Analytical trajectory prediction of high-eccentricity spacecraft transfer orbits considering J2 perturbation

Using the perturbation method, the problem of high-accuracy rapid prediction for high-eccentricity spacecraft transfer orbit considering the J2 perturbation is solved. First, an auxiliary geocentric coordinate system is constructed based on the main flight plane of the spacecraft, and a generalized dynamics model considering the J2 perturbation is established by introducing the auxiliary longitude as the independent variable in that coordinate system. Since the J2 term is quite small, using the perturbation method, the dynamics model is decomposed into a zeroth-order system and a first-order system, where the solution of the zeroth-order system is just the analytical solution of the Kepler orbit, but the first-order system is complex and thus difficult to solve. The exact solutions for the first-order heading angle and auxiliary latitude are derived successfully. The approximate analytical solutions for first-order speed, flight path angle, and auxiliary longitude are obtained using a collocation method. Finally, Chebyshev polynomials are employed to derive an approximate analytical solution for the first-order flight time. Simulation results affirm the superiority of the proposed analytical solutions over Kozai's mean elements method and Biria's improved intermediary method.