Minimum-time constant acceleration orbit transfer with first-order oblateness effect

The analysis of the minimum-time thrust and J(2)-perturbed orbit transfer b etween elliptic orbits of arbitrary size, shape, and orientation, and using continuous constant acceleration whose direction is optimized, is presente d for two different formulations using nonsingular equinoctial orbit elemen ts. A previous formulation that used the equinoctial orbital rotating frame for the component resolution of the perturbation vector is extended to a r ecently developed formulation that uses the true longitude as the sixth sta te variable and the polar frame for the component resolution of the thrust and J(2)-induced accelerations. This new analysis is much simpler because i t provides the simplest form of the differential equations for the adjoints and removes the need for solving Kepler's transcendental equation during t he numerical integration of the dynamic and adjoint system of equations. Be cause of these simpler features, the corresponding software is also more ro bust resulting in improved convergence to the optimal solution of interest. The constant power and constant I-sp case that results in constant thrust is a trivial extension of the constant acceleration case studied here becau se the acceleration is easily updated by updating the mass of the vehicle d uring the numerical integration.