Gravity and Orbits

Fire a cannonball and watch gravity decide its fate

In the 1680s Isaac Newton imagined a cannon on a very tall mountain, firing horizontally. Fire it slowly and the ball drops to the ground nearby. Fire it faster and it lands farther away. Keep going and something remarkable happens: the ground curves away as fast as the ball falls. Use the slider to run Newton's experiment. The planet here is Earth-sized and the air has been removed, so only gravity acts.

The same force that drops an apple holds the Moon

The story of the apple is probably tidied up, but the idea behind it is real. Newton asked whether the force that pulls things to the ground might reach all the way to the Moon, only weaker. He knew the Moon is about 60 times farther from Earth's centre than an apple is. If gravity weakens with the square of distance, the pull there should be 60 × 60 = 3,600 times smaller than at the surface.

Do the sum. Surface gravity pulls things down at 9.8 metres per second, every second. Divide by 3,600 and you get about 0.0027, which makes the Moon fall roughly 1.4 mm each second. Newton compared that to how much the Moon's path actually bends and found they matched. The ground and the sky, which people had treated as separate worlds for thousands of years, obeyed one rule.

Astronauts are not floating because there is no gravity

Picture being in a lift whose cable snaps. You and the lift fall together, so you would drift weightlessly inside it even though gravity is working fully. The ISS is that lift, except it also moves sideways at about 7.7 km/s, or about 27,600 km/h. It falls constantly and constantly misses Earth, completing a lap in about 92 minutes. The crew see around 16 sunrises every day.

To catch a satellite ahead of you, you slow down, not speed up

Orbits behave in ways that trick everyday intuition. Higher orbits are slower, not faster, because gravity is weaker there and less sideways speed is needed to keep missing. Yet to reach a higher orbit, a spacecraft has to fire its engine forward to speed up. Here is what happens next:

1. The spacecraft speeds up with a short burn, so its path stretches into an oval that rises on the far side of Earth.
2. As it climbs, it trades speed for height and slows down, just like a ball thrown upward.
3. At the top of the oval it fires again to round the path into a new circle, now at a higher altitude and moving slower than before.

Tides, satellites and the reason your phone knows where you are

Newton told us how gravity behaves. Einstein suggested what it is.

Newton's formula predicts orbits superbly, but he admitted he did not know why masses attract one another. In 1915 Albert Einstein proposed general relativity: mass and energy bend space and time, and objects follow the straightest possible path through that bent space. A planet orbits not because a string pulls it but because the space around the Sun is curved.

A common picture is a heavy ball sinking into a stretched rubber sheet while marbles roll around it. It is a helpful image with a flaw, because on a sheet "down" is itself caused by gravity. The real bending involves time as well as space, which is why GPS clocks need correcting.

• 1687: Newton publishes his law of universal gravitation in the Principia.
• 1798: Henry Cavendish weighs the Earth indirectly by measuring the tiny attraction between lead balls.
• 1915: Einstein publishes general relativity.
• 1919: Starlight is seen bending around the Sun during an eclipse, matching Einstein's prediction.
• 1957: Sputnik 1 becomes the first artificial satellite.
• 2015: LIGO detects gravitational waves, ripples in space-time from colliding black holes.

Three orbits that quietly run modern life

Because orbital speed depends on height, each altitude gives satellites a different job. Here are the three families you rely on, with the numbers that define them.

Notice that the higher the orbit, the longer the lap. That is Kepler's rule in action, found by studying planets centuries before spacecraft existed: the farther out, the slower the pace. It is also why a satellite in geostationary orbit must be exactly 35,786 km up. At any other height its lap would not match Earth's rotation.

The slingshot that took Voyager to the edge of the Solar System

A spacecraft cannot carry enough fuel to reach Neptune quickly. Instead, mission planners use gravity assists. As a probe swings close to a moving planet, gravity bends its path, and the probe gains a little of the planet's orbital speed. The planet slows by an immeasurably small amount, since it is billions of billions of times heavier.

Voyager 2 used this trick at Jupiter, Saturn and Uranus on the way to Neptune. That journey was only possible because, in the late 1970s, the four giant planets were arranged in a favourable sweep, an alignment that comes around roughly once every 175 years. Miss it, and the same trip would have needed far more fuel or decades more time.

Why you weigh slightly less at the equator than at the poles

The number 9.8 m/s² is an average. At the poles it is about 9.83, and at the equator about 9.78. Two things cause this: Earth bulges at the equator, so you are a little farther from the centre, and the spin reduces your effective weight there. The difference is about half a percent, so a 70 kg person would read around 0.35 kg lighter at the equator. Mountains, ocean trenches and the rock beneath you also change it very slightly, and satellites can map those differences to study the planet's interior and ice sheets.

At the other extreme is gravity so strong that nothing escapes. A black hole is a region where the escape velocity exceeds the speed of light. If the Sun were swapped for a black hole of the same mass, Earth would continue in its orbit exactly as before, though it would be a cold, dark place.

Feel orbits with things you already own

1. The bucket swing. Put a little water in a bucket with a sturdy handle and swing it in a fast vertical circle, outdoors. The water stays inside at the top because the bucket is falling away from it at the same time. This is the same falling-and-missing as an orbit.
2. The paper and the book. Drop a book and a flat sheet of paper together: the book wins. Now place the paper on top of the book and drop both: they fall together. Air resistance, not weight, made the difference.
3. The ball on a string. Whirl a small ball on a string. The string plays the role of gravity, pulling the ball inward. Let go, and the ball moves off in a straight line, just as a planet would if the Sun's pull vanished.