Science: tell me about...escape velocity

Everyone knows what happens when you throw a stone upwards. Gravity eventually makes it fall back to the ground, accelerating it at 9.8 metres per second per second (so one second after it stops rising, its downward speed is 9.8 m/s, one second after that it is 19.6 m/s, and so on).

But imagine if you threw that stone hard enough, and in the right direction - just off-vertical. It would reach a point where it stopped rising; but because you had thrown it so hard, the surface of our spherical world would curve away under it as fast as gravity made it fall. The object would be in orbit, and remain circling the Earth for eternity unless something slowed it down.

Now imagine throwing another object, a bit faster. It will not enter orbit. Instead it will break free from the Earth's gravity and shoot off into space. It has achieved escape velocity, defined as the minimum velocity that will enable a small object to escape from the gravitational attraction of a larger one.

Escape velocity is calculated by the formula 2Gm/r, where G is the gravitational constant, m is the mass in kilograms of the planet from which you want to escape, and r is the distance in metres from the planet's centre. For the Earth, escape velocity at the surface works out as 11.2km per second, or about 25,000mph in old money.

But accelerating a spaceship to 25,000mph needs a lot of heavy fuel, and huge engines. Earth's inconveniently high escape velocity is why the Apollo moon rockets were the size of skyscrapers. If you want to send people to Mars from Earth, and bring them home again, you would need even bigger rockets.

If you could build and launch your spaceship from a place with a much lower escape velocity, the problem would be much simpler. The Moon has only one-sixth of the gravity of its parent planet, and hence a much lower escape velocity - a mere 5,300 mph. Until recently though this was thought to be of little use. Even if you built your spaceships on the Moon, you would still need to cart the fuel for them from the Earth, thus defeating the point of the exercise.

But earlier this month, Nasa scientists excited the world by announcing that they had detected millions of tonnes of rocket fuel on the Moon - in the form of water ice. Water can be separated by solar power into hydrogen and oxygen. Mixed together and ignited, they produce a lot of energy. That means a Mars rocket could be built and launched on the Moon.

- Michael Hanlon

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