Direct Calculation Methods of Hansen Coefficients and Their Derivatives |
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Institution: | 1. Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023;2. School of Astronomy and Space Science, University of Science and Technology of China, Hefei 230026;3. National Basic Discipline Public Science Data Center, Beijing 100190 |
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Abstract: | Seven direct calculation methods of Hansen coefficients and their derivatives are reviewed. The computational efficiencies of these methods are compared, and their computational stabilities are analyzed. We show that the recursion relations of Hansen coefficients can be used to determine the stabilities of calculation results. Finally, it is pointed out that Wnuk's method (double precision computation) and McClain's methods (quadruple precision computation) are stable, which can be used to calculate orbit perturbations. Because of small orbital eccentricities of most satellites, the perturbation calculations without singularities are required, and McClain's first method (quadruple precision computation) is recommended. |
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Keywords: | Celestial mechanics Perturbation theory: perturbation function and its expansion method methods: numerical |
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