How Gravity Works: From Newton to Einstein's General Relativity

Gravity is the most familiar force in daily life. It keeps you in your chair, holds the Moon in orbit, and shapes the large-scale structure of the cosmos. Yet it is also the weakest of the four fundamental interactions by an enormous margin, the hardest to reconcile with quantum mechanics, and the one that most dramatically changed our picture of space and time. The story runs from Newton's apple to ripples in spacetime detected by one of the most precise instruments ever built, and it is not finished.

This article focuses on gravity itself: what Newton got right, why it was not enough, what general relativity actually says about falling objects and orbits, and the experiments that put Einstein's theory to the test. For a broader tour of both of Einstein's theories, including special relativity, length contraction and E = mc², see our separate explainer on Einstein's relativity, special and general.

Key takeaways

• Newton's law of universal gravitation (1687) describes gravity as an instant force between masses that weakens with the square of distance; it remains accurate enough for most spaceflight.
• Newton's law cannot explain an extra 43 arcseconds per century in the precession of Mercury's orbit, or the full amount by which the Sun bends starlight.
• Einstein's general relativity (1915) treats gravity as the curvature of spacetime by mass and energy; free-falling objects follow the straightest possible paths through that curved geometry.
• The theory has passed every experimental test so far, including Mercury's orbit, the 1919 eclipse, gravitational redshift, GPS clock rates, frame dragging measured by Gravity Probe B, and gravitational waves.
• The detection of the neutron-star merger GW170817 showed that gravitational waves travel at the speed of light to within roughly one part in 10¹⁵.

Newton's gravity: a force at a distance

Isaac Newton's law of universal gravitation, published in the Principia in 1687, was one of the great intellectual achievements in history. Newton showed that the force pulling an apple to the ground is the same force that holds the Moon in orbit and the planets around the Sun. The law is compact: every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Written as an equation, F = G·m₁·m₂ / r². The constant G is tiny, which is why gravity between everyday objects is imperceptible. The first laboratory measurement of the attraction between known masses came from Henry Cavendish's torsion-balance experiment in 1798, more than a century after the Principia.

The inverse-square law was spectacularly successful. It explained Kepler's three laws of planetary motion, accounted for the tides through the differential pull of the Moon and Sun (see what causes tides), predicted the return of Halley's comet, and led to the discovery of Neptune in 1846, when Urbain Le Verrier calculated where an unseen planet must be to explain irregularities in the orbit of Uranus and Johann Galle found it close to the predicted spot. For two centuries, Newton's gravity was simply physics.

The cracks in Newton's picture

There were two kinds of problem, one observational and one conceptual.

The observational problem was Mercury. Planetary orbits are ellipses, and the point of closest approach to the Sun, the perihelion, slowly shifts around the Sun over time. Most of that shift is caused by the pull of the other planets and can be calculated with Newton's law. But in the 19th century, astronomers found that Mercury's perihelion moved slightly faster than Newtonian theory allowed, by about 43 arcseconds per century once every known effect had been subtracted. An arcsecond is 1/3,600 of a degree, so the discrepancy is tiny, but the measurements were good enough to show it was real. Le Verrier, fresh from his success with Neptune, proposed an unseen inner planet, later nicknamed Vulcan. Astronomers searched for it for decades. It does not exist.

The conceptual problem was action at a distance. Newton's law says the Sun's pull on Earth changes instantly if the Sun moves, across 150 million kilometers of empty space, with no mechanism. Newton himself found this troubling and declined to speculate about the cause. After 1905, when special relativity established that no signal can travel faster than light, instant action across space became impossible to accept as fundamental. Gravity needed a theory compatible with a universal speed limit.

The equivalence principle: Einstein's "happiest thought"

Albert Einstein later described the key insight behind general relativity as the happiest thought of his life. It came to him in 1907 while he was working at the Swiss patent office in Bern: a person falling freely does not feel their own weight.

Imagine being in a sealed elevator whose cable has snapped. You, the elevator and everything in it fall together at the same rate, so a dropped pen floats in front of you. No experiment inside the box can tell you whether you are falling in Earth's gravity or floating in deep space far from any mass. Now imagine the box far from any planet but pulled upward by a rocket at a steady acceleration of 9.8 meters per second squared. The floor presses on your feet, and a dropped pen falls to the floor exactly as it would on Earth. Again, no experiment inside can tell the difference.

