The problem of calculating the precession of the equinoxes due to the torque of the sun and moon on the Earth is often cited in mechanics texts as a classic example of the behavior of a heavy symmetrical top. Unfortunately this problem is often alluded to but seldom solved. A simple equatorial band model for the Earth and smeared out mass distributions for the sun and moon are used herein to solve this problem. It is found that one intuitively apparent approximation for the gravitational force on the band results in a precession period that is too long by a factor of 3/2, whereas a slightly more sophisticated approach provides an answer good to better than one percent.