Optimum rocket propulsion for energy-limited transfer

In order to effect large-scale return of extraterrestrial resources to Earth orbit, it is desirable to optimize the propulsion system to maximize the mass of payload returned per unit energy expended. This optimization problem is different from the conventional rocket propulsion optimization. A rocket propulsion system consists of an energy source plus reaction mass. In a conventional chemical rocket, the energy source and the reaction mass are the same. For the transportation system required, however, the best system performance is achieved if the reaction mass used is from a locally available source. In general, the energy source and the reaction mass will be separate. One such rocket system is the nuclear thermal rocket, in which the energy source is a reactor and the reaction mass a fluid which is heated by the reactor and exhausted. Another energy-limited rocket system is the hydrogen/oxygen rocket where H2/O2 fuel is produced by electrolysis of water using a solar array or a nuclear reactor. The problem is to choose the optimum specific impulse (or equivalently exhaust velocity) to minimize the amount of energy required to produce a given mission delta-v in the payload. The somewhat surprising result is that the optimum specific impulse is not the maximum possible value, but is proportional to the mission delta-v. In general terms, at the beginning of the mission it is optimum to use a very low specific impulse and expend a lot of reaction mass, since this is the most energy efficient way to transfer momentum. However, as the mission progresses, it becomes important to minimize the amount of reaction mass expelled, since energy is wasted moving the reaction mass. Thus, the optimum specific impulse will increase with the mission delta-v. Optimum I(sub sp) is derived for maximum payload return per energy expended for both the case of fixed and variable I(sub sp) engines. Sample missions analyzed include return of water payloads from the moons of Mars and of Saturn.