Extension of the solution of Kepler's equation to high eccentricities |
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| Authors: | Sandro Da Silva Fernandes |
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| Institution: | (1) Departamento de Mecânica do Vôo e Orbital, Instituto Tecnológico de Aeronáutica, 12228-900 São José dos Campos - SP, Brazil |
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| Abstract: | The classic Lagrange's expansion of the solutionE(e, M) of Kepler's equation in powers of eccentricity is extended to highly eccentric orbits, 0.6627 ... <e<1. The solutionE(e, M) is developed in powers of (e–e*), wheree* is a fixed value of the eccentricity. The coefficients of the expansion are given in terms of the derivatives of the Bessel functionsJ
n
(ne). The expansion is convergent for values of the eccentricity such that |e–e*|< (e*), where the radius of convergence (e*) is a positive real number, which is calculated numerically. |
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| Keywords: | Kepler's equation Lagrange's series |
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