Celestial Mechanics and Dynamical Astronomy

, Volume 62, Issue 4, pp 305–321 | Cite as

Some expansions of the elliptic motion to high eccentricities

  • Sandro Da Silva Fernandes


Some classic expansions of the elliptic motion — cosmE and sinmE — in powers of the eccentricity are extended to highly eccentric orbits, 0.6627...<e<1. The new expansions are developed in powers of (ee*), wheree* is a fixed value of the eccentricity. The coefficients are given in terms of the derivatives of Bessel functions with respect to the eccentricity. The expansions have the same radius of convergence ρ(e*) of the extended solution of Kepler's equation, previously derived by the author. Some other simple expansions — (a/r), (r/a), (r/a) sinv, ..., — derived straightforward from the expansions ofE, cosE and sinE are also presented.

Key words

Expansions of the elliptic motion Lagrange's series 


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Copyright information

© Kluwer Academic Publishers 1995

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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