Correction of precession-nutation and polar motion in analytical solutions of satellite equations of motion

Abstract

In the analytical solutions of satellite equations of motion, the precession-nutation and polar motion (PNPM) effects are usually not considered. For the first-order orbit theory, the magnitude of these effects is small enough to be neglected; however, it might be a different case for a higher order solution, which could possibly be applied in precise orbit prediction or determination in the near future. To clarify the influence of PNPM acting on the Keplerian elements of near-Earth satellite orbits in analytical theory, this paper gives both theoretical and numerical analysis of these effects based on Gaussian equations of motion. From the analysis, the impact of PNPM can be divided into two parts. The first part is a rotational error on the perturbing force vector since the force vector is converted into a coordinate system without considering PNPM; the other part is caused by the error of the satellite coordinates computed in the Earth-Centered Earth-Fixed (ECEF) or True-of-Date (TOD) coordinate system when the PNPM effects are neglected. More importantly, an easy-to-use semi-analytical correction procedure is proposed. It can be applied to the Keplerian elements directly without having to derive again the solutions. With this method, the error caused by neglecting the PNPM can be well corrected.