Thrust Limited Coplanar Aeroassisted Orbital Transfer

Abstract

Two fuel-minimal aeroassisted orbital transfers are examined. Transfers from geosynchronous orbit to a low Earth orbit are considered. Instead of assuming an impulsive thrust on initial and Ž nal orbit, limited thrust on a nonvanishing interval on each orbit is introduced. In the atmospheric part, the transfer vehicle is controlled via the lift coefŽ cient. The in uence of Earth’s rotation is considered also. Whereas in the atmospheric part an Earth-Ž xed frame of reference is used, the nonatmosphericparts are considered in an inertial frame of reference. This leads to an optimal control problem with well-deŽ ned jumps in the state and adjoint variables at the junction points between atmospheric and nonatmospheric arcs. The necessary conditions, including adjoint differential equations, boundary and interior point conditions, and control conditions, are derived to set up a boundary value problem. Solutions for a high and a low maximummagnitude of thrust with Earth’s rotation, Ž rst neglected and later included, are presented.