This is the equivalence principle: locally, the effects of gravity and of acceleration cannot be distinguished. It rests on a fact Newton knew but could not explain, that all objects fall at the same rate regardless of their mass or composition. Galileo is said to have tested this; Apollo 15 astronaut David Scott famously dropped a hammer and a feather on the airless Moon, and they landed together. Modern experiments have tested it to extraordinary precision.

The principle had immediate consequences. A beam of light fired horizontally across an accelerating rocket would appear to curve toward the floor, because the floor rises while the light crosses. If acceleration and gravity are equivalent, gravity must bend light too. And a clock at the top of an accelerating rocket would be seen from the bottom to run fast, which implies that clocks higher in a gravitational field run faster than clocks lower down. Both predictions would later be confirmed.

Spacetime curvature: what general relativity actually says

Between 1907 and 1915, Einstein worked to turn the equivalence principle into a full theory. He needed mathematics he did not know, the geometry of curved spaces developed in the 19th century by Bernhard Riemann and others, and he enlisted his friend the mathematician Marcel Grossmann to help. After several false starts, Einstein presented the final field equations to the Prussian Academy of Sciences in November 1915.

The Einstein field equations are often summarized in a sentence attributed to the physicist John Wheeler: spacetime tells matter how to move; matter tells spacetime how to curve. Mathematically, they are ten coupled equations relating the curvature of four-dimensional spacetime to the density and flow of energy, momentum and pressure in it.

Falling as following a straight line

In Newton's picture, space and time are a fixed stage, and gravity is a force pulling objects off their natural straight-line paths. In general relativity, there is no gravitational force in that sense. Spacetime itself is curved by mass and energy, and an object with no other force on it follows a geodesic, the straightest possible path through curved spacetime. A planet orbiting the Sun is not being pulled sideways; it is moving as straight as the geometry allows.

The popular picture is a heavy ball on a rubber sheet, making a dip that smaller balls roll into. It captures one idea, that mass shapes geometry and geometry shapes motion, but it is misleading in two ways: it shows curved space only, and it relies on ordinary gravity to pull the balls down into the dip.

A better way to think about it uses time. Even an object sitting still in space is moving through time. Near a massive body, time runs at different rates at different heights. An object at rest "drifts" toward the region where time runs slower, and that drift is what we experience as falling. For everyday gravity such as Earth's, almost all of the effect comes from the warping of time rather than of space. This is why clock measurements are such powerful tests of the theory.

Newton as a special case

General relativity does not throw Newton away. In weak gravitational fields and at speeds far below light, its equations reduce to Newton's law to excellent accuracy. That is why spacecraft trajectories to the planets can be planned with Newtonian mechanics plus small relativistic corrections. The two theories differ noticeably only where gravity is strong, where speeds are high, or where measurements are extremely precise.

Feature	Newtonian gravity	General relativity
What gravity is	A force between masses	Curvature of spacetime
Speed of influence	Instantaneous	Speed of light
Effect on light	None in the strict theory; half the observed bending if light is treated as a particle	Full bending (1.75 arcseconds at the Sun's edge)
Effect on time	None	Clocks run slower deeper in a gravitational field
Mercury's perihelion	Leaves about 43″ per century unexplained	Accounts for it
Gravitational waves	Not predicted	Predicted and observed
Black holes	No consistent description	Predicted (Schwarzschild solution, 1916)
Where it works well	Weak fields, low speeds	Tested from laboratory to cosmic scales

Testing general relativity: the classic tests

Mercury's perihelion (1915)

When Einstein applied his new equations to Mercury, they predicted an extra perihelion shift of about 43 arcseconds per century, the amount that had defied explanation for half a century. It came out of the theory without any adjustable parameters. Einstein later wrote that the result left him beside himself with excitement for days. It was the first sign that the theory was right, and it was a postdiction: it explained a known anomaly rather than forecasting a new one.

The bending of starlight (1919)

General relativity predicts that light grazing the Sun's edge is deflected by 1.75 arcseconds, twice what a Newtonian calculation gives if light is treated as a stream of particles. The only way to see stars close to the Sun is during a total solar eclipse. In May 1919, expeditions organized by Arthur Eddington and Frank Dyson photographed stars around the eclipsed Sun from Sobral in Brazil and the island of Príncipe off West Africa. Their measurements agreed with Einstein rather than Newton, and the announcement that November made Einstein world-famous. The 1919 plates were not precise by modern standards, and the analysis has been debated since, but later radio measurements of quasars passing near the Sun have confirmed the deflection with very high precision. Our piece on the 1919 eclipse expedition covers the expedition and the controversy.

