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Moonflight

If I were an Olympic high jumper would I be able to jump high enough to escape the moon’s gravity? I suspect not, but some astronauts on the moon’s surface seemed to float in the air for a long time. Exactly how high and how fast would I have to jump to escape the moon’s pull, or simply to fly over its surface? As there is no atmosphere, are my aerodynamics irrelevant?

• Sadly, even an Olympic high jumper would be unable to break free of the moon’s gravity. However, they would be able to leap a lot higher than their earthly counterparts, as the moon’s surface gravity is about six times weaker than Earth’s. The world record is 2 metres 45 centimetres, therefore the moon record would be somewhere in the vicinity of 15 metres.

To escape the moon’s gravity entirely you would have to jump at what is called the escape velocity. This is the speed you need to reach before you can entirely escape a body’s gravitational field at a single kick. For Earth, this is about 11 kilometres per second. To escape the moon’s gravity, the speed is more leisurely but still way beyond a high jumper’s take-off speed.

Escape velocity is the speed which is needed to escape with no further propulsion, but if you gave a slug a very long ladder and sufficient lettuce, it could keep slithering along all the way to infinity without ever having to travel at escape velocity. And so it was with the Apollo lunar modules, which didn’t need to reach escape velocity to get back into orbit because they had an engine providing sustained power.

To fly over the surface of the moon would effectively require going into orbit (or simply leaping a very long distance). An orbit is really just a jump which never comes back down because the body over which you move is spherical and its surface is falling away from you as fast as you are falling towards it. In order to go into orbit just above the surface of the moon, a high jumper would need to leap at about 1 kilometre per second – still rather out of range.

So all the moon is really good for, if you are a high jumper, is setting new extraterrestrial records. You’ll need to find a planet significantly smaller before you can fly off into the sunset – even with a high jumper’s legs.

Andrew Steele

Newport, Shropshire, UK

• To escape the clutches of the moon’s gravity you would need an escape velocity of 2.38 kilometres per second, about a fifth of the 11.2 kilometres per second required to escape from Earth. Gravity is six times weaker on the surface of the moon than it is on Earth, so in theory athletes on the moon would be able to jump six times as high as they can on Earth. The moon record for the high jump would then be 14 metres 70 centimetres. Pole-vaulters would be able to clear the twin towers of the old Wembley Stadium in London and TV programmes could dispense with slow-motion action replays because the jumps would take six times longer. However, all this could be achieved only if athletes could run as fast on the moon as they can here on Earth and, given the difficulties experienced by moonwalking astronauts, this seems unlikely.

Nonetheless, those who can clock a respectable 11.4 seconds for the 100 metres would be running fast enough to launch themselves from the asteroid Toro: discovered in 1964, Toro has a radius of only about 5 kilometres. Those who are not quite as nimble on their feet might want to choose one of several smaller asteroids. With a radius of only 1 kilometre, a brisk walk on Geographus, for example, might do the trick. It’s gravitational field strength is less than one 6000th that of the moon.

Assuming however, that you are restricted to the moon but really needed to escape its gravitational field, you could climb a ladder to escape. According to the British government’s Department of Health, the average man needs to consume about 2550 calories per day. Our bodies are about 40 per cent efficient at converting food into useful energy. Assuming no other losses and that the food consumed was used solely for climbing the ladder, it would take an average man 49 days of continuous climbing, 24 hours a day, to escape the moon’s gravitational field.

Mike Follows

Willenhall, West Midlands, UK

• You would not be able to jump very high on the moon – the slow movements of astronauts are only relative to our perceptions which have evolved on Earth. Even a rifle bullet would not escape from the moon if fired vertically upwards.

You would need a very small body, such as the asteroid Eros, which passes relatively close to the Earth, to have a chance. Eros is 34 kilometres long and has an estimated escape velocity of 3.1 metres per second at the pole – about the speed of an Olympic high jumper.

However you can also leave the surface travelling horizontally if you achieve orbital speed. This speed is equal to the escape velocity of the asteroid multiplied by 0.707 (for a sphere) minus any speed due to the body’s rotation. On the moon you would need to be travelling at 6000 kilometres per hour, but you could orbit Eros at just 6.5 kilometres per hour, which would give a new meaning to the term space walk.

Jerry Humphreys

Bristol, UK

Even if we allow an athlete the use of a stored-energy device, such as a catapult, the amount of energy required to achieve escape velocity from the moon is equivalent to 17 ascents of Everest, starting from sea level. It would be a long and exhausting process.

However, using stored energy or a system of levers, it might be feasible for a human to put a small object into orbit about the moon. A golf ball can exceed 320 kilometres per hour and levers could transform this into a much higher speed. Additionally, if a weight was swung round on a string while you progressively play it out, because of the lack of air resistance on the moon, the weight could attain the required speed and travel into orbit when released.

Terence Collins

Harrogate, North Yorkshire, UK

This week’s question

Leading astray

I have noticed that there are strange cylinders around the leads of most computer peripherals. On further investigation these seem to contain two crescent-shaped magnets that form the outside of the cylinder, while the lead runs through the middle. What do these do and how do they do it?

Richard Bradish

No address supplied