[Rhodes22-list] How Much Energy To Launch A Payload Into Space?

[Roger Pihlaja]

Gentlemen,

I don't think you folks appreciate how much energy it requires to lift a payload into space.  Just for snicks and grins, I did the following rough calculation:

Suppose we want to be able to shoot 10 tons (9091 kg) off the earth into the sun.  To do this, we must somehow accelerate the mass from rest up to so-called escape velocity.  Escape velocity from the earth is about 25000 mile/hr (11176 m/s).  Suppose we build a "rail gun" up the side of a mountain.  Now, once per day, the earth's rotation will have our rail gun pointed in the correct direction to shoot a payload into the sun.  Let's say we can build our rail gun 10 km long.  For the sake of simplicity, we will assume the acceleration in the rail gun will be constant over the entire 10 km and there are no losses due to friction, magnetic coupling, electrical resistance, etc.  How much power do we have to feed this rail gun?

The required acceleration is 6245 m/s^2 or about 637 g's!  The payload will have to withstand this acceleration for 1.79 seconds.  The energy required is 5.677E11 joules and the power is 3.172E11 watts.  That's 31720 megawatts!  Keep in mind that a big nuclear power plant is typically rated at around 1500 megawatts.  So, our rail gun facility needs about 211 world scale nuclear power plants all operating at rated capacity to supply it with sufficient power to launch one 10 ton payload per day into the sun.

The power requirement for an explosive powered cannon is similarly astronomical!

Yeah I know, I need to get a life. :)

Roger Pihlaja
S/V Dynamic Equilibrium