Gravitational redshift (1959)

The equivalence principle predicts that light climbing out of a gravitational field loses energy and shifts toward the red. In 1959 Robert Pound and Glen Rebka at Harvard measured this effect over a vertical distance of about 22.5 meters inside a university building, using gamma rays and the very sharp resonance of the Mössbauer effect. Their result agreed with the prediction. The shift is minuscule, a few parts in 10¹⁵, which is why it took until the late 1950s to measure.

Time dilation with clocks

Gravitational redshift is the same thing as gravitational time dilation viewed another way. Clocks closer to a mass run slower than clocks farther away. In 1971, Joseph Hafele and Richard Keating flew cesium atomic clocks around the world on commercial airliners and compared them with clocks on the ground, confirming the combined effects of speed and altitude predicted by relativity; see our article on the Hafele–Keating experiment. Today's optical atomic clocks are so precise that they can detect the difference in the passage of time between two clocks separated in height by a fraction of a meter.

The Shapiro delay

In 1964, Irwin Shapiro pointed out a fourth classic test: radar signals passing close to the Sun should take slightly longer to make the round trip, because spacetime near the Sun is curved. Radar echoes from Mercury and Venus confirmed the delay in the late 1960s and 1970s. Tracking of the Cassini spacecraft in 2002 produced one of the most precise confirmations of this effect.

GPS: general relativity in your pocket

The Global Positioning System is the most familiar everyday application of gravitational time dilation. GPS satellites orbit at an altitude of about 20,000 kilometers, where Earth's gravity is weaker. Two effects act on their atomic clocks, as explained in Ohio State University's astronomy course notes:

Effect	Cause	Change in satellite clock vs ground
Special relativity	Satellite's orbital speed	About 7 microseconds per day slower
General relativity	Weaker gravity at altitude	About 45 microseconds per day faster
Net effect	Both combined	About 38 microseconds per day faster

Thirty-eight millionths of a second sounds trivial. But GPS works by timing radio signals that travel at the speed of light, about 30 centimeters per nanosecond. Left uncorrected, the clock drift would build up into position errors growing by roughly 10 kilometers a day. Engineers set the satellite clocks to tick slightly slow before launch so that they run at the correct rate in orbit, and receivers apply further small corrections. Our articles on how GPS uses Einstein's relativity and the invention of GPS go deeper into the engineering.

Frame dragging: Gravity Probe B

General relativity predicts more than curvature from mass at rest. A rotating mass should drag spacetime around with it, an effect called frame dragging or the Lense–Thirring effect, after the Austrian physicists who derived it in 1918. A gyroscope in orbit should also slowly change its orientation because it is carried through curved spacetime, which is called the geodetic effect.

NASA and Stanford University's Gravity Probe B mission, launched in April 2004, carried four of the most perfectly spherical objects ever made, quartz gyroscopes coated in niobium, in a polar orbit about 640 kilometers up. The idea was to measure how their spin axes shifted relative to a distant guide star over about a year. The final results, published in 2011, were:

Effect	General relativity prediction	Gravity Probe B measurement
Geodetic effect	−6,606.1 milliarcseconds per year	−6,601.8 ± 18.3 milliarcseconds per year
Frame dragging	−39.2 milliarcseconds per year	−37.2 ± 7.2 milliarcseconds per year

Both agree with Einstein within the measurement uncertainty. The geodetic effect was confirmed to about 0.3% and frame dragging to about 20%. Frame dragging is a small effect around Earth, but near rapidly spinning black holes it becomes enormous and helps power some of the most energetic jets in the universe.

Gravitational waves: from prediction to detection

In 1916, shortly after completing general relativity, Einstein showed that the theory allows ripples in spacetime: gravitational waves, produced by accelerating masses and traveling at the speed of light. He doubted for years whether they were physically real or an artifact of the mathematics. The effects at Earth would be so small that for decades few people thought they could ever be measured.

Indirect evidence: the Hulse–Taylor pulsar

The first strong evidence came from astronomy rather than a detector. In 1974 Russell Hulse and Joseph Taylor discovered a pulsar orbiting another supernova. About 20 km wide but containing more mass than the Sun.">neutron star. Over the following years, they found that the orbit was slowly shrinking at exactly the rate general relativity predicted for a system losing energy to gravitational waves. The discovery earned Hulse and Taylor the 1993 Nobel Prize in Physics.

