How it works

The speed for Newton’s cannon can be worked out from two facts.

Anything dropped near the ground falls about 5 metres in its first second. And the Earth’s surface curves away from a level line by about 5 metres for every 8 km you travel. Put them together: if the ball covers 8 km in the second it takes to fall 5 metres, the ground has dropped away by the same 5 metres, and the ball is no nearer to it than before. So the speed needed is about 8 km every second. The exact figure at the surface is 7.9 km/s.

Real orbits. The International Space Station flies about 400 km up, at 7.7 km/s, and goes round the Earth in 93 minutes. Higher orbits are slower, because gravity is weaker further out and less sideways speed is needed to keep missing. A satellite 35,786 km up moves at 3.1 km/s and takes one whole turn of the Earth to go round, so it hangs over one spot on the equator. That is where television and weather satellites sit. The Moon, 384,400 km away, moves at just 1 km/s and takes 27.3 days.

Floating is falling. People on the Space Station are not beyond gravity. At that height it is still nearly 90% as strong as on the ground. They float because they, the station and everything in it are all falling together, so nothing presses on anything else.

Too slow, too fast. Below the circular speed, the path dips towards the ground on the far side and, close to the Earth, runs into the air. A little above it, the orbit stretches into an oval that swings out further on the far side. At 1.41 times the circular speed the oval never closes, and the ball leaves for good. From the Earth’s surface that escape speed is 11.2 km/s.

Not one of these numbers depends on what is being thrown. A grain of dust and a space station at the same height keep the same orbit at the same speed.