Newtonian gravitation

Every object with mass pulls on every other object with mass — you, this screen, and a distant star are all tugging on each other, just with forces too small to notice in most cases. Newton's insight was that a single formula describes all of it, from falling apples to orbiting planets.

The force depends on the product of the two masses and falls off with the square of the distance between them: double the distance and the force drops to a quarter, not a half — a common trip-up, since "inverse square" often gets misremembered as "inverse."

Weight and mass get confused here too. Your mass stays the same everywhere, but your weight — the gravitational force on you — depends on what you're standing on. A more massive planet doesn't automatically pull harder at its surface than a less massive one; a small, dense planet can have stronger surface gravity than a large, fluffy one, because surface gravity depends on mass and radius together.