At present, the north star Polaris is located very near the celestial north pole. However, because Earth is inclined 23.5 degrees, the moon's gravitational pull on Earth is uneven. As a result, Earth slowly precesses (moves in) like a spinning top, and the direction celestial traces a out a circular path once every 26,000 years. For example, in approximately A.D. 14,000 years the star Vega- not the star Polaris- will be located at the celestial north pole. As viewed from the center C from the circular path, calculate the angle (to the nearest second) through the celestial north pole moves each year.
The pole completes one revolution every 26,000 years. One revolution is a complete circle of 360 degrees. There are 60 minutes of arc in one degree and 60 seconds of arc in one minute. Thus 360 degrees consists of:
360 degrees = 360*60*60 = 1,290,000 seconds of arc
The angular rate of the pole precession is one revolution (360 degrees = 1,290,000 seconds) every 26,000 years. The angle swept out in arc seconds in one year will be:
(1,290,000)/(26,000) = ?
Can you complete the calculation? Since the question wants the answer to the nearest second of arc, round the answer to the nearest second of arc.
Note: In scientific notation, 1,290,000 = 1.29 * 106; 26,000 = 2.60*104, so the problem can be expressed as:
(1.29/2.6)*(106/104) = (1.29/2.6)*102
Note that 1.29 is almost 1.3 which is 1/2 of 2.6.