The forces between heavenly bodies are the same type of force as terrestrial gravity.
What kind of force was it? It probably wasn't magnetic, since magnetic forces have nothing to do with mass.
Then came Newton's great insight
. Lying under an apple tree and looking up at the moon in the sky, he saw an apple fall. Might not the earth also attract the moon with the same kind of gravitational force?
The moon orbits the earth in the same way that the planets orbit the sun, so maybe the earth's force on the falling apple, the earth's force on the moon, and the sun's force on a planet were all the same type of force.
There was an easy way to test this hypothesis numerically. If it was true, then we would expect the gravitational forces exerted by the earth to follow the same F m/r2 rule as the forces exerted by the sun, but with a different constant of proportionality appropriate to the earth's gravitational strength. The issue arises now of how to define the distance, r, between the earth and the apple.
An apple in England is closer to some parts of the earth than to others, but suppose we take r to be the distance from the center of the earth to the apple, i.e., the radius of the earth. (The issue of how to measure r did not arise in the analysis of the planets' motions because the sun and planets are so small compared to the distances separating them.) Calling the proportionality constant k, we have
Fearth on apple = k mapple/r2 earth
Fearth on moon = k mmoon/d2 earth-moon .
Newton's second law says a = F/m, so
aapple = k / r2 earth
amoon = k / d2 earth-moon .
The Greek astronomer Hipparchus had already found 2000 years before that the distance from the earth to the moon was about 60 times the radius of the earth, so if Newton's hypothesis was right
, the acceleration of the moon would have to be 602 = 3600 times less than the acceleration of the falling apple.
g / The moon's acceleration is 602 = 3600 times smaller than the apple's.
Applying a = v2/r to the acceleration of the moon yielded an acceleration that was indeed 3600 times smaller than 9.8 m/s2, and Newton was convinced he had unlocked the secret of the mysterious force that kept the moon and planets in their orbits.