Analytical solutions for optimal low-thrust limited-power transfers between coplanar orbits

Abstract

In this paper, analytical solutions, which include the short periodic terms, for the problem of optimal time-fixed low-thrust limited power transfers (no rendezvous), in an inverse-square force field, between coplanar orbits are revisited. These solutions are expressed in classical orbital elements for transfers between elliptical orbits and in nonsingular elements for transfers between orbits with small eccentricities. In both cases, the solutions are derived through anonical transformation theory. A brief discussion about the solution of the two-point boundary value problem of going from an initial orbit to a final orbit at the prescribed final time, based on the analytical solutions, is also presented.