Approximate analytic solution of motion for spacecraft around an oblate planet

Abstract

The oblateness of a planet has an important effect on the surrounding spacecraft and is usually regarded as a significant perturbation factor to spacecraft’s motion. In this paper, an approximate analytic solution of motion for spacecraft which considering this perturbation factor is investigated. The perturbed dynamic model which taking true anomaly as the independent variable is firstly built in non-inertial coordinate system moving with a Kepler two-body orbit, then the six-dimensional state transition matrix about the state deviation vector is introduced. After that, the expression of J2 term’s gravitational potential in this non-inertial coordinate system is obtained based on spherical trigonometry, and the analytic solution for every variable of the state deviation vector is then derived by complicated mathematic transformation. Numerical simulation results done by the presented method have been compared with that done by numerical integration as well as an existing first-order analytic solution. The comparison results show that the presented method has high accuracy, and is more accurate than the first-order analytic solution within one or few orbit revolutions, which makes it more suitable for short-term orbit prediction of the satellites, especially for those suborbital flight vehicles.