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Newton's cannon

Gravity and orbits · level 2, lesson 5 of 6

A question to start

You throw a ball sideways and it lands a few metres away. A strong throw lands farther. What if you could throw really hard, faster than anything? Where would the ball land?

The idea

Isaac Newton asked this about 340 years ago. He imagined a very tall mountain, so high that it pokes above the air, with a cannon on top that fires sideways.

slowfasterfaster stillfast enough: it never lands
  • A slow shot curves down and lands near the mountain.
  • A faster shot goes farther before it lands.
  • A faster shot still lands far round the curve of the Earth.
  • Fast enough, and something wonderful happens. The ball falls, but the ground curves away beneath it just as fast as it falls. It never reaches the ground. It falls all the way round the Earth and comes back to the cannon.

That is an orbit. A thing in orbit is falling all the time and missing all the time. It is how the Moon goes round, how the space station goes round, and how a ship waits in orbit around Mars before landing.

How fast is fast enough? Just above the Earth, about 8 km every second: from one end of a city to the other in a couple of seconds. On Mars, which pulls less, it is about 3.5 km a second. That is one reason getting off Mars takes much less fuel than getting off the Earth.

Worked examples

1. Why the mountain is above the air. Air slows a cannonball down. At the height of the space station (about 400 km up) there is almost no air, so a satellite can keep going round for years.

2. The space station. The International Space Station goes round the Earth about 16 times a day. The astronauts in it are falling round the Earth together with it, which is why they float.

Try it

  1. What happens to a cannonball fired sideways slowly?
  2. Why does the fastest cannonball never land?
  3. About how fast must something go to orbit just above the Earth?
  4. Is it easier to get into orbit around Mars or around the Earth? Why?
Answers
  1. It curves down and lands nearby.
  2. As it falls, the curved ground drops away beneath it just as fast, so it keeps missing.
  3. About 8 km a second.
  4. Around Mars: it pulls less, so you only need about 3.5 km a second.

Common mistake

"Satellites stay up because there is no gravity in space." Gravity at the space station is still about nine tenths as strong as on the ground. The station stays up because it is moving sideways so fast, not because gravity is gone.

Where it leads