If the earth were a sphere, the gravitational attraction of the sun, moon, and planets would at

Question:

If the earth were a sphere, the gravitational attraction of the sun, moon, and planets would at all times be equivalent to a single force R acting at the mass center of the earth. However, the earth is actually an oblate spheroid and the gravitational system acting on the earth is equivalent to a force R and a couple M. Knowing that the effect of the couple M is to cause the axis of the earth to process about the axis GA at the rate of one revolution in 25,800 years, determine the average magnitude of the couple M applied to the earth. Assume that the average specific weight of the earth is 3 344 lb/ft , that the average radius of the earth is 3960 mi, and that I =2/5mR2.