La Zapetera Prodigiosa

Other-http://www.real-world-physics-problems.com/rocket-physics.html
Rockets fly. We all know that. But how do they fly? And more importantly, how can we calculate how they will fly given certainparameters? The simple answer is that rockets fly by using Newtons third law, for every action there is an equal and opposite reaction. But the calculations that govern rocket motion are much morecomplicated than this. I will go over the derivation of these calculations here.
To figure out how a rocket will accelerate, we rely heavily on conservation of momentum. That is, for a given system, inour case the rocket-gas system, the TOTAL momentum will remain constant even if individual components move around. So if some component of the system (the gas) moves in one direction with a givenmomentum, some other object (the rocket) will have to move such that the two momentums exactly cancel each other out.
If a rocket is moving through space with a given velocity, V, it is quite easy tofigure out its momentum, Pi, Since it is simply equal to the mass of the rocket times it's velocity.

Once you apply thrust, however, the situation becomes more complicated. You now have two masses todeal with, and two momentums to deal with. However, keep in mind that the total momentum of the system remains unchanged. So if we call the change in the velocity of the rocket dV, the mass of the gasemitted dM, and the velocity of the gas emitted relative to a stationary observer U, then the situation becomes Pf=U*dM+(M-dM)(V+dV), since the momentum of the system is equal to the momentum of thegas plus the new momentum of the rocket.

We now have all the elements we need to relate the velocity of the gas emitted to the velocity of the rocket, and to find the final momentum of the system. Todo this, we will need to solve the above equation for the velocity of the gas. Our first step is to write U in terms of the velocity of the gas relative to the rocket and the velocity of the...