He was led to this demonstration through considering the orbital motion of the moon.
According to the familiar story, which has become one of the classic myths of science, Newton was led to take up the problem through observing the fall of an apple.

Voltaire is responsible for the story, which serves as well as another; its truth or falsity need not in the least concern us.

Suffice it that through pondering on the familiar fact of terrestrial gravitation, Newton was led to question whether this force which operates so tangibly here at the earth's surface may not extend its influence out into the depths of space, so as to include, for example, the moon.

Obviously some force pulls the moon constantly towards the earth; otherwise that body would fly off at a tangent and never return.

May not this so-called centripetal force be identical with terrestrial gravitation?
Such was Newton's query.