Newton's Law of Universal Gravitation: From Kepler's Laws to the Formula

Between 1609 and 1619, Johannes Kepler published three laws that described, with precision, how the planets move around the Sun: elliptical orbits, equal areas swept in equal times, a fixed ratio between orbital period and distance from the Sun. He had worked them out from data gathered by the Danish astronomer Tycho Brahe, whose assistant he had been in Prague. These were empirical laws: they worked, but they said nothing about why the planets moved that way.

Almost seventy years later, Isaac Newton found the answer. According to Encyclopedia.com, Newton built the law of universal gravitation out of Kepler’s planetary laws, the notion that bodies can pull on each other across empty space, and his own laws of motion; he also leaned on Galileo’s observations of falling bodies, extending gravity’s reach to every piece of matter, not just the heavens. He published the result in 1687, in the Philosophiae Naturalis Principia Mathematica.

How Isaac Newton Discovered Gravity, from Kepler’s Laws

Kepler’s three laws lay out the planets’ paths, the steadiness of the areas they sweep, and the link between orbital period and distance from the Sun. They are descriptive laws, drawn from observational data: the physical cause of that motion falls outside their scope. Readers who want the full breakdown of the three laws can find it in the Recap on Kepler’s laws.

Newton started there and added an ingredient Kepler never had: his own laws of motion, already worked out for bodies on Earth (the same framework is covered in the Recap on Newton’s laws of motion). By combining them with the planetary laws and with the idea of action at a distance — two bodies pulling on each other without any physical contact — he reached a broader conclusion: the force that keeps a planet in orbit and the force that pulls an object down on Earth are one and the same force.

Worked example: a satellite orbiting Earth is often described as floating free of gravity, but it’s actually falling toward Earth exactly like an apple. Its horizontal speed is just high enough that the ground curves away beneath it at the same rate it falls, which turns that fall into an orbit.

According to NASA GSFC, Newton was the first to recognize that a falling apple, the Moon’s orbit, and the orbits of the planets all follow the same principle, F = ma. That is the unification that makes the law “universal”: it holds for any two bodies with mass, anywhere in space: a stone and the Earth, the Earth and the Moon, or the Sun and the planets described in the Recap on the solar system.

The Formula, Piece by Piece

The law of universal gravitation is written like this:

F = G · m₁ · m₂ / r²

The force grows as the masses grow, and it falls off sharply with distance, because r is squared and sits in the denominator: double the distance between two bodies and the force drops to a quarter. G is the number that fixes how strong that force is for given masses and a given distance: per NIST, the value recommended by CODATA 2022 is 6.674 30 × 10⁻¹¹ m³ kg⁻¹ s⁻², with a relative uncertainty of 2.2 × 10⁻⁵.

Where the Law Still Holds Up, as of 2026

According to NASA Science, as of 2026 scientists still rely on Kepler’s laws — in the version Newton generalized — to plan spacecraft trajectories and to measure the masses of distant moons and planets. Kepler’s third law, recast by Newton in terms of mass and the constant G, is the basis for most measurements of celestial masses calculated as of 2026: more than three centuries after the Principia was published, it remains the tool for weighing celestial bodies no one can touch.

The Apple Story, with Caution

Many people who know the law of universal gravitation associate it with an apple falling on Newton’s head. According to the Royal Society, the only account of this episode is a manuscript written by William Stukeley, a friend and contemporary of Newton, in 1752 — decades after the fact. It is, in short, a secondhand account, passed along by a friend of Newton’s long after the fact. NASA GSFC credits Newton with the insight while setting aside the more colorful versions of the tale, the ones where the fruit actually strikes his head. It still works as a memorable way to hold onto the core of the law: the same force that pulls down a piece of fruit keeps the Moon in orbit.