I. The Shape of the Earth A. During the Dark Ages, most Europeans believed that the earth was flat. To this day, there is an "International Flat Earth Society"! You think I'm making this up? Check it out by clicking here. B. Today, we've gone back to the ancient Greek and mediæval Arab idea that the earth is round. C. Actually, the earth isn't perfectly round. In fact, there's an entire branch of science, known as "geodesy," devoted to accurate measurement of the shape and size of the planet. 1. If the planet were uniform in composition (or at least uniformly layered) and not rotating, its gravitational force would pull on it evenly in all directions and thus produce a perfectly round sphere. 2. The actual shape of the earth, however, reflects the planet's rotation around its axis. a. Rotation produces centrifugal force, which partially offsets the gravitational acceleration downward. b. This centrifugal force is greatest along the equator, where the earth is widest and, therefore, spinning the fastest along the surface. c. So, the planet bulges a bit along the equator and is flattened a bit at the poles (where the surface spinning is slowest), which distorts the earth's shape into a flattened oval. This shape is called an "oblate spheroid." d. The polar diameter (a pin stuck through the earth from the North Pole through the center of the earth to the South Pole) is about 12,640 km (~7,900 mi.). e. The equatorial diameter (a pin stuck through the earth from one point on the equator through the center of the earth and out through the equator at the exact opposite point, or antipode) is about 12,680 km (~7,962 mi.) 3. In addition to this rotation-caused "oblateness," the earth's shape is further distorted from a perfect sphere by complex variations in the density of the materials in the earth's interior a. This affects gravitational acceleration at the surface, creating wide areas with slight dips or bulges in the surface of the earth. i. I don't mean valleys and mountains (though they, too, can distort gravitational fields) ii. These broad dips and bulges would be seen even in a completely oceanic planet, because they are the result of anomalies in the interior of the planet. b. The deepest such dips are in the northern Indian Ocean just south of India, the western Atlantic east of the Caribbean, central Africa, and in the western Pacific: The surface dips anywhere from 10 meters to 100 meters (about 30 to 330 feet). c. The highest such bulges are found in the eastern Pacific, the northern Atlantic, and in the southern Indian Ocean just southeast of Africa: The surface bulges anywhere from 20 to 60 meters (roughly 60 to 200 feet). d. The result is a somewhat lumpy shape, which has been given a name, a "geoid" (or Earth-shaped object, in case we bump into any others in space!) 4. Further complications, of course, include the complex surface structure of the earth: There are mountains (Mt. Everest, near the Nepal, Tibet, and Bhutan borders, is roughly 9,500 m high [about 29,000']) and abyssal basins in the oceans (the Marianas Trench east of the Philippines is about 12,000 m deep [about 36,000'], deep enough to lose Everest in!), and these can themselves affect local gravitational attraction. D. For the time being, though, we'll just assume that the earth is a perfect sphere, that all points on its surface are equally distant from its center. All these distortions are quite small, after all. II. Size of the Earth A. The planet's circumference is about 40,000 km or, more precisely, 39,800 km (roughly 24,900 mi.) -- this is measuring the "girth" of the planet along the equator. B. Its diameter varies. 1. The equatorial diameter is 12,680 km. 2. The polar diameter is 12,640 km. 3. We can round that to about 13,000 km (or 8,000 mi.). III. Earth Motions A. The earth and the solar system to which it belongs is constantly in motion in space ("the Final Frontier"). B. We are not subjectively aware of this due to gravity and to sharing the planet's momentum. C. This motion is apparent to us in more indirect fashions, of course: 1. Day and night alternate as the earth rotates around its axis toward the sun and away from it. 2. The sun, moon, planets, and stars seem to rise in the east and set in the west, because our planet rotates from west to east. 3. Rotation also distorts the path of moving objects. 4. The revolution of the earth around the sun is indirectly revealed in the experience of seasons and the different lengths of day and night with season and latitude. D. Gravity is what keeps us on the planet's surface, in spite of the centrifugal force of rotation. 1. Gravitation is the mutual attraction between any two masses. a. It declines with the distance between the two masses, specifically with the square of the distance between their two centers. A relationship where one thing increases as another decreases is called an "inverse" relationship, which looks like this when you graph it: lots |* g | * r | * a | * v | * i | * t 0|____________* 0 far out distance squared b. Gravitation increases with the mass of the objects involved, specifically with the product of their two masses. A relationship between two things where one increases as the other increases is called a "direct" relationship. Graphed, it looks like this: lots | * g | * r | * a | * v | * i | * t 0*_____________ 0 way heavy mass 1 X mass 2 c. Newton's law of gravitation, then, is: F = Gm1m2/r2, where: F = the force of gravitation G = the gravitational constant m1 = the first object's mass m2 = the second object's mass r2 = the square of the distance between them I won't require you to memorize the equation, just the idea that gravitation varies directly with the product of the masses involved and inversely with the square of the distance involved. Or, even more basically, gravitation is stronger between larger masses and weaker with distance between them. 2. Gravity is a special case of gravitation, which is more relevant to understanding processes on this earth: It involves the attraction between a huge object (e.g., the planet) and a much dinkier one (e.g., you). 