Newton's Law of Universal Gravitation

Drop an apple from a tree and it falls straight down. Earth is pulling it down hard. But here's the twist: the apple pulls on Earth with exactly the same force. Earth is so enormously heavier than the apple that you never see it budge.

The Moon in the night sky moves by the very same rule. The Moon naturally wants to fly off in a straight line into deep space. But Earth keeps tugging on it with an invisible giant rope. That's why the Moon doesn't shoot away and instead circles around Earth.

An apple falling to the ground and the Moon orbiting in the sky are the same thing. Isaac Newton tied the physics of the ground and the physics of the heavens together with one simple idea: every object in the universe pulls on every other object.

Before that, people believed the rules for the moving stars and the rules for things on Earth were completely different. Thanks to the discovery of universal gravitation, we finally realized the whole universe runs on one and the same order.

The strength of the pull between two objects depends on just two things: their mass, which is how much matter they contain, and the distance between them.

First, the more massive the objects, the stronger the pull. Right now, there's a real pull between you and the desk next to you. But your body and the desk have tiny mass compared with the whole Earth, so you can't feel it at all.

Second, when the distance grows, the pull weakens faster than you might expect. Double the distance and the force doesn't drop to half. It falls to one-fourth, because it is inversely proportional to the square of the distance. Triple the distance and the force drops to one-ninth.

This inverse-square rule is why the many planets of the solar system can keep steady orbits. Planets far from the Sun feel only a weak pull and move slowly. Planets close to the Sun feel a strong pull and race around it.

In everyday talk, we use "universal gravitation" and "gravity" as if they meant the same thing. To be more precise, the gravity we feel on Earth every day is pure gravitational attraction with a little bit of centrifugal force, caused by Earth's spinning, mixed in. People also mix up weight and mass. Weight is the force you get when gravity acts on mass, so it changes from place to place. Mass stays the same everywhere.

Newton's law works very well for calculating a falling apple or a satellite's orbit. But modern physics has widened the picture one step further. Einstein did not see gravity as an invisible hand pulling objects directly.

According to Einstein, gravity is a curve in space-time that objects with mass create by pressing a dent into it. Put a heavy steel ball on a taut rubber sheet and the sheet sags around it, so a small marble nearby rolls toward it. This isn't a perfect picture, though, because the marble rolls only since gravity is already pulling it down. The real key is that not just space but the flow of time bends too.

Modern science explains gravity as the bending of space-time. Still, in everyday conditions, where nothing moves near the speed of light and nothing is as extremely heavy as a black hole, Newton's law alone can predict nature's motion with amazing accuracy.