Multiorbit Transfers to a Geostationary Orbit with Switching Low Thrust Off in the Shadow Region

Abstract

Transfers in the central Newtonian field are considered under the assumption that low thrust that is constant in magnitude is zeroed when spacecraft with solar batteries enters the Earth’s shadow. Using the maximum principle, the two-point boundary-value problem is formed, in which, however, the conditions for optimal intersection of the shadow boundaries are not considered, which significantly complicates the problem. For this reason, the boundary-value problem is found to be “incomplete” and its solutions are not optimal. Nevertheless, for transfers to a geostationary orbit from highly elliptical orbits, it allows one to obtain “good” trajectories with working substance costs less than those on trajectories without zeroing the thrust, or slightly exceeding them. This is shown by the example of transfers from the initial orbit with an inclination of 13° and with a distance at the perigee of ≈15.6 Mm and at the apogee of ≈83.2 Mm.