Gravity

Gravity reaches out for ever, but it fades, and Newton’s law says how fast. Measure distance from the centre of the Earth. At twice the distance the pull is a quarter as strong, at three times it is a ninth, and at ten times it is divided by 100. The pull falls with the square of the distance, and the rule is called the inverse-square law.

There is a reason for the square. Picture the Earth’s pull spreading like light from a lamp. At twice the distance it covers a sphere with four times the surface, so each patch receives a quarter.

Newton tested it on the Moon, which is about sixty times as far from the Earth’s centre as an apple on a tree. The pull there should be weaker by sixty times sixty, or 3,600. That is just the pull needed to hold the Moon in its path.

Your mass is the amount of matter in you, and it is the same wherever you go. Your weight is something else. It is the force with which gravity pulls on that mass, and it depends on where you are standing.

How hard a planet or a moon pulls at its surface depends on its mass and on how far the surface lies from its centre. The Moon has about one eightieth of the Earth’s mass. But it is also much smaller, so its surface lies nearer its centre, and the pull there works out at about a sixth of the Earth’s. An astronaut there has a sixth of the weight she has at home and can bound along in a heavy suit. On Mars the pull is a little more than a third of the Earth’s. In neither place has her mass changed at all.

The International Space Station circles about 400 kilometres up. At that height the Earth’s gravity is still about nine-tenths as strong as on the ground. So why do the astronauts float?

Because they are falling. The station, the astronauts and everything inside are falling freely around the Earth together, at the same rate. You feel your weight only when something stops you falling: the floor pushing up on your feet, or a chair against your back. When the floor is falling exactly as fast as you are, it pushes on nothing.

So “weightless” is the wrong word. The astronauts have nearly their full weight. They are in free fall, and floating is what falling together feels like. The same is true of us all on a larger scale. The Earth is falling around the Sun, and you fall with the Earth, which is why you never feel the Sun’s pull.

What keeps the station up? Newton pictured a cannon on a very high mountain, firing level. A slow ball curves down and lands nearby. A faster one lands farther off. Now fire it at about 8 kilometres a second. In one second the ball drops about 5 metres, but over the 8 kilometres it has travelled, the round Earth curves away beneath it by the same 5 metres. The ball is still falling, and it is no nearer the ground. It will go on falling all the way round the planet.

That is an orbit: sideways speed and falling at once. The Moon is doing exactly this. It falls toward the Earth all the time, and its sideways motion carries it past just as fast. Nothing holds it up, and nothing needs to.

The closer a satellite is to the Earth, the stronger the pull on it, and the faster it must move sideways to keep missing the ground. The space station, 400 kilometres up, travels at nearly 28,000 kilometres an hour and circles the Earth in about 90 minutes. The Moon, nearly 400,000 kilometres away, takes about a month.

In between lies a useful height. About 36,000 kilometres above the equator a satellite takes one day to go round, the same time the Earth takes to spin once. Seen from the ground it hangs at one point in the sky. Such an orbit is called geostationary, and it is where television and weather satellites are parked. A dish on a wall can point at one of them and never has to move.

The same falling holds the solar system together. The Sun contains more than 99 per cent of all the mass in it, so its pull rules everything else. Each planet falls around the Sun as the Moon falls around the Earth, and the Earth takes a year to go round once.

The paths are not perfect circles. In 1609 Johannes Kepler, working from years of careful measurements of Mars, showed that the planet moves in an ellipse, a slightly stretched circle, and moves faster when it is nearer the Sun. The other planets do the same. Kepler could describe the pattern and could not explain it. Newton could. He proved that a pull obeying the inverse-square law must produce exactly such paths. Kepler’s rules, found by measurement, turned out to follow from the one law of gravity.

Throw a ball upward and it slows, stops and comes back. Throw it harder and it goes higher first. Is there a speed at which it would never come back? There is. Because gravity weakens with distance, a body moving fast enough keeps outrunning the pull and is never brought to a stop. The least speed that will do this is called the escape velocity. From the Earth’s surface it is about 11 kilometres a second, some 40,000 kilometres an hour.

Escape velocity depends on the mass and size of the world being left. From the Moon it is about 2.4 kilometres a second, and that is why the Moon has no air. Gas molecules dart about at hundreds of metres a second, and the fastest of them exceed the Moon’s escape velocity, so in time any gas there leaks away into space. The Earth’s stronger gravity keeps its atmosphere.

On most coasts the sea rises twice a day and falls back twice. The main cause is the Moon. Its pull is stronger on the side of the Earth facing it than on the far side, because that side is nearer. The difference stretches the oceans along the line toward the Moon and raises two bulges of water, one facing the Moon and one on the opposite side. The second surprises people. There the water is pulled least of all, and it is left behind as the Earth itself is pulled away from it.

As the Earth spins, each coast passes through both bulges in a day, so high tides come a little over 12 hours apart. The Sun raises tides too, a little under half as high as the Moon’s. At full moon and new moon the two line up, and the tides are at their largest.

Gravity is by far the weakest of the fundamental forces of nature. A fridge magnet lifts a paperclip against the whole Earth’s pull.

That weakness makes gravity hard to measure. In 1798 Henry Cavendish did it in a closed shed with a torsion balance: a rod hung from a fine wire, a small lead ball at each end. Two large lead balls brought close pulled on the small ones and twisted the wire. From the twist he worked out the Earth’s density.

Density becomes mass once the Earth’s size is known, which had been measured more than once long before. About 1020 al-Bīrūnī did it from one mountain top at Nandana, in what is now Pakistan: he measured how far the horizon dipped below the level, and trigonometry gave him the Earth’s radius. As his units are usually converted, his result is within a few per cent of today’s value.

Small bodies in space come in any shape, and many asteroids look like potatoes. But large bodies, from several hundred kilometres across, are nearly always round, and gravity is the reason. Each piece of a large body is pulled toward its centre. On something as massive as a planet that pull is stronger than rock, so anything that sticks out is slowly dragged down and every hollow is filled. Gravity pulls evenly inward from every side, and the only shape with no high ground left to fall from is a sphere.

The same inward pull makes stars. A star begins as a huge cloud of gas. Gravity draws the cloud together, and as the gas falls inward it is squeezed, and the energy of its fall turns into heat. When the centre reaches about ten million degrees, nuclear reactions begin there, and they keep the star shining.

Newton’s law says how strongly gravity pulls, and never how the pull crosses empty space. In 1915 Albert Einstein gave a different account. A mass, he said, bends space and time around it, and other things follow the straightest path they can through that curved space and time. The Earth circles the Sun as a marble circles a dip in a stretched sheet.

The theory made a bold prediction. Light has no mass, yet it too must follow the curve. During the solar eclipse of 1919, astronomers photographed stars near the edge of the darkened Sun and found them shifted by about the amount Einstein had calculated.

Squeeze enough mass into a small enough space and the escape velocity passes the speed of light. Then nothing gets out, light included. Such an object is a black hole, and in 2019 astronomers published the first picture of the shadow of one.