Angle Through the Celestial North Pole Moves

Question

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.

Answer 1

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.