Science › Classical physics
Newton's law of gravity
1687· Theory
ProvenTested many times; part of working physics.
Newton's 1687 rule that every mass attracts every other mass, with the pull weakening by the square of the distance.
See it on the Science map →How it works
Double the distance between two bodies and the pull drops to a quarter; double either mass and it doubles. The same force that drops an apple holds the Moon in orbit, which Newton checked by comparing the Moon's fall toward Earth with an apple's. Combined with his laws of motion, it explains elliptical orbits, tides and comet paths. Henry Cavendish first measured the force between lab objects in 1798.
Why it matters
It united earthly and celestial physics for the first time. It still plots most spacecraft trajectories and satellite orbits.
How we know
Halley's comet's return (1758), the discovery of Neptune (1846), and Cavendish's torsion balance (1798). It is slightly off for Mercury's orbit and near very strong gravity, where general relativity takes over.
Still a mystery
Galaxies rotate faster than their visible mass allows under this law. Most physicists blame unseen dark matter; a minority suspect gravity itself needs modifying.
Connections (6)
▸Isaac Newton discovered Newton's law of gravityProven
The relationship
Newton realised the force pulling an apple down could reach to the Moon, weakening with distance. He calculated that an inverse-square force keeps the Moon in orbit and, with his laws of motion, reproduces Kepler's elliptical planetary orbits. One law replaced separate explanations for falling objects and heavenly motion.
How the link was found
Newton worked on the idea from about 1666. Halley's 1684 question about orbit shapes prompted him to publish full proofs in the Principia (1687). Robert Hooke disputed credit for the inverse-square idea.
Why it's proven
Accurate planetary predictions, Halley's comet's return (1758), Neptune's discovery (1846), and Cavendish's 1798 lab measurement of the pull between lead spheres.
Open questions and mysteries
Newton could not say how gravity acts instantly across empty space. Einstein's curved spacetime answered that; how gravity works at the quantum level is still unknown.
▸Newton's law of gravity was replaced by General relativity: gravity is curved spacetimeProven
The relationship
Newton treated gravity as an instant force pulling across empty space. General relativity replaced that picture with curved spacetime, where changes travel at light speed. For weak gravity and slow speeds, Einstein's equations give back Newton's results almost exactly, so Newton remains a highly accurate approximation used for most engineering and spaceflight.
How the link was found
Einstein built general relativity from 1907 to 1915, deliberately requiring that it reproduce Newton's law in everyday conditions.
Why it's proven
General relativity matches Newton where Newton works, and beats it where Newton fails: Mercury's orbit, light bending, gravitational waves and clock rates.
Open questions and mysteries
Galaxy rotation speeds disagree with both theories unless unseen dark matter exists; a few physicists instead propose modifying gravity again.
▸Newton's law of gravity was the first of The four forces of natureProven
The relationship
Newton's 1687 law was the first time any force was captured by a single universal formula: every mass attracts every other, weakening with the square of distance. The same rule ran apples and planets. That set the template for finding the other forces: look for a simple law that applies everywhere.
How the link was found
Isaac Newton, in the Principia (1687). Charles-Augustin de Coulomb found a similar square-of-distance law for electric charges in 1785.
Why it's proven
Newton's law predicted planetary orbits and, in 1846, Neptune's location. Henry Cavendish measured gravity's strength in the lab in 1798.
Open questions and mysteries
Newton could not say what gravity is or how it acts across empty space. Einstein answered partly in 1915; gravity's quantum nature remains unknown.
▸Mercury's orbit puzzle solved exposed a flaw in Newton's law of gravityProven
The relationship
Mercury's elliptical orbit slowly rotates around the Sun. Newton's gravity, including tugs from other planets, accounts for most of that drift but leaves about 43 arcseconds per century unexplained. That small leftover showed Newton's law is not exact; Einstein's general relativity later accounted for it precisely.
How the link was found
Urbain Le Verrier identified the anomaly in 1859, Simon Newcomb refined it in 1882, and Einstein explained it in November 1915.
Why it's proven
Modern radar ranging and spacecraft tracking confirm both the anomaly and general relativity's prediction to high precision.
Open questions and mysteries
Settled, but instructive: a tiny discrepancy overturned a theory. Physicists now watch other anomalies, such as galaxy rotation, the same way.
▸Vera Rubin found galaxies spinning too fast for Newton's law of gravityWell supported
The relationship
Under Newton's gravity, stars far from a galaxy's centre should orbit more slowly, as outer planets do around the Sun. Vera Rubin and Kent Ford measured star speeds and found they stayed roughly constant far out. Either galaxies hold large amounts of unseen mass (dark matter) or gravity behaves differently at those scales.
How the link was found
Rubin and Ford, measuring the Andromeda galaxy in 1970 and many spiral galaxies through the 1970s. Fritz Zwicky had seen hints in a galaxy cluster in 1933.
Is it proven?
Flat rotation curves are confirmed in thousands of galaxies. Dark matter is strongly supported by other evidence too, but has never been detected directly.
Open questions and mysteries
What dark matter is made of, and whether modified-gravity ideas like MOND (1983) explain some data better.
▸MOND: modified gravity instead of dark matter changes, at very weak pull, Newton's law of gravitySpeculative
The relationship
In Newton's law, pull weakens with distance squared. MOND keeps that for strong pulls but, below about a hundred-billionth of Earth's surface gravity, makes the pull weaken only with distance. Galaxies' outer stars feel such weak pulls, so they get extra grip. The Sun's pull on Earth is tens of millions of times above the threshold, so Solar System tests see pure Newton.
How the link was found
Mordehai Milgrom, Weizmann Institute, Israel, in three 1983 papers. Jacob Bekenstein and Milgrom built a fuller version, derived from an energy principle, in 1984.
Is it proven?
Not proven. It matches galaxy rotation with one new constant. Widely separated star pairs, where pulls are weak, test it directly; Gaia-based studies in 2023–24 reached opposite conclusions, most favoring Newton.
Open questions and mysteries
Why would gravity change at that particular acceleration, about a sixth of the speed of light times the universe's expansion rate? Possibly a clue, possibly coincidence.