In “Gravity’s Terms and Conditions”, clause five dealt with astronauts. They float, it said, not because the service is switched off in space but because they are falling, “with very good aim”. It sounds like a joke. It’s actually an exact piece of physics, and you can work out the aim required with nothing more than the Earth’s size and how fast things fall.
First, the clause’s claim that gravity is still running up there. The space station orbits about 400 kilometres above the ground. That sounds far, but the Earth’s radius is about 6,400 kilometres, so the station is only about six per cent further from the Earth’s centre than you are. Gravity weakens with the square of the distance, and at that height it is still around 90 per cent as strong as on the ground. If you could build a tower 400 kilometres high and stand on top, you would feel almost exactly as heavy as you do now.
So why don’t astronauts fall? The answer is that they do. Newton explained how with a thought experiment, published after his death. Imagine a cannon on top of an impossibly high mountain, firing horizontally. Fire gently and the ball curves down and lands near the foot of the mountain. Fire harder and it lands further away. But the Earth is round. If you fire it fast enough, by the time the ball has curved down towards the ground, the ground has curved away beneath it. It keeps falling. It keeps missing. It comes back round and hits the cannon from behind.
How fast is fast enough? Here is where the numbers fall into place beautifully. Anything dropped near the Earth falls about five metres in its first second. And the Earth is curved in such a way that if you travel eight kilometres in a straight line, the ground below has curved away by, again, about five metres. So imagine a ball travelling sideways at eight kilometres every second. In one second it falls five metres, and in that same second it travels eight kilometres, over which the ground has dropped five metres. It is no closer to the ground than when it started. The next second, the same thing happens again, and the next, and the next. That is an orbit: a fall that never lands, because it is too fast to hit anything.
Real orbits need to be above the thick part of the atmosphere, or air resistance slows them down, which is why the space station flies at 400 kilometres, where the air is so thin that it only needs an occasional boost. At that height, the speed required is a little less, about 7.7 kilometres a second, or around twenty-eight thousand kilometres an hour. At that speed, the station goes round the Earth in about an hour and a half. Its crew see sixteen sunrises every day.
Now the weightlessness. What you feel as weight isn’t gravity itself. It’s the floor pushing back on you. Stand on a weighing scale, and the number it shows is how hard the scale has to push up to stop you falling. In the space station, the floor is falling too, at exactly the same rate as the astronaut, because gravity accelerates everything equally, as clause two of the terms promised. So the floor never has to push. The astronaut, the floor, the walls, a floating pen and a blob of water all fall together, side by side, around the planet. Nothing presses on anything. That is what weightless means: not without gravity, but without support.
You’ve felt a tiny version of this yourself, in the sinking feeling at the top of a swing or as a lift starts quickly downwards. For that moment, the seat or floor stops pushing on you as hard, and your stomach notices. Astronauts feel it all the time. It takes some getting used to, and their bodies change: without weight to carry, bones lose minerals and muscles weaken, which is why crews exercise for around two hours a day on treadmills, with harnesses pulling them down onto the belt.
The same rule works at every height, but the speed changes. Further out, gravity is weaker, so orbiting things don’t need to go as fast to keep missing, and they have further to go round. About 36,000 kilometres up, an orbit takes exactly one day, so a satellite there keeps pace with the Earth’s spin and seems to hang still above one spot. Much further out, at about 384,000 kilometres, the Moon takes almost a month. The Moon, too, is falling towards us, all the time, and missing. Every orbit in the solar system is the same trick: Newton’s cannonball, fired just right.