3. Gravity varies a bit on our planet's surface. a. Things weigh a bit less at the equator than at the poles and at the tops of mountains than in valleys, because they are a bit farther from the earth's center, from which Earth's gravity is exerted. b. This difference is so small, though, that we'll ignore it for the purposes of this class. 4. Effects of gravity include: a. Life forms and buildings must be built to withstand the crushing tendency of gravity. i. The larger a creature is, the greater the proportion of its body that must be given to support structures (and the less to vital organs). For a given species, this principle limits the upper size of bodies. ii. Some bodily forms, such as the exoskeleton model of insects, are thereby limited to very small creatures, who have to pack their vital parts into a rigid external frame, which grows proportionately larger as the mass of the creature does. iii. We big critters are built on the endoskeleton model, which gives our vital organs a little more flexible slack. iv. Our very forms reflect the constant gravitational force of our planet's size and density! b. Gravity provides energy for the work of earth processes. i. This is the potential energy of any object farther above the earth's center than a surface nearby ii. Once these objects begin to move, the potential energy is converted into the kinetic energy of motion (and the thermal energy of friction). iii. Some examples of earth processes driven by gravitational potential energy include river flow, glacier flow, landslides, cliff erosion by rockfall, soil creep down a slope, and avalanches. c. Gravity separates and layers substances of different densities, and we'll see this theme repeated throughout the course: i. The earth's atmosphere shows density layering. ii. The earth's interior shows this layering. iii. Geo-nerd experiment: Shake some oil and vinegar together vigorously, thoroughly mix them up, and then let the bottle alone. Voilà!!!: Gravity layering. Admire for a bit, repeat, and enjoy your salad. E. Rotation is the movement of the earth around its own axis. 1. The speed of rotation is 15° per hour, or 360° (full circle) each day. How'd I get 15? Divide 360° by 24 hours. a. At the equator, this works out to roughly 1,660 km/hr (about 1,040 mph). b. So, why didn't I just say that in the first place? Because this speed is only true at the equator, which is a great circle 39,800 km around (divide that by 24 hours and you get ~1,660 km/hr). The problem is that the speed of rotation drops as you move away from the great circle route of the equator: At 60° N or S, the circumference of that parallel is only half that of the equator, so the speed is only 830 km/hr. That's why we use angular speed when describing the rotation of a sphere. 2. Major side effects of rotation include: a. Day and night alternate as a location spins toward the sun and then away from the sun. b. The sun, moon, and stars rise in the east and set in the west, spinning around the North Star or the Southern Cross, as Planet Earth spins from west to east. Our planet rotates in the opposite direction from the apparent motion of the (relatively) stationary sun. F. Revolution is the motion of the earth around the sun each year. 1. Revolution is NOT the same thing as rotation, and it is important to use these two terms correctly in the earth sciences. 2. Where rotation takes one day, revolution takes one year. Our calendar, the tropical year, is based on this earth motion. 3. Plot complications: a. Revolution is not an even multiple of rotation: The two motions are not synchronized. b. Revolution takes a skosh under 365 and a quarter days (that's 365.24219352 days for you precision freaks) in a tropical year. c. So, what do we do about that not-quite-a-quarter-day bit? Yep, leap year. i. Every fourth year, we add a day to February. ii. We experience a February 29th on any year that can be evenly divided by four: 1960, 1964, 1968, ... 2004, 2008 iii. But that still doesn't take care of the problem, because the difference isn't a perfect quarter day. So we DON'T have a February 29th on the turns of centuries: 1900 was not a leap year, nor was 1800 or 1700. iv. And that still doesn't do the trick, so we DO have a leap year on the turns of centuries IF they can be divided evenly by 400 (sigh). That's why we had a 29th of February in 2000 (and 1600 and 2400). v. So, calendars are a pain. Given enough time, they get out of synch. The best system was the Mayan calendar. Our system is hairier. a. It has its roots in Babylonian, Egyptian, and Greek systems adopted and modified by the Romans and then tweaked by order of a Christian Emperor, Justinian, in 526 CE (or AD). b. Justinian asked a monk named Dionysius Exiguus to create a calendar reckoned from the birth of Jesus, instead of the traditional founding of the city of Rome (April 21, 753 BCE or BC). He was a bit innumerate. He somehow decided that Jesus was born 753 years after the founding of Rome (never mind that the governor, Herod, who figures in the birth story, had died in 749), which would make Jesus' execution in AD 33 square up with his reported age at death of 33. Now, all that confusion is understandable. Dionysius Exiguus did something goofy, though: number forward from 1 (Anno Domini or AD or, to non-Christians, CE for Common Era) AND backward from 1 (Before Christ or BC or Before the Common Era or BCE): There's no year 0 in his system! That's why "The Millenium" does not start until 1 January 2001. 