How much energy does it take to get into space? | NumberHub with Timandra Harkness | Head Squeeze


It's world space week already have seen my film on how far away is extra-terrestrial life? But I'm back with another question, How much energy does it take to get to space? Now I'd love to get into space but there is just one thing stopping me — gravity. How much gravity? Thanks to Isaac Newton we can work that out if we know mass of the two bodies involved, in this case me and the earth, so 70 kilos and quite a lot more than that, and how far away the two bodies are or rather the square of how far away they are. So in this case I'm on the surface of the earth about 6000 kilometres from the centre so it's the square of 6000 kilometres. Now you can think about gravity as an acceleration if you imagined if I jumped out of a plane I'd accelerate towards the earth unless I was wearing a jet pack that was exerting an equal and opposite force pushing me away from the earth.

So using that we can work out the velocity, the speed away from the earth that I would need to get a certain distance in space. And we can work out that if I travel 11,184 meters per second that's enough to take me to infinity, so if I travel faster than that I can get to infinity and beyond. But I don't want to go to infinity, I want to go to the moon, how much speed will I need to get me there? Well this is where the force of gravity can help because if I get a certain distance towards the moon, the moon's gravity will pull me in. because the Earth's mass is 81 times that of the moon, it is in theory 81 times stronger but it also depends on the square of the distance. If I get nine tenths of the way towards the moon then the earth's gravity has not diminished in strength by the power of nine, it's the square of nine so it's a factor of 81. So that's enough to balance the difference in mass between the earth and the moon. And if I get slightly passed that point then the moon's gravity will be stronger as far as I'm concerned and pull me in the last bit of the way.

So how fast do I need to be going to get just past that point? I need to be travelling just over 11, 168 meters per second. Great so all we need is a great gun that will fire me at 11,168 meters per second and I'll go all the way to the moon. One problem here is the atmosphere. Obviously if we didn't have an atmosphere we wouldn't be here making these films and you and me watching them, but it does have some problems because of the air resistance will slow me down I'll need about 10% extra speed just to overcome that. And also the friction, if I was to be launched out of a gun at 11,168 meters per second the friction just from the air would incinerate me. Even if I was inside a spaceship the heat would be ridiculous. This is why rockets are so great because with rockets you don't have to start at that speed you can accelerate towards it. Because a rocket works by another of newton's rules, if you chuck enough energy out the back in the form of exhaust gases it will fire you forward at the same speed and you will keep accelerating.

The rockets that took Apollo 11 towards the moon weighed 2,766,913 kilograms at launch. And that is a lot of mass to accelerate to 11,168 meters per second. But most of that weight is fuel, so if every tonne of fuel I'm burning, not only am I accelerating in the direction I want to go but it's also reducing the mass it has to move by a tonne. And this is a continually changing process which is why we need Newton's other great invention Calculus. And by using this we can work out exactly how much fuel we'll need to get the bit that we actually want to get a spaceship with me out as far as the moon. And there is a lovely equation for that. You take the initial mass the great hefty rocket fuel on the launch pad, you divide it by the final mass the little bit with me going off into space, you take the logarithm of that because of the whole business with Calculus, you multiply it with the effective exhaust velocity, and then that gives you the difference in velocity. So using that and knowing the velocity we're aiming for in the end, 11,168 meters per second, we can work out exactly how much fuel we need to get us from a great heavy rocket on the launch pad to me shooting off towards the moon.

So in short the answer to how much energy to get into space is…depends on your rocket. Talking of using up energy find out what happened with Head Squeeze pushed Greg Foot's body to the max, and how much energy is in an Easter egg..