The earths rotation axis, which is tilted 23.5 from the

Chapter 12, Problem 12.131

(choose chapter or problem)

The earths rotation axis, which is tilted 23.5 from the plane of the earths orbit, today points to Polaris, the north star. But Polaris has not always been the north star because the earth, like a spinning gyroscope, precesses. That is, a line extending along the earths rotation axis traces out a 23.5 cone as the earth precesses with a period of 26,000 years. This occurs because the earth is not a perfect sphere. It has an equatorial bulge, which allows both the moon and the sun to exert a gravitational torque on the earth. Our expression for the precession frequency of a gyroscope can be written = t/Iv. Although we derived this equation for a specific situation, its a valid result, differing by at most a constant close to 1, for the precession of any rotating object. What is the average gravitational torque on the earth due to the moon and the sun?