The Earth, Sun, and Moon

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.

Figure 4: The vernal equinox from two perspectives.

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.

Figure 6: 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. *Image illustrative only; number of intersections is greater.

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.