A rocket engine operates on the principle that hot gas is expelled backwards through a nozzle in order to produce a thrust on the ship in the opposite direction. Since momentum is conserved in this operation, we can derive the result that the effective force on the ship is
Feffective = Mu
where M is the mass expulsion rate, and u is the exhaust velocity relative to the ship. Thus it is important for both M and u to be high. The exhaust velocity varies as the square root of the ratio of the temperature of the combustion chamber and the molecular mass of the exhaust.
In conventional rocket engine design, large fuel tanks carry liquid hydrogen and oxygen, and these react by chemical combustion to yield water vapor. The water vapor, due to its high temperature, shoots out of the nozzle, and the ship is thrust forward.
In an experimental engine design, nuclear fission of uranium is used to heat a supply of hydrogen to high temperatures (around 2200 K). The hydrogen is then expelled through a nozzle at 1.0 x 104 m/s, about twice the exhaust velocity as that for conventional rockets. One major engineering problem involves the heat exchange between the hydrogen gas and the site where the nuclear reaction takes place. Engineers are improving the design so that the hydrogen is heated at a faster rate than it is in current designs.
A rocket ship is going forward at 2000 m/s and fires its engines in order to speed up but not turn. If the absolute velocity of the exhaust gases is 3000 m/s going backwards, what is the exhaust velocity u relative to the ship?