Application of the Delta-Rho perturbation method to autonomous orbitcomputation

Abstract

Delta-Rho is a new perturbation method for the accurate numerical integration of trajectories, including those of Earth-orbiting satellites. It is most effective when used to calculate a set of dispersed orbits in the nearneighborhood of an accurately computed reference orbit. This paper considers the possible application in which the first orbit of an Earth satellite, generated in a large, ground-based computer, is taken as the reference orbit, and the second, third, and later are the dispersed orbits. Let the orbital period be T. To the extent that the sun and moon are higher harmonics of the Earth's gravitation acting on the second orbit, at time r, are the same as those which acted on the first at (t-T) 9 the method yields accurate results, with reduced computation load, relative to conventional approaches, thereby allowing for computation aboard moving vehicles with their limited computers, including the satellite itself. This paper is a report of an application of the Delta-Rho method to a geosynchronous, equatorial, circular orbit. Results of simulation studies are presented showing that with the perturbation force model truncated after the J 2 term, and five integration steps per orbit, the error after one orbit is 2.5 ft.