What is gravity? From Newton's apple to curved spacetime

Gravity is the attraction between things that have mass or energy. It is what makes an apple fall, holds the Moon in orbit around Earth and Earth around the Sun, and gathers gas into stars and galaxies. Isaac Newton described it in 1687 as a force between any two masses. Albert Einstein's general relativity, in 1915, explained it more deeply: mass and energy curve spacetime, and objects follow the curves.

In short

• Every mass attracts every other mass. Newton's law gives the size of the pull: it grows with both masses and weakens with the square of the distance.
• Gravity is by far the weakest of nature's forces, but it only ever attracts and it reaches across any distance, so on the scale of planets and galaxies it wins.
• Einstein's picture replaces the force with curved spacetime. It agrees with Newton in everyday life and is right where Newton is slightly wrong.

How does Newton's law of gravity work?

Newton's law of universal gravitation says that any two masses pull on each other with a force F = G × m₁ × m₂ ÷ r². Here F is the force in newtons, m₁ and m₂ are the two masses in kilograms, r is the distance between their centers in meters, and G is the gravitational constant, which NIST lists as 6.674 × 10⁻¹¹ newton square meters per kilogram squared. The word "universal" was the bold part: the same rule for an apple and for the planets.

A worked example: the pull between Earth and an apple

Take a 1 kg apple at Earth's surface. NASA's Earth fact sheet gives Earth's mass as 5.972 × 10²⁴ kg and its mean radius as 6,371 km, which is 6.371 × 10⁶ m.

1. Multiply G by the two masses: 6.674 × 10⁻¹¹ × 5.972 × 10²⁴ × 1 = 3.986 × 10¹⁴.
2. Square the distance: (6.371 × 10⁶)² = 4.059 × 10¹³.
3. Divide: 3.986 × 10¹⁴ ÷ 4.059 × 10¹³ = 9.82 newtons.

So Earth pulls a 1 kg apple with about 9.8 N, and by Newton's third law the apple pulls Earth with exactly the same 9.8 N. The apple accelerates at 9.8 m/s² because its mass is small. Earth accelerates toward the apple by 9.8 ÷ 5.972 × 10²⁴, about 1.6 × 10⁻²⁴ m/s², which nothing could ever detect.

The r² in the bottom is the inverse-square law: double the distance and the pull drops to a quarter. Newton tested it on the Moon. The Moon is about 384,400 km away, roughly 60 Earth radii, so Earth's pull there should be 60² = 3,600 times weaker than at the surface: 9.82 × (6,371 ÷ 384,400)², about 0.0027 m/s². The Moon moves at about 1.022 km a second in its orbit, and an object going round a circle at speed v and radius r must accelerate toward the center by v² ÷ r: 1,022² ÷ 384,400,000 = 0.0027 m/s². The force that drops an apple is the force that bends the Moon's path, to within about 1%.

Why is gravity so weak, if it runs the universe?

Gravity is extraordinarily weak between ordinary objects. Two people of 70 kg standing 1 meter apart pull on each other with 6.674 × 10⁻¹¹ × 70 × 70 ÷ 1², about 3.3 × 10⁻⁷ N, roughly the weight of a few hundredths of a milligram. A fridge magnet the size of a coin holds itself up against the pull of the entire planet.

It dominates at large scales for two reasons. It only attracts: electric charges come in plus and minus and mostly cancel out in bulk matter, but mass has no negative kind, so every kilogram adds to the pull. And it has no range limit; it weakens with distance but never stops. Put enough mass together and gravity rounds planets, lights stars by squeezing their cores, and, when the squeeze can't be resisted, makes black holes.

Henry Cavendish first measured the pull between masses in a laboratory, in experiments in 1797 and 1798, using lead balls on a torsion balance. That measurement is what let later physicists work out G, and from it Earth's mass.

What did Einstein change?

Newton's law says how strong gravity is, but not what it is or how it reaches across empty space. Newton himself found action at a distance hard to accept. Einstein's general relativity answers differently: gravity is not a force pulling through space but the shape of spacetime itself. Mass and energy curve spacetime, and an object with no force on it follows the straightest path the curved spacetime allows. Earth isn't being tugged sideways by the Sun; it is moving as straight as it can through spacetime that the Sun has curved.

