Saturday, March 14, 2009

Nautical Astronomy, The Celestial Sphere

The Earth and the Moon
The earth's major satellite the moon, has motions similar to those of the earth. With respect to the sun, the moon rotates on its axis once in a period of about. 29.5 days, and revolves in its orbit around the earth in exactly the same period of time. Like the earth, the moon's orbit is not a perfect circle. The point of the orbit where the moon is closest to earth is called perigee, and when it is at its greatest distance it is at apogee.

The orbit of the moon is inclined about 5° to the ecliptic, and its axis of rotation is inclined 6.5 degrees to the plane of its orbit. Like the earth, the moon's axis is moving due to precession. As the moon goes through one orbit around the earth, completing one lunar month, its appearance changes. And as it does so, the moon is said to go through a series of phases. Since the moons orbit is only inclined a small amount from the ecliptic it appears to follow the sun through the sky, but falls further behind each day.

At the start of the lunar month (new moon), the moon is between the earth and sun. Each day thereafter the moon appears to have moved about 12 degrees to the east of the sun due to movement in its orbit. This causes the moon to rise about 50 minutes later each day relative to the sun. After about three days, a crescent moon is visible from earth with the points or cusps pointed away from the sun. Because the visible moon is in the process of getting bigger, it is called a waxing crescent. The line dividing the illuminated side from the shadow is called the terminator. When the lunar month is a week old, half of the moon is visible (first quarter). The next phase is called gibbous which is followed by full moon.

At full moon the moon is again in line with earth and sun, but this time the earth lies in the middle. After full moon, the visible moon begins to shrink, or wane, going through gibbous, last quarter, and waning crescent phases back to new moon. Because the moon's orbit is inclined to the ecliptic, the earth, moon, and sun rarely line up perfectly to cause either the moon or earth to pass through the shadow of the other. When they do an eclipse occurs.

The Celestial Sphere and Apparent Motion
Use of heavenly bodies for celestial navigation requires the idea that was accepted as the truth hundreds of years ago and later proved totally false. To use celestial navigation's mathematical principles, you must assume the following to be true.

1. The center of the earth is the center of a great celestial sphere.
2. This sphere has a radius (distance from the center of the earth to the surface of the celestial sphere) of infinite length.
3. All the celestial bodies used in navigation are located on the surface of the celestial sphere at the same distance from the earth.
4. The earth is stationary and the surface of the celestial sphere rotates around the earth, causing the celestial bodies to appear to move across the sky.

What you see from earth, and use in your navigation calculations, is the apparent motion of these bodies on the sphere. It appears to observers on earth that the bodies rise in the east, move in a westerly direction across the sky, and set in the west each day. It also appears that the sun, moon and planets move north, then south, and then north again on the celestial sphere. All of this motion described above is called apparent motion.

Apparent motion is the result of the real motions of the earth, which in some cases are combined with the real motions of the other body. Actual motions effect each celestial bodies apparent motion on the celestial sphere follows:

Sun - The apparent motion of rising and setting results from the earth's rotation. Movement of the sun north and south in the sky with the seasons results from revolution and the inclination of earths axis.

Stars - Rising and setting results from earths rotation, other motions of the stars happen very slowly as a result of precession of the earth's axis.

Planets - Rising and setting and other apparent motions of the planets result from a combination of the earth's rotation and revolution, and the revolutions of the planets.

Moon - The apparent rising and setting and the movement of the moon north or south results from a combination of earth's rotation and revolution, taken together with the moon's rotation, revolution, and precession.