Third-body short-period terms in analytic orbit prediction.

摘要

This study details a project to analytically recover third body short period terms from the results of Long-Term Orbit Predictor (LOP) calculations using a double-averaged potential. A mission planning tool at the Jet Propulsion Laboratory, LOP is a trajectory propagation program for use in lifetime studies of orbiting spacecraft. Rather than the more traditional averaging methods, the code uses averaging-by-inspection, where the short period terms are removed by choosing indices in the potential that set the fast variable coefficient to zero. In the single-averaged case, only the central body fast variable term is removed, while in the double-averaged case, both the central and third body fast variable terms are removed. The code relies on Kaula's potential formulation, with the accompanying definitions for the eccentric and inclination functions.; Removing the third body fast variable terms results in the loss of the short period contributions to the lifetime of the orbit. The importance of being able to recover these contributions for the third body within LOP was realized when the Mars Global Surveyor aerobraking phase had to be re-analyzed due to the deployment problems with a solar array. To keep the computational speed and elegance of the double-averaged integration, yet still include the short-period terms, an adaptation of Kozai's method was applied to the problem. As a result, the third body short period contributions to each orbital element were developed analytically and then linearly added to the LOP post-integration solutions.; Two cases were chosen to illustrate the application of this method. Case A isolates the third body short period terms for a high-altitude, highly eccentric Earth orbit, building on research presented in a previous study. Case B looks at the short period contributions of the Sun on a capture orbit for Mars Global Surveyor. In both cases, the double-averaged results with the short period terms reintroduced are compared with both the single-averaged results and the reference orbits generated by Cowell's method.