The Earth, Sun and Moon
The
Earth
Earth,
which is our base from which we look into space, is constantly moving.
Understanding this movement is one of the most useful and important things in
astronomy.
The
earth orbits the sun in an elliptical orbit and the moon orbits the earth with
the same kind of orbit. Looking down from the north pole, the earth spins in a
counterclockwise direction on an imaginary line called its axis once every day.
This accounts for the fact that the sun rises in the east and sets in the west.
The earth’s axis is tilted with respect to the plane of its orbit at an angle of
about 23.4 degrees. If we position ourselves high above the north pole, we would
see that the earth orbits the sun in a counterclockwise motion, coming to the
same position among the stars every 365.26 earth days. We would also see that
the moon also orbits the earth in a counterclockwise motion. This is illustrated
in the following example.
Figure
1: The directions of the orbits of the earth and moon.
The
average distance from the earth to the sun, the semimajor axis of its orbit, is
149,597,890 km. This distance was not known until recently and it is called the
astronomical unit or AU. The distances of the other planets to the sun are
usually measured in astronomical units.
Because
of the tilt of the earth, not every place on earth gets light every day. Also,
some places have extremely short days.
As the
earth revolves around the sun, the place where light shines the brightest
changes. This motion gives us the different seasons. For instance, the poles
receive less light than does the equator because of the angle that the land
around the poles receive the sun’s light. When the north pole is tilted toward
the sun, the northern hemisphere is presented to the sun at a greater angle than
the southern hemisphere and the northern hemisphere gets warmer. When this
happens, the northern hemisphere gets summer while the southern hemisphere gets
winter. When the south pole is tilted toward the sun, the two seasons reverse
hemispheres. This is illustrated in the following
image.
Figure 2: The positions of earth at the different seasons.
Counterclockwise from lower left: summer, fall, winter, spring (northern
hemisphere).
The
earth’s orbit is called the ecliptic. The plane which contains the ecliptic is
the reference plane for the positions of most solar system bodies. Viewed from
earth, the ecliptic is the apparent motion of the sun among the
stars.
The
earth’s equator is a circle going around the earth which is on a plane that is
perpendicular to the earth’s axis. The equator and the plane on which it lies
are illustrated in the following image.
Figure 3: The equatorial plane.
The
Equinoxes
This
equatorial plane is one of the most important in astronomy because it intersects
the plane of the ecliptic and gives us a reference point in space by which we
can measure the positions of stars. This plane also divides the earth into
halves, the northern half being the northern hemisphere, the other half being
the southern hemisphere. The intersection of these planes is a line, which for
convenience we will call the line of equinoxes. The real definition of equinox
is the point on the celestial sphere which intersects this line, but since the
celestial sphere is an imaginary sphere with any size, the equinoxes are really
lines. Also, for some purposes and illustrations, it is more convenient to think
of the equinoxes as a line extending into space. For other purposes, it is
convinient to think of the equinoxes as directions. The two planes are
illustrated below.
One
half of this line is called the vernal equinox; the other half is called the
autumnal equinox. At two points in the earth’s orbit this line intersects the
sun. These two places mark the start of two of the four seasons, autumn or
spring. The autumnal equinox starts autumn around September 23. From earth, this
marks the time when the sun looks as if it is crossing the plane of the equator
on its way south. The vernal equinox starts spring around March 21. This marks
the time when the sun looks as if it is crossing the plane of the equator on its
way north. The earth carries the plane of the equator along with it. When the
sun looks as if it is on its way north or south, the earth is actually carrying
the equatorial plane along so that it crosses the
sun.
Perpendicular to this line of equinoxes is a line which contains the
solstices. The solstices are points on the ecliptic which start the other two
seasons, summer and winter, when they cross the sun. The summer solstice is one
half of this line, the winter solstice is the other half of this line. The half
of this line that is north of the celestial equator is the summer solstice, the
half that is south of the celestial equator is the winter solstice. Currently,
the winter solstice starts winter for the northern hemisphere at about the time
the earth is closest to the sun. This line is illustrated in the following
example.
Figure 5: The summer and winter solstices.
Because
of centrifugal force involved when an object spins, the earth is not a perfect
sphere, but is somewhat flattened at the poles and bulges out at the equator.
The distance from any point on the equator to the center of the earth is longer
than the distance from either pole to the center of the earth. This is
illustrated in the following image which is exaggerated for clarity. The form
caused by this equatorial bulge is called a
geoid.
