Re: how many times greater is the earth's gravitational force on the moon than

Actually, the gravitational forces of the Moon on the Earth and Earth on the Moon are exactly the same size. The only difference is that they point in opposite directions (the Moon is pulled toward the Earth and the Earth toward the Moon). You can see this by looking at the equation for gravitional forces: F = G*M*m/(d*d) where F is the force, G is a constant number, M and m are the two masses, and d is the distance between them. The equation doesn't discriminate between the two masses, so the force is the same for both.

However, the acceleration of the two masses, a=F/m, can be different. In the case of the Earth and Moon, the Moon's acceleration is about 81 times greater than the Earth's, because the Moon has 81 times less mass.

Any high school or college physics textbook will give you more information on this topic.

Pauline