The motion of a rocket is governed by the conservation of momentum principle. A rocket's momentum changes by the same amount (with the opposite sign) as the ejected gases. As time goes by, the rocket's mass (which includes the mass of the remaining fuel) continuously decreases, and its velocity increases. Therefore, the principle of conservation of momentum is used to explain the dynamics of a rocket's motion. The ideal rocket equation gives the change in velocity that a rocket experiences by burning off a certain mass of fuel, which decreases the total rocket mass. This equation was originally derived by the Soviet physicist Konstantin Tsiolkovsky in 1897.
The total change in a rocket's velocity depends on the mass of the fuel that is being burned during the flight, which is not linear. Furthermore, the rocket's acceleration depends on the speed of the exhaust gases. Therefore, the speed of the exhaust gas should be as high as possible to achieve the maximum velocity. Also, for a given speed of the exhaust gas, the maximum speed for the rocket is achieved when the ratio of the initial mass to the final mass of the rocket is as high as possible; that is, the mass of the rocket without fuel should be as low as possible, and it should carry a maximum amount of the fuel. The ideal rocket equation only accounts for the reaction force exerted by the exhaust gases on the rocket. It does not account for any other forces acting on the rocket.
This text is adapted from Openstax, University Physics Volume 1, Section 9.7: Rocket Propulsion.
