The Application of Quasi-Mean-Element-Method to LEO under Additional Perturbation due to Change of Coordinate System

The perturbation caused by the oscillation of Earth's equator plane must be taken into account when working on the motion of satellite on a low Earth orbit (LEO) in the geocentric celestial coordinate system. Since 1960 s, an intermediate orbit coordinate system using true equator and mean equinox (TEME) is introduced. It effectively solves the problem and has been widely used in various applications till today. But this traditional reference frame is purely conceptual and has always been a headache when performing the transition between these systems especially for those who are unfamiliar with celestial frames. As proved in a previous paper, it is possible to avoid the intermediate TEME frame, and conversions between osculating elements and mean elements can be completed in a consistent geocentric celestial coordinate system where only short-period terms are required. In this paper, after including the improved secular and long-period terms, the quasi-mean-element-method is available to predict the orbit analytically, reaching the accuracy of 10−6 in Earth's radius. And all these can be done in the same celestial frame. The results suggest that the celestial coordinate system (J2000.0 nowadays) can be used throughout any applications without having to introduce TEME system as intermediate frame any more.