Newton's law of universal gravitation

Here is one of the biggest ideas in all of science: every object that has mass pulls on every other object that has mass. The Earth pulls the apple, so it falls. But the apple also pulls the Earth (just far too weakly to notice), and the Earth pulls the Moon, and the Sun pulls every planet. Newton's astonishing claim was that the very same rule that makes an apple drop also keeps the Moon circling us. That is why it is called universal: one law for the heavens and the ground.

Precisely, the gravitational force between two objects is attractive, points along the straight line joining their centres, and has magnitude F = G m1 m2 / r^2. Here m1 and m2 are the two masses, r is the distance between their centres, and G is the gravitational constant, a fixed number that sets the overall strength. Read the formula in words: the pull grows if either mass grows, and it weakens fast as they move apart, dropping with the square of the distance.

A point that trips people up: by Newton's third law, the Earth pulls the apple with exactly the same force that the apple pulls the Earth. They are equal in size and opposite in direction, even though the masses are wildly different. The apple accelerates a lot because it is light; the Earth barely budges because it is enormous. Newton's law is superbly accurate for everyday life and space travel; only in very strong fields or at very high speeds does Einstein's general relativity take over.