Newton was familiar with Galileo's work on projectiles, and suggested
that the moon's orbit could be understood as a natural extension of that
theory. He imagined a gun shooting a projectile horizontally from a very
high mountain, and supposed that successive shots drove the projectile
faster and faster.
The parabolic paths become flatter and flatter as the cannon is fired
faster. He imagined that the mountain was so high that air resistance
could be ignored, and the gun was sufficiently powerful.
Eventually the point of landing is so far away that the curvature of the
earth must be taken into account in finding where it lands. In fact if
the curvature of the cannon's path matched that of the Earth the ball
returned to hit the artilleryman on the back of his head. Newton's diagram
of this explanation is shown opposite.
Newton's mountain was impossibly high but he realized that the moon's
circular path around the earth could be caused by the same gravitational
force that pulls cannonball in its orbit, in other words, the same force
that causes objects to fall.
Exercises on this to come soon...