CLOSED-FORM SOLUTIONS FOR OPEN ORBITS AROUND AN OBLATE PLANET

The paper develops the closed-form solution for the motion around an oblate planet in the situation when the orbit is unbounded. It is proven that when the effect of the J(2) zonal harmonic is taken into account, the orbit is different from its Keplerian counterpart, having a marked influence on the deflection angle, thereby changing the Keplerian flyby geometry. Numerical simulations quantify this difference, which is closely related to the minimum flyby altitude of the spacecraft. The analytic developments can be applied to the preliminary design of gravity-assisted maneuvers.