The Dynamics of Low-Thrust Spacecraft Manoeuvres

Abstract

Summary Orbital manoeuvres by means of impulsive thrusts, such as those available with chemical rockets, are well known, but a different treatment is needed for the small, continuous thrusts that are typical of electrical propulsion systems. It is shown that with the aid of these small forces it is possible to change independently all the orbital elements of a spacecraft, and thus to proceed slowly from a given orbit to any other. For each manoeuvre there exists an equivalent velocity which depends only on the initial and final orbital states, and which can be related directly to the spacecraft propulsion parameters. For any form of propulsion where the propellent acquires some or all of its energy from a separate energy source, as in electrical propulsion, it is found that optimum time-varying relations exist between the flow of mass and of energy, which may also be expressed in terms of the exhaust velocity and the thrust. In particular, the optimum exhaust velocity is shown to be an increasing function of time, related to the way in which the energy is released. The practical realisation of electrical propulsion depends on the development of efficient propulsion units and of lightweight power supplies; these and other spacecraft components are discussed, and a number of examples of orbital manoeuvres are given, including close-Earth, far-Earth and lunar orbits. The paper concludes with a discussion of these orbital transfers in relation to their possible uses, including communication satellites and a test of relativity theory