The
Moon
The
moon is the earth’s only natural satellite. Its average distance from the earth
is 384,403 km. Its revolution period around the earth is the same length and
direction as its rotation period, which results in the moon always keeping one
side turned toward the earth and the other side turned away from the earth. This
type of motion is called synchronous rotation. The side turned away from the
earth is called the moon’s dark side, even though it is lit half of the time.
The moon’s sidereal period of revolution is about 27.32 days long. This means
that a line drawn through the center of the earth and the moon would point to
the same star every 27.32 days. Due to slight variations in the orbital velocity
of the moon, over a 30 year period, 59% of the moon’s surface is made visible.
This is known as libration.
The
moon’s orbit is not in the plane of the ecliptic and because of the elliptical
nature of the moon’s orbit, it is not always the same distance from the earth.
At the two intersections of the moon’s orbit and the plane of the ecliptic are
two nodes. These nodes regress along the plane of the ecliptic, making one
complete rotation every 18.61 years. See Orbits.
The effect of the Moon
The
moon has a noticeable effect on the earth in the form of tides, but it also
affects the motion and orbit of the earth. The moon does not orbit the center of
the earth, rather, they both revolve around the center of their masses called
the barycenter. This is illustrated in the following
animation.
Figure
7: The earth and moon revolving around the barycenter. Notice how the earth
moves slightly.
The sun
acts on the earth and its moon as one entity with its center at the barycenter.
Since the earth revolves around the barycenter, which in turn orbits the sun,
the earth follows a wobbly path around the sun. This is illustrated in the
following example. To complicate things further, the barycenter is not always in
the same place due to the elliptical nature of the moon’s
orbit.
Figure
8: The wobble of the earth's orbit.
The sun
attracts the moon in such a way that it perturbs its orbit every 31.807 days,
this phenomenon is called evection. The moon also changes the position of the
earth’s equinoxes. The sun and moon each attract the earth’s equatorial bulge,
trying to bring it into alignment with themselves. This torque is counteracted
by the rotation of the earth. The combination of these two forces is a slow
rotation of the earth’s axis, which in turn results in a slow westward rotation
of the equinoxes. Looking down from the north pole, the equinoxes would appear
to be rotating in a clockwise motion. The equinoxes and poles complete a
rotation every 25,800 years. The equinoxes move at a rate of about 50.27 arc
seconds per year. This phenomenon in known as the precession of the equinoxes
and is illustrated in the following image.
Figure
9: The precession of the equinoxes. The blue disk is the equatorial plane. The
white line is the equinoxes. The green plane is the plane of the ecliptic.
The
north pole is currently pointing to a spot near the star Polaris. Because the
vernal equinox is the starting point for most star charts, the charts must be
made for a certain period. The star charts must be updated periodically to
account for this movement of the reference point.
Because
of the seasonal changes in the ice, snow, atmospheric distribution, and perhaps
because of movements in the material within the earth, the geographic poles
constantly change position in relation to the earth’s surface. This phenomenon
is known as the Chandler wobble. Scientists have resolved the change into two
almost circular components, the first with a radius of about 6 meters and a
period of 12 months, the second with a radius of 3-15 meters and a period of
about 14 months.
The sun
and moon, because of their varying distances and directions in relation to the
earth, constantly vary their gravitational attractions on the earth. This makes
the poles wander irregularly by about + or - 9 arc seconds from its average, or
mean, position. This phenomenon is known as nutation and has a period of about
18.6 years. The primary component of this is from the moon and is known as lunar
nutation.
The sun
and moon also constantly change the earth’s rate of
spin.
Star
charts use the mean equinox instead of the true equinox for their zero points.
The mean equinox is the position of the equinox corrected for the slight but
noticeable changes caused by nutation and the Chandler wobble. The mean equinox
is still affected by precession, however, and does change position, but does it
at a constant, predictable rate. Scientists requiring up-to-date precision
information about the position of the earth can use the International Earth
Rotation Service or IERS. This information can be found at the IERS web site at
http://maia.usno.navy.mil/
The
Sun
Because
of the elliptical nature of the earth’s orbit and constant changes in the
earth’s rate of spin because of the previously mentioned phenomena, the sun, as
seen from earth, is moving at a non-uniform rate. This makes it difficult to use
the real position of the sun as a reference for time keeping. For these
purposes, a point which moves at a constant rate around the earth is used
instead of the real position of the sun. This point is called the mean sun and
is the basis for mean solar time
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