Direct detection: LIGO

The Laser Interferometer Gravitational-Wave Observatory (LIGO) consists of two L-shaped detectors, in Hanford, Washington, and Livingston, Louisiana, each with arms 4 kilometers long. A laser beam is split, sent down both arms, reflected back by mirrors and recombined. A passing gravitational wave stretches one arm and squeezes the other by a tiny amount, changing how the light waves line up.

On 14 September 2015, both LIGO detectors recorded the signal now called GW150914. According to the LIGO Scientific Collaboration, it came from two black holes, each about 30 times the mass of the Sun, merging about 1.3 billion light-years away. The detectors' arms changed length by roughly a thousandth of the diameter of a proton. In its final fraction of a second, the merger radiated more power in gravitational waves than all the stars in the observable universe emit as light. The discovery was announced on 11 February 2016, and three of LIGO's founders, Rainer Weiss, Barry Barish and Kip Thorne, received the 2017 Nobel Prize in Physics. Our article on the LIGO detection of GW150914 explains the signal in more detail.

The waveform itself was a test. As the black holes spiraled together, the signal rose in frequency and strength (the "inspiral"), peaked at the merger, then faded as the new black hole settled down (the "ringdown"). The shape matched numerical solutions of Einstein's equations for strong, rapidly changing gravity, a regime that had never been tested before.

The speed of gravity: GW170817

On 17 August 2017, LIGO and the European Virgo detector recorded gravitational waves from two neutron stars merging. About 1.7 seconds after the merger moment recorded in the gravitational-wave signal, NASA's Fermi satellite and ESA's INTEGRAL detected a short burst of gamma rays from the same part of the sky. Telescopes then found the glowing aftermath in a galaxy about 130 million light-years away. Because the two signals had traveled for so long and arrived so close together, the joint LIGO, Virgo, Fermi and INTEGRAL analysis constrained the difference between the speed of gravity and the speed of light to between about −3 × 10⁻¹⁵ and +7 × 10⁻¹⁶ of the speed of light. Gravity travels at light speed, as general relativity requires. The result also ruled out a number of alternative theories of gravity that had been proposed to explain cosmic acceleration.

Gravitational lensing

The bending of light by gravity, first measured in 1919, has become one of astronomy's most useful tools. When light from a distant galaxy or quasar passes a massive object on its way to us, the intervening mass acts as a gravitational lens.

Strong lensing produces arcs, rings (Einstein rings) and multiple images of the same source when the alignment is close to perfect. Because the amount of bending depends on the total mass of the lens, including invisible dark matter, lensing by galaxy clusters provides some of the most direct measurements of dark matter's distribution.

Weak lensing produces subtle, statistical distortions in the shapes of millions of background galaxies. Large surveys use these distortions to map dark matter on cosmic scales and to test models of how structure grows.

Microlensing occurs when a star or planet passes in front of a more distant star and briefly brightens it. The technique is sensitive to planets far from their stars, complementing transit and radial-velocity searches.

Black holes: gravity at its most extreme

In 1916, within weeks of reading Einstein's final paper, the German astronomer Karl Schwarzschild found an exact solution of the field equations for the spacetime outside a spherical mass. It contained a boundary, now called the event horizon, inside which nothing, not even light, can escape. For decades many physicists, including Einstein, considered this a mathematical curiosity. Today black holes are observed directly: by the orbits of stars around the center of our galaxy, by gravitational waves from their mergers, and in the images of the shadow of the black hole in the galaxy M87 released by the Event Horizon Telescope in 2019, described in our article on the first image of a black hole. The size and shape of that shadow matched general relativity's predictions.

Summary of the major tests

Test	First result	What it confirmed
Mercury's perihelion	1915 (calculation)	Extra 43″ per century from spacetime curvature
Light bending	1919 eclipse	Light deflected by about 1.75″ at the Sun's edge
Gravitational redshift	1959 (Pound–Rebka)	Light loses energy climbing out of gravity
Shapiro delay	Late 1960s (radar)	Signals slowed passing near the Sun
Clock time dilation	1971 (Hafele–Keating)	Clocks at altitude run faster
GPS	Operational system	Net 38 µs per day correction
Binary pulsar	1974 discovery; decay measured over following years	Energy loss to gravitational waves
Frame dragging	2011 (Gravity Probe B)	Rotating Earth drags spacetime
Gravitational waves	2015 (GW150914)	Waves exist and match strong-field predictions
Speed of gravity	2017 (GW170817)	Equals the speed of light to ~10⁻¹⁵

What general relativity still cannot explain

For all its success, general relativity is almost certainly not the final word.

