Approximate solution of spacecraft motion with an inward constant radial acceleration

This Short Communication analyzes the motion of a spacecraft whose primary propulsion system generates an inward, radial propulsive acceleration of constant magnitude. Starting from the classical literature results regarding the more common outward radial-thrust case, the proposed mathematical model uses a set of modified non-singular orbital elements to describe the spacecraft motion around a generic primary body. Assuming a circular parking orbit and a small propulsive acceleration magnitude, a perturbation method, based on an asymptotic series expansion truncated at second order, is used to obtain analytical expressions of the spacecraft propelled trajectory. The obtained results are applied to an orbital targeting problem and, in this context, the resulting spacecraft trajectory is accurately approximated through analytical functions. The proposed procedure is also able to well estimate the thrust level and the swept angle required to reach the target state.