Both Kepler's
and Galileo's experiments and calculations involved objects
moving faster the closer they were to other objects. Newton
was the one to explain why.
Newton told
the story of how he was sitting in his mother's garden when
suddenly he was disturbed by the sound of a falling apple
in a nearby tree. It was at that moment he had the idea of
a universal force. The force that was pulling the apple could
be the same force that was holding the moon in orbit!
Newton knew
Kepler's laws and so he suggested that the rate at which an
object falls depends on the strength of the GRAVITATIONAL
FORCE acting on it.
The further
you are away from the Earth - the weaker the force of gravity
pulling you back.
He worked out
that the size of the force acting on the two objects changes
according to the INVERSE-SQUARE LAW.

What Newton
discovered was that everything has gravity! The law of Universal
Gravitation.