Velocity-to-Be-Gained Deorbit Guidance Law Using State Space Perturbation Method

Abstract

Deorbit guidance laws steer a reentry spacecraft from the parking orbit to the entry interface (EI) while satisfying some terminal constraints. The guidance precision has great influence on the shape of the reentry trajectory, heat flux, aerodynamic overload, and safety. When the Earth’s j2 effect is taken into consideration, the guidance law becomes either complicated or of heavy computational load. Therefore this paper proposes a velocity-to-be-gained deorbit guidance law as a simple and precise solution. The main portion of the velocity to be gained is obtained from solving a two-body two-point boundary value problem, and the correcting portion related to the j2 term is calculated analytically through the state space perturbation method (SSPM). The SSPM uses a linearized perturbation motion equation derived in local vertical, local horizontal coordinates. A numerical simulation is conducted to verify the validity and accuracy of the proposed method. The guidance law can satisfy terminal constraints on flight path angle and location of the EI and can be generalized with little effort to cases in which other terminal constraints are specified or Earth’s higher-order nonspherical gravity is considered.