That is a pretty small number. Gravity is a pretty weak force as fundmental forces go. If m E is the Earth and m m is the moon, Newton's second law for the Moon becomes Notice how the moon's mass goes away in the last equation. That is why Galileo was right about heavy and light falling bodies. They both fall with the same acceleration.
Lets look at the apple and the moon problem.
Newton knew Earth-Moon distance was about 60 Earth radii. That is the prediction. Remember the centripetal accretion formula above. With this we can compare what Newton predicts and what is really seen. The two values of a c come out pretty close.