Evaluation of J2-perturbed APSIS height computation methods

Accurate apsis height computations are nearly always essential to spacecraft mission success. it is often convenient and computationally efficient to perform this task using an analytic method which receives an osculating state vector as input. When periapsis height is sufficiently low, the analytic method must account for perturbations from the J(2) zonal gravity harmonic, or inaccuracies and time-dependent inconsistencies will result. Various analytic methods are applied to the problem of apsis height computation in which otherwise conic spacecraft trajectories are perturbed only by the gravitating body's J, harmonic. Computation results are presented which serve as the basis for evaluating each method's merit using three criteria. 1) Does the method's formulation permit it to execute on digital processors double dagger? 2) To what precision does the method compute "correct" apsis heights as the trajectory is sampled at different times? 3) To what consistency does the method compute apsis heights as the trajectory is sampled at different times? Because each method is applied to a broad, but plausible, spectrum of trajectory cases, no single method is able to best satisfy all criteria in all cases.