4. Orbital dynamics: a. The earth is roughly 150,000,000 km (or 93,000,000 mi.) from the sun (that's 1.0 atronomical units, or AU, which works out to 149,597,870.7 km for you precision fans). This is measured along the semi-major axis, that is, taking the long or major axis of the earth's orbit and dividing by two. b. The semi-minor axis is 149,576,880.8 km (taking the short or minor axis and dividing by two). c. This disparity between the semi-major and the semi-minor axes means that the earth's orbit is elliptical, with an eccentricity at the present time of 0.017, which is pretty close to circular. d. Because the earth's orbit is faintly elliptical, however, the earth gets as close as 146,400,000 km to the sun, when it crosses the major axis of its orbit around ... January 3 (yes, in our Northern Hemisphere winter), a day called "perihelion" for "close to the sun." e. Similarly, when the earth crosses its major axis on the other side of the year, it gets as far as 151,200,000 km from the sun. This takes place around the 4th of July, a day called "aphelion" or "far from the sun" (another reason to go watch fireworks!). f. The difference between perihelion and aphelion only makes about a 7 percent difference in incoming solar radiation. g. The direction of revolution: If you were out in space, the Final Frontier, suspended above the North Pole, the earth would revolve counterclockwise around the sun, the same direction as it rotates each day. 5. The major effect of revolution is the seasons a. As we've already seen, though, revolution all by itself cannot explain seasons (remember, there's only about 7 percent difference in incoming solar radiation between perihelion and aphelion, and don't let's forget that the Northern Hemisphere and the Southern Hemisphere have opposite seasons). b. There is a second co-factor, which combines with revolution to create the seasons: The tilt of the earth's axis. i. The earth's axis is tilted not quite 23½° from the vertical. Hunh? Vertical to what? you might ask. How can you figure out what is vertical, what is up or down, when you're dealing with a spinning sphere in outer space? ii. There IS a plane of reference, a plane from which we can say the earth's axis is "tilted." This is the "plane of ecliptic." This is the plane of the earth's orbit around the sun. You can picture it as an imaginary flat surface, like a sheet of glass, which sits on the hoop of the earth's orbit and cuts through the exact center of the sun and the exact center of the earth at all points during the year. This imaginary surface is the plane of ecliptic: the plane of the earth's orbit. iii. Geotrivia for you: The reason it's called the plane of ecliptic is this plane forms the zone in the sky from which eclipses of the sun are seen. iv. Interesting geotidbit: The plane of the ecliptic for Planet Earth pretty closely coïncides with those of the other planets in the solar system. This is because the planets formed out of a disk of gas and dust that surrounded the infant sun, so their orbital planes reflect that of this "planetary nebula" out of which they formed. v. So, the earth's axis is tilted 23½° from the perpendicular of the plane of ecliptic (or from the vertical of the plane of ecliptic). For you precision hounds, that'd be 23°26'28". vi. The earth's axis is always tilted at exactly the same angle and in the same direction all year round (well, at least over the course of our lives and that of several generations before and after us). That is, the North Pole of the axis points at Polaris, the Pole Star, or the North Star; the South Pole of the axis points at a small constellation called the Southern Cross. This would be obvious to a "sidereal" observer, someone in a UFO in outer space (with nothing to do and a year to do it in): vii. To a "solar" observer, however, the impression is pretty different. Imagine standing on the surface of the sun's photosphere, looking back at Earth. In the brief nanoseconds before you vaporized, you would see the axis pointing in different directions with respect to you, depending on the time of year you found yourself in this unfortunate situation: 6. The geometry of revolution, axial tilt, and seasonality is governed by the locations of two distinct types of sun ray. a. One of these is the direct ray. i. This is the single solar beam, which strikes the surface of the earth at a right (90°) angle. ii. This is a noon occurence: The direct ray hits the lucky spot at noon. iii. If you are at the location experiencing the direct ray at noon, this sun beam will come precisely out of the zenith (or spot in the midheavens directly above your head). iv. You could think of the direct beam as defining the "noon overhead sun." v. The place experiencing the noon overhead sun is termed the declination of the sun (more precisely, the declination is the latitude experiencing the direct ray). vi. The direct ray of the sun is the peak of concentrated solar energy. b. The other key ray is the tangent ray. i. This is the ray of the sun which strikes the earth at 0°, that is, just brushes the earth and continues on into space. ii. If you were at this location, you would see the sun right on the horizon. iii. In other words, we experience this beam each sunrise and sunset: There is an infinite number of such tangent rays. iv. If we drew a line connecting all places on Earth experiencing tangent rays, all places experiencing either sunrise or sunset, we would create the "circle of illumination." v. The circle of illumination divides the earth into a day half and a night half. vi. The northernmost tangent ray falls somewhere between 66½° N and the North Pole (90°), depending on the time of year; the southernmost tangent ray falls somewhere between 66½° S and the South Pole (90°). vii. Because of atmospheric scattering of light, we actually experience the circle of illumination, not as a sharp line (the way you would on the moon) but as a shaded zone (twilight, dusk, or gloaming). c. Because of the constant tilt of the earth's rotational axis as the planet revolves around the sun, the direct and tangent rays change position over the course of the year, and this is what gives us seasonality. Lecture III.F.7 continues here.
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First placed on web: 09/04/00 Last revised: 02/01/04