• low thrust trajectories
• optimal control

Electrically propelled spacecraft in geocentric orbit-raising trajectories transit through the Van Allen radiation belts over months and accumulate a considerable amount of charged particle radiation dosage resulting in significant degradation of the solar panel performance. This implies that such missions will have to carry additional solar panel mass to compensate for the optical degradation. This study is concerned with solving the low-thrust trajectory optimization problems for spacecraft in geocentric missions propelled with an electric thruster powered by solar panels alone. Geocentric low-thrust trajectory optimization problems which minimize the payload mass for the launcher, fuel consumption and transfer duration are studied. The mass minimization problems are formulated to minimize the initial mass with the final payload mass fixed, which is often how the practical mission requirements arise. Optimal control problems are formulated on a state dynamics formed by coupling the optical degradation dynamics with the low-thrust spacecraft dynamics written using an equinoctial orbital element set. The dynamics also includes the effect of eclipses and perturbations, with the J2 perturbation implemented in this study. The optimal control equations are derived with periodic averaging applied to the state dynamics to eliminate fast-time-scale variations due to the unperturbed natural rate of the fast orbital element. The method of averaging is utilized in a manner not violating the conditions of its applicability to derive the two-point boundary value problems of optimal control for both orbit transfer problems and rendezvous problems. Transversality conditions for indirect optimal control are derived from the first principles to be able to write the two-point boundary value problem equations for minimum initial mass problems and time-limited problems, and to be able to couple optical degradation terminal conditions with spacecraft mass terminal conditions. Numerical techniques have been developed to solve the two-point boundary value problems of optimal control and in particular it is seen that the numerical techniques developed are able to converge from arbitrary initial conditions for both geocentric and heliocentric transfer problems when optical degradation is not included. Some practical solutions for faster computation of conservative estimates for mass budget calculations during the preliminary mission analysis phase are also proposed.