have enough energy to move, but the atoms still chemically bond with each other. A liquid still has a definite volume, but a liquid has an indefinite shape; a liquid can flow. A gas is the state of matter at relatively hot temperatures where the atoms have so much energy that they can move completely freely from one another. As a result, a gas not only has an indefinite shape like a liquid but has an indefinite volume as well. The process by which a solid becomes a liquid is called melting. The reverse of melting is called freezing, the process by which a liquid becomes a solid. The process by which a liquid becomes a gas is called vaporizing. The reverse of vaporizing is called condensing, the process by which a gas becomes a liquid. The process by which a solid turns directly into a gas (skipping the liquid state) is called subliming. The reverse of subliming is called deposing, the process by which a gas turns directly into a solid (skipping the liquid state).

A substance composed of only one type of atom is called an element. A substance composed of only one type of molecule (which is itself composed of more than one type of atom) is called a compound. A substance composed of a variety of different compounds is called a mixture. At any particular pressure, elements and compounds usually suffer a phase change at a specific temperature. In this case, the melting temperature is always the same as the freezing temperature since melting and freezing are simply reverse processes of one another, and the vaporizing temperature is always the same as the condensing temperature since vaporizing and condensing are simply reverse processes of one another. For example, the compound H₂O is ice in the solid phase, liquid water in the liquid phase, and water vapor (or steam) in the gas phase. At normal atmospheric pressure, ice melts to liquid water at zero degrees celsius (or thirty-two degrees fahrenheit), but this means that liquid water freezes to ice also at zero degrees celsius (or thirty-two degrees fahrenheit). Similarly, liquid water vaporizes to water vapor (or steam) at one hundred degrees celsius (or two hundred and twelve degrees fahrenheit) at normal atmospheric pressure, but this means that water vapor (or steam) condenses to liquid water also at one hundred degrees celsius (or two hundred and twelve degrees fahrenheit) at normal atmospheric pressure. Caution: since mixtures are composed of a variety of different compounds, a mixture will suffer a phase change over a range of different temperatures, even at a particular pressure.

copyeditor: Michael Brzostek (Spring2023)

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

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