A luminous star with the same density as the Earth and a diameter 250 times that of the Sun would not, because of its attraction, allow any of its rays to reach us. It is therefore possible that the largest luminous bodies in the universe are, for that very reason, invisible. — Pierre-Simon Laplace, Exposition of the System of the World (1796) These sentences are in the first edition of the Exposition of the System of the World. Laplace wrote them at a time when people believed, like Newton, that light was made of particles. If light is a swarm of corpuscles, gravity must pull on them as it pulls on a stone. And then, if a star is compact enough, the light it emits will fall back, like a stone thrown upward.
To know how a planet attracts a point, one must add up the attraction of each of its pieces. Each piece pulls in a different direction, and adding forces is laborious: they are vectors, with three components each. Eighteenth-century mathematicians discovered a shortcut, and Laplace turned it into a tool. Adding numbers instead of arrows For a mass $M$ concentrated at a point, consider the number $$V = \frac{M}{r},$$where $r$ is the distance to the mass (we leave out the constant $G$). This number, which later received the name potential, holds all the information about the force: the components of the attraction in each direction are the derivatives of $V$ in that direction. And the great advantage is that, for several masses, the potentials simply add like numbers. First one adds the potential of all the pieces of the planet; then, with a derivative, one gets the force.
If the apple falls, why doesn’t the Moon? Before Newton the answer seemed simple: heaven and Earth followed different rules. On Earth, things fall. In the heavens, the stars and planets turn in perfect circles forever. Newton’s great idea was to distrust that separation: perhaps the Moon is falling all the time. Newton’s cannon The apple tree in the orchard of Woolsthorpe Manor that tradition identifies as “Newton’s tree”.David Smith · Wikimedia Commons · CC BY-SA 2.0 In a draft for the Principia, Newton proposed a thought experiment. Imagine a cannon on top of a very high mountain, firing horizontally. With little powder, the ball lands nearby. With more, it lands further away. But the Earth is round: if the ball is fast enough, the ground curves away beneath it exactly as fast as it falls. The ball falls forever and never reaches the ground. It is in orbit.