The idea starts from a simple observation: in free fall you feel no weight, as astronauts on the space station show. Einstein took that seriously: if falling cancels weight exactly, then gravity and acceleration can't be told apart in a small enough region, the equivalence principle, which also explains why inertial and gravitational mass are always equal. The full theory, its strange effects on time, and the evidence for it are in the theory of relativity.

Newton or Einstein: which is right?

Both are right within their ranges, and Einstein's is right in more places. Engineers still use Newton's law to send probes to the planets.

	Newton (1687)	Einstein (1915)
What gravity is	A force between masses, acting instantly at any distance	The curving of spacetime by mass and energy
What it explains well	Falling objects, tides, orbits of planets and moons, spacecraft paths	All of Newton's cases, plus strong gravity and very precise timing
Mercury's orbit	Off by about 43 arcseconds a century	Matches
Light passing the Sun	Bends half as much as observed, or not at all	Matches, first seen in the 1919 eclipse
Clocks in orbit	No effect	Run faster higher up; [[how-does-gps-work
Gravitational waves	None	Predicted in 1916, detected on 14 September 2015
Where it fails	Strong gravity, high precision	Inside black holes and at the Big Bang, where quantum effects matter

The gravitational waves came from two black holes merging about 1.3 billion light-years away, as LIGO describes: ripples in spacetime that, by the time they reached Earth, stretched and squeezed the detectors' 4 km arms by an amount 10,000 times smaller than the nucleus of an atom.

What do people get wrong about gravity?

The most common mistake is thinking there is no gravity in space. At the space station's height, gravity is still about 90% as strong as on the ground. The crew floats because the station and everyone in it are falling around Earth together, missing it because they move sideways at about 7.7 km a second.

The second is thinking heavier things fall faster. A heavier object is pulled harder but has proportionally more inertia, so in a vacuum everything falls at the same rate. A feather lags only because of the air.

The third is the rubber-sheet picture: a heavy ball denting a stretched sheet so a marble rolls toward it. It helps to show curvature, but it uses gravity to explain gravity, since the ball sinks only because Earth pulls it down, and it shows only curved space. In relativity, most of what you feel as everyday gravity comes from the curving of time, not space: clocks lower down run slower, and objects drift toward where time runs slowest.

What don't we know about gravity?

General relativity and quantum mechanics are each confirmed to great precision, but they don't fit together. Every other force has a quantum description; gravity doesn't. Inside a black hole and at the first instant of the Big Bang, both theories should apply at once, and nobody yet knows how to combine them. String theory and loop quantum gravity are the best-known attempts; neither has made a prediction that has been confirmed by experiment.

Still argued

Galaxies spin faster at their edges than the gravity of their visible stars and gas can account for. Most astronomers explain this with dark matter, unseen mass that NASA estimates makes up about 27% of the universe against about 5% for ordinary matter. A minority argue that gravity itself behaves differently at very weak accelerations, an idea called modified Newtonian dynamics, proposed by Mordehai Milgrom in 1983. Dark matter fits the cosmic microwave background and colliding galaxy clusters better; modified gravity predicts some galaxy rotation patterns strikingly well. No dark-matter particle has been detected so far.

Gravity also stores energy: lifting a mass gives it gravitational potential energy, which turns into motion when it falls. That exchange drives everything from hydroelectric dams to the heat inside a forming planet.

Check yourself

• Without looking back: if Earth pulls an apple with 9.8 N, how hard does the apple pull Earth, and why doesn't Earth visibly move?
• Why does gravity dominate the motion of planets and galaxies when it is far weaker than electric and magnetic forces?
• What does it mean to say gravity is the curving of spacetime rather than a force?

Sources

• Newtonian constant of gravitation — National Institute of Standards and Technology
• Earth Fact Sheet — NASA Space Science Data Coordinated Archive
• Moon Fact Sheet — NASA Space Science Data Coordinated Archive
• What are gravitational waves? — LIGO, Caltech
• Dark matter — NASA
• Gravity — Wikipedia