Trajectory Optimization of a Low-Thrust Geostationary Orbit Insertion for Total Ionizing Dose Decrease

Abstract

The paper considers a method of the dose exposure decrease from the charged particles of Earth’s radiation belts (ERBs) affecting a reusable orbital transfer vehicle, which is launched from a low circular orbit into geostationary orbit using a nuclear electric propulsion system. The main idea of the method consists in numerical continuation of a solution of the minimum time problem with respect to an ionizing radiation dose accumulated at the end of a transfer. To do this, equations of motion of the orbital transfer vehicle are supplemented by an additional equation for the radiation dose, and the boundary condition for the dose at the right end is introduced. In calculating the dose, the AE8/AP8 MIN, AE8/AP8 MAX, and AE9/AP9 models of fluxes of charged particles of ERBs were used. By changing the insertion trajectory shape, it became possible to lower the radiation dose by 25–38% relative to the minimum time trajectory. At the same time, the transfer time increased no more than by 7% of the minimum time of launching into geostationary orbit, and the characteristic velocity expenses increased by 320–560 m/s.