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Celestial Mechanics and Dynamical Astronomy

, Volume 63, Issue 3–4, pp 375–408 | Cite as

Expansions of (r/a)mcosjv and (r/a)msinjv to high eccentricities

  • Sandro da Silva Fernandes
Article

Abstract

Expansions of the functions (r/a)cosjv and (r/a)msinjv of the elliptic motion are extended to highly eccentric orbits, 0.6627 ... <e<1. The new expansions are developed in powers of (e−e*), wheree* is a fixed value of the eccentricity. The coefficients of these expansions are expressed in terms of the derivatives of Hansen's coefficients with respect to the eccentricity. The new expansions are convergent for values of the eccentricity such that |e−e*|<ρ(e*), where the radius of convergence ρ(e*) is the same of the extended solution of Kepler's equation. The new expansions are intrinsically related to Lagrange's series.

Key words

Expansions of the elliptic motion Lagrange's series Hansen's coefficients 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Sandro da Silva Fernandes
    • 1
  1. 1.Departmento de Mecânica do Vôo e OrbitalInstituto Tecnológico de AeronáuticaSão José dos Campos, SPBrazil

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