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Celestial Mechanics and Dynamical Astronomy

, Volume 58, Issue 3, pp 297–308 | Cite as

Extension of the solution of Kepler's equation to high eccentricities

  • Sandro Da Silva Fernandes
Article

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*|<ρ(e*), where the radius of convergence ρ(e*) is a positive real number, which is calculated numerically.

Key words

Kepler's equation Lagrange's series 

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References

  1. Tisserand, F.: 1960,Traité de Mécanique Céleste, Gauthier-Villars, Paris (re-edition).Google Scholar
  2. Wintner, A.: 1941,Analytical Foundations of Celestial Mechanics, Princeton University Press, New Jersey.Google Scholar
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  5. Cayley, A.: 1861,Mem. Roy. Astron. Soc. 29, 191.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Sandro Da Silva Fernandes
    • 1
  1. 1.Departamento de Mecânica do Vôo e OrbitalInstituto Tecnológico de AeronáuticaSão José dos Campos - SPBrazil

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