What is gravity?

Gravity is a pull between any two things that have mass. You pull on this screen, the screen pulls on you, and the Earth pulls on both of you. Isaac Newton wrote down the rule in 1687:

F = G × m₁ × m₂ ÷ r²

F is the force in newtons, m₁ and m₂ are the two masses in kilograms, and r is the distance between their centres in metres. G is the gravitational constant, 6.674 × 10⁻¹¹ N m²/kg². That is a tiny number, so between everyday things gravity is feeble: two 1-tonne lead balls 1 m apart pull with 0.000 067 N, the weight of about 7 mg.

The r² is the famous inverse-square law. Double the distance and the pull drops to a quarter; triple it and it drops to a ninth. Picture the pull spreading out like light from a bulb: at twice the distance the same pull is shared over four times the area.

How do you measure something so weak? In 1798 Henry Cavendish hung a rod with two small lead balls on a thin wire and swung two big balls close. The rod twisted by a hair. From that twist he worked out how dense the Earth is, which later gave G, and so the mass of the Earth: about 6 × 10²⁴ kg. People call it "weighing the Earth".

Put the Earth into the formula and you get your weight: W = G × M × m ÷ R², about 9.8 N for every kilogram you have. That 9.8 is g. The pull goes both ways: you pull the Earth up exactly as hard as it pulls you down (Newton's third law, see NewtonClear). The Earth is just too heavy to notice.

Near a planet, gravity makes everything fall with the same acceleration, whatever its mass. We call it g. On Earth g = 9.81 m/s²: a falling ball gains about 10 m/s of speed every second. On the Moon g is only 1.62 m/s², on Mars 3.71, and at Jupiter's cloud tops 24.8.

Your mass is the same everywhere, but your weight is not: W = m × g. A 50 kg student weighs 491 N on Earth, 81 N on the Moon and about 1,240 N on Jupiter. A bathroom scale on the Moon would read about 8 kg.

g also shrinks as you go higher, because you get further from Earth's centre (the inverse-square law again). But slowly: at the International Space Station, about 400 km up, g is still 8.7 m/s², 89% of what you feel on the ground.

So why do astronauts float? Because the station and everyone in it are falling together. Nothing presses on their feet, so they feel weightless. They never hit the ground because they are also moving sideways at 7.7 km/s, so the ground curves away as fast as they fall.

Newton pictured this in a book he drafted as part of the Principia: fire a cannonball sideways from a very tall mountain, with no air. Slowly, it lands nearby. Faster, it lands further round. At about 7.8 km/s the Earth curves away as fast as the ball falls, and it goes all the way round: an orbit. At about 11 km/s it escapes for good. How speed and falling add up is in MotionClear.

An orbit is a fall that never ends. For a circle, gravity must supply exactly the pull needed to bend the path, which gives the orbital speed: v = √(GM ÷ r). The closer in, the faster you must go.

The International Space Station, about 400 km up, flies at 7.66 km/s (27,600 km/h) and goes round in about 92 minutes, so its crew sees 16 sunrises a day. GPS satellites, 20,200 km up, take 12 hours (11 h 58 min). Further out, gravity is weaker and the path is longer, so orbits get slower.

At 35,786 km one lap takes exactly as long as the Earth takes to turn once. A satellite there over the equator seems to hang still in the sky: a geostationary orbit. That is why a dish on your roof can point at one spot. India's INSAT and GSAT satellites carry TV, weather pictures and phone links from there, and most of the NavIC navigation satellites use it too. ISRO's Chandrayaan missions went the other way: round the Earth in ever-bigger ellipses, then over to the Moon's gravity.

The tides are gravity too. The Moon pulls the side of the Earth facing it a little harder than the centre, and the centre a little harder than the far side. That difference stretches the oceans into two bulges, one towards the Moon and one away from it. The Earth turns under them, so most coasts get two high tides a day, about 12 h 25 min apart.

The Sun does the same, at 46% of the Moon's strength (it is far bigger, but much further away). At new and full Moon the two line up: big spring tides. At half Moon they pull at right angles: small neap tides. Coasts can funnel the tide much higher: the Gulf of Khambhat in Gujarat sees about 10 m.

Water runs downhill, and many Indian homes use that: a pump lifts water to an overhead tank once, and gravity delivers it all day. The weight of the water above the tap makes its pressure: p = ρ × g × h. Every 10 m of height gives about 1 bar (100 kPa). The pipes to a geyser work the same way: tank pressure pushes cold water in at the bottom and hot water out at the top (see WaterHeaterClear). An RO purifier needs about 5 bar to squeeze water through its membrane, far more than a rooftop tank gives, so it has a booster pump (see ROClear).

Your heart pumps blood uphill to your brain. Standing, the blood in your arteries is a tall column: the pressure is about 27 mmHg lower at your head and about 95 mmHg higher at your feet than at your heart. Lying down, the difference nearly vanishes. That is why you can feel dizzy if you stand up fast: for a few seconds your brain gets less blood until your body tightens its vessels (see HeartClear). A giraffe's heart pushes about twice as hard as ours to lift blood 2 m.

Freewheel down a hill on a bicycle and gravity pushes you along the slope with m g sin θ. You speed up until air drag grows to match it. On a 5% slope that is about 40 km/h without pedalling (see CycleClear). Cars feel the same pull uphill, which is why a loaded car needs a low gear on a ghat road (see CarClear).

A pendulum swings back and forth in a time set only by its length and by g: T = 2π √(L ÷ g). Heavy or light bob, it doesn't matter. A 99.4 cm pendulum ticks once a second: the heart of a grandfather clock. Take it to the Moon and it runs 2.5 times slow.

Newton's law predicts tides, orbits and eclipses. But it never said how gravity reaches across empty space. In 1915 Albert Einstein gave a new answer in his general theory of relativity: mass and energy curve spacetime, and things move along the straightest paths they can through that curved spacetime. We see those paths bend, and call it gravity.

The usual picture is a rubber sheet with a heavy ball in the middle: a marble rolls round the dent like a planet round the Sun. It helps, but be honest about its limits. It uses gravity (pulling the marble down) to explain gravity. It shows only two dimensions of space. And the biggest effect near Earth is really the curving of time: clocks lower down tick slower.

That is not just theory. GPS satellites carry atomic clocks. Weaker gravity up there makes them run 45.7 µs a day fast; their speed makes them 7.2 µs slow. The net +38 µs a day sounds tiny, but light goes 11 km in that time. Without Einstein's correction, your phone's map would drift by kilometres every day.

Squeeze enough mass into a small enough space and nothing, not even light, can climb out: a black hole. To become one, the Sun would have to be squeezed into a ball about 6 km across, and the Earth into one smaller than a marble, under 2 cm. When two black holes spiral together they shake spacetime itself, sending out gravitational waves. In 2015 LIGO caught one: its 4 km arms stretched by a thousandth of a proton's width. How waves carry energy is in WaveClear.

Myth: there's no gravity in space. At the ISS, gravity is 89% as strong as on the ground. Astronauts float because they are falling. Myth: heavier things fall faster. In 1971 Apollo 15's David Scott dropped a hammer and a feather on the airless Moon. They landed together. Only air makes a feather slow (see ForceClear, NewtonClear and InertiaClear for why mass doesn't matter).