# Lecture: The Earth in Space

## Earth Shape, Size, Rotation, Revolution

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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
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
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
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
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
iv. You could think of the direct beam as defining the "noon
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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Document and © maintained by Dr. Rodrigue
First placed on web: 09/04/00
Last revised: 02/01/04