A linear solution of the equations of motion of an earth-orbiting satellite based on a Lie-series |
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| Authors: | Dieter J Lelgemann |
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| Institution: | 1. Mitteilung aus dem Institut für Angewandte Geod?sie, Frankfurt, Germany
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| Abstract: | Using Hill's variables, an analytical solution of a canonical system of six differential equations describing the motion of a satellite in the gravitational field of the earth is derived. The gravity field, expanded into spherical harmonics, has to be expressed as a function of the Hill variables. The intermediary is chosen to include the main secular terms. The first order solution retains the highly practical formal structure of Kaula's linear solution, but is valid for circular orbits and provides of course a spectral decomposition of radius vector and radial velocity. The resulting eccentricity functions are much simpler than the Hansen functions, since a series evaluation of the Kepler equation is avoided. The present solution may be extended to higher order solutions by Hori's perturbation method. |
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