Every object with mass attracts every other object with mass. This is Newton’s law of universal gravitation (1687):

$$F = \frac{GMm}{r^2}$$

where $G \approx 6.674 \times 10^{-11}$ N·m²/kg² is the gravitational constant, $M$ and $m$ are the two masses, and $r$ is the distance between their centres.

The inverse square law

Double the distance → one quarter the force. Triple it → one ninth. This inverse square relationship is why gravity weakens with distance but never quite reaches zero. It also explains why orbits are ellipses — a result Kepler discovered empirically and Newton derived mathematically.

Why gravity dominates

Gravity is by far the weakest of the four fundamental forces — roughly $10^{36}$ times weaker than electromagnetism. But it has two decisive advantages:

1. It’s always attractive. Electromagnetic charges cancel (positive + negative = neutral), but mass can’t be negative. Every atom in the Earth pulls on every atom in you.
2. It has infinite range. The strong and weak nuclear forces are confined to atomic scales. Gravity reaches across the universe.

At everyday scales, electromagnetism dominates (it’s what holds your body together). At cosmic scales — planets, stars, galaxies — gravity wins because everything adds up.

From Newton to Einstein

Newton’s law works beautifully for almost everything: predicting planetary orbits, launching spacecraft, calculating tides. But it treats gravity as an instantaneous force acting at a distance, which troubled Newton himself.

Einstein’s general relativity (1915) reframes gravity as the curvature of spacetime caused by mass and energy. Objects follow the straightest possible paths (geodesics) through curved spacetime. For weak fields and slow speeds, this reduces to Newton’s law — but it also predicts gravitational waves, black holes, and the bending of light, all confirmed by observation.

For orbital mechanics, Newton is enough. For GPS satellites (which need nanosecond precision), you need Einstein.