An Analytical Solution of the Lagrange Equations Valid also for Very Low Eccentricities: Influence of a Central Potential |
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Authors: | Florent Deleflie Gilles Métris Pierre Exertier |
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Institution: | 1. Observatoire de la C?te d’Azur, UMR GEMINI, Av. N. Copernic, F-06130, Grasse, France
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Abstract: | This paper presents an analytic solution of the equations of motion of an artificial satellite, obtained using non singular
elements for eccentricity. The satellite is under the influence of the gravity field of a central body, expanded in spherical
harmonics up to an arbitrary degree and order. We discuss in details the solution we give for the components of the eccentricity
vector. For each element, we have divided the Lagrange equations into two parts: the first part is integrated exactly, and
the second part is integrated with a perturbation method. The complete solution is the sum of the so-called “main” solution
and of the so-called “complementary” solution. To test the accuracy of our method, we compare it to numerical integration
and to the method developed in Kaula (Theory of Satellite Geodesy, Blaisdell publ. Co., New York. 1966), expressed in classical
orbital elements. For eccentricities which are not very small, the two analytical methods are almost equivalent. For low eccentricities,
our method is much more accurate. |
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Keywords: | analytic integration artificial satellites eccentricity vector short and long period terms spherical harmonics zero eccentricities |
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