Escape velocity - how it works

For those who haven't caught Ricky Gervais' new show it stars one Karl Pilkington whose utterances can leave you flabbergasted as to where they came from. Then I get reminded that there are others around just like him.


I won't get into the details, but I was talking to someone about atmospheric bleed and dust and how in theory dust particles could become suspended in an air current and be bounced up to a point where they are freed from the Earth and float into space. His response was that this was impossible as dust was heavier than air. After acknowledging that aircraft are also heavier than air yet manage to fly the next argument presented was that it wasn't travelling fast enough as it needed to reach escape velocity. After refuting this logic I was asked

"So what is stopping an aeroplane from just flying to the Moon?"

Well in theory nothing. This led to talk about space elevators etc. but I just kept getting a shake of the head and the words "Escape velocity" thrown at me despite explaining he'd got the wrong idea about what it was.

So here we go hopefully something presented in a simple format that everyone can understand:

Gravity is a result of mass, the Earth has a lot of mass and thus a lot of gravity compared to, say, you or I. Gravity shows itself in the everyday world as a constant acceleration downwards. The reason we don't really feel it is because we're used to it, but still we're being constantly accelerated downwards and in the case of the Earth at 10m/s/s; that's 10 metres a second for every second.

So to move anything away from the Earth I need to use a force that provides it with enough energy to counter that constant drag. If I provide enough energy to move an object upwards at 11m/s/s then after one second it'll only have an acceleration of 1m/s/s and so only be travelling at 1m/s as gravity pulls it back downwards.

So imagine I throw an object into the air such that after one second it has a speed of 20m/s, but no acceleration. Another second passes and the speed is 10m/s as gravity pulls it down and nothing forces it upwards. After the third second it has a speed of 0m/; it's stopped.

Then what?

Well it starts to fall gaining 10m/s every second. At the fourth second it falls at 10m/s at the fifth 20m/s at the sixth 30m/s and so on until it hits the ground (assuming no air resistance).

Now if I say after one second it was at ground level then it would manage to reach a height of 30m from the ground before the force I gave it was countered by the relentless pull of gravity. So if I made it move faster it should go higher, if I can move it fast enough I could make it reach a height where the pull of the Earth's gravity became negligible and thus it would never fall.

The speed I would need to reach to do this is the escape velocity.

Is an object that doesn't reach this speed destined to fall back to the Earth? Well no. The bit that tends to be overlooked when discussing escape velocity is that I've thrown the object up and then done nothing to it. That means the only force working on it is the initial amount of energy I used to get it into the air and that 'runs out' which is why it starts to fall if it hasn't got far enough to escape the pull of gravity.

What if I could keep giving my object some extra force to keep it moving; I could fit rockets to it. Does it still need to reach escape velocity in order to leave? Again no; if I could move it at a constant speed of 10m/s my object would reach geosynchronous orbit in about 41 days. Better yet if my object was large enough to contain people they wouldn't suffer from any form of "g-force" other than that provided naturally by gravity itself.

If that's the case why do space rockets travel so fast with such high acceleration and subject the occupants to g-forces? Isn't this to reach escape velocity? Yes and no. If they had enough fuel on board to provide a constant speed upwards until they reached orbit it wouldn't matter what speed they were travelling at. However in the current design of craft the fuel necessary to provide the force is carried by the craft. Fuel has mass and the more mass the more force is required to move an object; add more fuel to compensate and you've just added yet more mass.

So the amount of fuel you would need to carry to allow a craft to provide a constant speed of 10m/s for 41 days wouldn't be enough to move the combined mass of the craft and the fuel. So you compromise and carry enough fuel that will move the craft and accelerate it hard so you reach escape velocity in the shortest possible time. Once you've reached that speed you no longer need the extra force and can conserve fuel for the return trip.

What's the point in talking about travelling at a constant 10m/s then? Well the current hard acceleration is all based on having to take the fuel (or energy source) with you. What if you could leave it behind?

Imagine a conveyor belt - it has an engine at one end that turns a wheel that moves the belt. Rotate it from the standard horizontal position to the vertical, fit hooks to the belt and attach craft to the hooks. The amount of force required to move the belt would depend on the mass of the objects attached to it, but that force is supplied separately at the base. So long as it can take the strain and the engine keeps getting fed the belt can move at a constant speed.

For another idea imagine a sailboat that moves due to the pressure of the wind. Alter the sail to the horizontal and put a fan underneath it; like the belt so long as the fan is fed and provides enough force to lift it the craft it can travel upwards at a constant speed.

Of course in both cases I'm being allegorical the 'belt' would be a carbon-nano tube fibre and the 'fan' would be a high-powered laser, but still it's possible to leave this planet without hitting the magical escape velocity.