Kepler determined that the orbits of the planets were not perfect circles, but ellipses, with the Sun at one focus.
Kepler determined that a planet moves faster when near the Sun, and slower when far from the Sun.
Keplerís Laws provided a complete kinematical description of planetary motion (including the motion of planetary satellites, like the Moon) - but why did the planets move like that?
Isaac Newton realized that the motion of a falling apple and the motion of the Moon were both actually the same motion, caused by the same force - the gravitational force.
Newtonís idea was that gravity was a universal force acting between any two objects.
Newton knew that the gravitational force on the apple equals the appleís weight, mg, where g = 9.8 m/s2.
W = mg
Newton reasoned that the centripetal force on the moon was also supplied by the Earthís gravitational force.
Fc = mg
Newtonís calculations showed that the centripetal force needed for the Moonís motion was about 1/3600th of Mg, however, where M is the mass of the Moon.
Newton knew, though, that the Moon was about 60 times farther from the center of the Earth than the apple.
And 602 = 3600
From this, Newton reasoned that the strength of the gravitational force is not constant, in fact, the magnitude of the force is inversely proportional to the square of the distance between the objects.
Newton concluded that the gravitational force is:
Directly proportional to the masses of both objects.
Inversely proportional to the distance between the objects.