Here we will retrace the calculation, which linked the gravity observed on Earth with the Moon's motion across the sky, two seemingly unrelated observations. If you want to check the calculation, a hand-held calculator is helpful. We assume that the Moon's orbit is a circle, and that the Earth's pull is always directed toward's the Earth's center. The distance R to the Moon is then about 60 R E . If m is the mass of the Moon, that is the force which keeps the Moon in its orbit.
R E Suppose the time required for one orbit is T seconds.
Whatever velocity the Moon has was probably acquired when it was created. With a hand held calculator, it is easy to find the square roots of the two terms. The capital G is known as the constant of universal gravitation. That is the number we need to know in order to calculate the gravitational attraction between, say, two spheres of 1 kilogram each. Unlike the attraction of the Earth, which has a huge mass M, such a force is quite small, and the number G is likewise very, very small.