Analytical solutions for low-thrust orbit transfers

Abstract

This paper presents analytical solutions for the estimation of the Δ V cost of the transfer of a spacecraft subject to a low-thrust action. The equations represent an extension of solutions already available in the literature. Moreover, the paper presents novel analytical solutions for low-thrust transfers under the effect of the second-order zonal harmonics of the Earth’s gravitational potential. In particular, the paper is divided into two parts. The first part presents analytical expressions for the Δ V cost of transfers. All analytical equations were validated through numerical integration of the dynamics of the spacecraft. The second part of the paper introduces new analytical equations for low-thrust transfers between circular inclined orbits with different values of the right ascension of the ascending node, under the effect of the second-order zonal harmonic of the Earth’s gravitational potential. Both in the first and second parts, analytic solutions for the variation with time of the orbital elements during the transfer are presented. The proposed equations are applicable to low-thrust transfer realised through a long spiral trajectory.