How Rockets Work
Rocket of initial mass M and velocity vo releases fuel of mass Dm at velocity vfuel relative to rocket.
Initial momentum Pi = Mvo
(M-Dm)(vo+Dv)+Dm(vo-vfuel)
Divide Dt by & use algebra:
Effective force on rocket is the rate it gives momentum to fuel!
Notes:
The fuel exits as exhaust gas, whose velocity is determined by the chemical potential energy per unit mass that is released by burning of the fuel. The “effective force” on the rocket is proportional to that exhaust speed, so we need high chemical energy per unit mass in the fuel to make an efficient rocket.