Geography 140
Introduction to Physical Geography

Lecture: The Earth in Space

Earth Shape, Size, Rotation, Revolution


  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 
           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."

              [ oblate spheroid, courtesy of NASA ]

           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 
                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!)

              [ geoid, courtesy of NASA ]

        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 
           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.

                   [ plane of ecliptic ] 

              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".

                   [ tilt of the earth's axis ] 

               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):

         [ sidereal view of axial tilt ] 

              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:

                   [ solar view of axial tilt ] 

        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 
           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 
                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 
              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.


Document and © maintained by Dr. Rodrigue
First placed on web: 09/04/00
Last revised: 02/01/04