衛星運動方程數值解解法之分析:GPS及TOPEX/POSEIDON衛星個案研究

Abstract

本研究針對衛星運動方程式之直角座標型式及equinoctial軌道元素 型式進行數值解,以GPS及TOPEX/POSEIDON兩種衛星所給定的初始條件作個 案分析。結果顯示直角座標的Class I型式在精度及效率上都不佳，不宜 用來作軌道預測；而直角座標的Class II及equinoctial型式，在精度的 比較上，對GPS衛星而言，Class II優於equinoctial型式；對TOPEX/ POSEIDON，則equinoctial型式優於Class II，這意味著對高軌衛星進行 軌道積分使用Class II可能較有利，但對低軌衛星進行軌道積分則使用 equinoctial型式可能會較有利；在效率的比較上，Class II型式不管是 在對GPS衛星或TOPEX/POSEIDON衛星測試中，都是最省時的。 加入 Encke 的方法後，不管是直角座標的Class I、Class II型式或 equinoctial型式,其精度都有提昇，尤其，是在對TOPEX/POSEIDON衛星， equinoctial型式精度的提昇遠大於其他兩者。 This work investigates numerical solutions of satellite's equation ofmotion(EOM) in the cartesian and the equinoctial coordinate systems. Casestudies were performed for the GPS and TOPEX/POSEIDON satellites. Resultsshow that, in terms of accuracy and efficiency, the Class I type EOM is notsuitable for predicting orbit. Moreover,the accuracy comparison for the twosatellites of different altitudes shows that the Class II type EOM is betterthan the equinoctial type EOM for the GPS satellite. However,the oppositeresult is obtained for the T/P satellite. These comparisons suggest that theClass II type EOM can be used to integrate the orbit for a satellite of highaltitude, and the equinoctial type EOM is better for integrating low-altitudedsatellite. Furthermore, the Class II type EOM results in most efficient orbitintegration. The accuracies for all cases are improved when Encke's method is used.Especially for the T/P satellite, the accuracy from the equinoctial type EOM ismost improved among all types of EOM.