Newton's reasoning for the orbit of the Moon

Newton reasoned that the same laws of motion and gravity that determine the fall of an apple also determine the motion of the Moon around the earth.

Here is his picture, adapted from the Principia

Here is what Newton did.

He didn't know the value of G.
But by measuring the acceleration of an apple when he dropped it, he could measure M G
Supposing that the mass of the Moon is much less than the mass of the Earth, that is enough to get the relation between the period P of the Moon's orbit and its distance a from Earth.
He knew the distance a to the Moon.
So he could calculate its period P.
"I deduced that the forces whch keep the Planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve; and thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the earth, and found them to answer pretty nearly."

Note that the same laws that govern matter on Earth are those that govern the heavens. This was a complete change in thinking from the Aristotle.

Davison E. Soper, Institute of Theoretical Science, University of Oregon, Eugene OR 97403 USA soper@bovine.uoregon.edu