Minimum-Time Constant Acceleration Orbit Transfer with First-Order Oblateness Effect

Abstract

The analysis of the minimum-time thrust and J2-perturbed orbit transfer between elliptic orbits of arbitrary size, shape, and orientation, and using continuous constant acceleration whose direction is optimized, is presented for two different formulations using nonsingular equinoctial orbit elements. A previous formulation that used the equinoctial orbital rotating frame for the component resolution of the perturbation vector is extended to a recently developed formulation that uses the true longitude as the sixth state variable and the polar frame for the component resolution of the thrust and J2-induced accelerations. This new analysis is much simpler because it provides the simplest form of the differential equations for the adjoints and removes the need for solving Kepler’s transcendental equationduring the numerical integration of the dynamicand adjoint system of equations. Because of these simpler features, the corresponding software is also more robust resulting in improved convergence to the optimal solution of interest. The constant power and constant Isp case that results in constant thrust is a trivial extension of the constant acceleration case studied here because the acceleration is easily updated by updating the mass of the vehicle during the numerical integration.