Quantum gravity. General relativity treats spacetime as smooth and continuous. Quantum mechanics describes forces through discrete particles and uncertainty. Attempts to quantize gravity in the same way as the other forces lead to infinities that cannot be removed. Inside black holes and at the Big Bang, the theory predicts infinite densities, which most physicists read as a sign that it breaks down there. String theory and loop quantum gravity are leading approaches, but neither has produced a confirmed experimental prediction.

Dark matter and dark energy. Galaxies rotate faster at their edges than visible matter can explain, and the expansion of the universe is accelerating. The standard explanations, invisible dark matter and dark energy, keep general relativity intact. A minority of researchers instead explore modified theories of gravity. GW170817's speed measurement eliminated many such alternatives, but the debate continues.

Why gravity is so weak. Gravity is vastly weaker than electromagnetism: the electric repulsion between two protons exceeds their gravitational attraction by a factor of roughly 10³⁶. Why should that be? There is no accepted answer.

Common misconceptions about gravity

"There is no gravity in space." Astronauts on the International Space Station float because they are in free fall around Earth, not because gravity is absent. At the station's altitude, Earth's gravity is still about 90% as strong as at the surface.

"Heavier objects fall faster." In the absence of air resistance, all objects fall at the same rate. This is the observation that the equivalence principle elevates into a law.

"Gravity is just a force, so general relativity is a refinement." For most practical work, yes. Conceptually, general relativity replaces the force with geometry, and that change predicts phenomena Newton's theory has no room for, such as gravitational waves, black holes and the effect of gravity on time.

"Gravity acts instantly." Changes in gravity propagate at the speed of light, as GW170817 confirmed.

FAQ

Q: Why can't we combine gravity with quantum mechanics? A: General relativity describes gravity as smooth, curved spacetime, while quantum mechanics describes forces through discrete particles and probabilities. When physicists treat gravity as exchange of a hypothetical particle, the graviton, calculations produce infinities that cannot be removed. String theory and loop quantum gravity attempt to resolve this, but neither has a confirmed experimental prediction yet.

Q: Does general relativity replace Newton's law of gravity? A: Not in practice. Newton's law is the limit of general relativity for weak fields and low speeds, and it is accurate enough for most engineering and spacecraft trajectory planning. Relativistic corrections are needed for precise timing systems such as GPS, for strong gravity near neutron stars and black holes, and for gravitational waves.

Q: What is gravitational time dilation? A: It is the slowing of time deeper in a gravitational field. Clocks on Earth's surface run slightly slower than clocks in orbit; GPS satellite clocks gain about 45 microseconds per day from weaker gravity and lose about 7 from their speed, a net gain of about 38 microseconds per day that must be corrected.

Q: How was the bending of light by gravity first measured? A: During the total solar eclipse of May 1919, expeditions to Sobral in Brazil and Príncipe off West Africa photographed stars near the darkened Sun. Their apparent positions were shifted by an amount consistent with general relativity's prediction of 1.75 arcseconds at the Sun's edge, about twice the Newtonian value. Modern radio measurements confirm it far more precisely.

Q: Are gravitational waves dangerous? A: No. Even the waves from GW150914, a merger of two black holes about 30 times the Sun's mass, changed the length of LIGO's 4-kilometer arms by about a thousandth of a proton's diameter by the time they reached Earth. Astrophysical gravitational waves pass through people and planets with no measurable effect on living things.

Q: How fast does gravity travel? A: At the speed of light. In August 2017, gamma rays from the neutron-star merger GW170817 arrived about 1.7 seconds after the merger time marked by the gravitational waves, after a journey of about 130 million years. That constrains any difference between the speed of gravity and light to roughly one part in 10¹⁵.

Q: What is frame dragging? A: Frame dragging is the twisting of spacetime by a rotating mass. NASA and Stanford's Gravity Probe B measured it around Earth using orbiting gyroscopes and reported in 2011 a drift of 37.2 ± 7.2 milliarcseconds per year, against a predicted 39.2. Near spinning black holes the effect is much stronger.

Sources

• Everitt, C. W. F. et al. (2011). Gravity Probe B: Final Results of a Space Experiment to Test General Relativity. Physical Review Letters 106, 221101.
• LIGO Scientific Collaboration. GW150914: the first detection of gravitational waves.
• LIGO, Virgo, Fermi GBM and INTEGRAL (2017). Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817A.
• Pogge, R. W. Real-World Relativity: The GPS Navigation System. Ohio State University.

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