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

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

Mar 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cemda..58..297d&link_type=abstract

Celestial Mechanics & Dynamical Astronomy, vol. 58, no. 3, p. 297-308

Astronomy and Astrophysics

Astronomy

5

Eccentric Orbits, Eccentricity, Kepler Laws, Lagrangian Function, Power Series, Series Expansion, Bessel Functions, Hamiltonian Functions

Scientific paper

The classic Lagrange's expansion of the solution E(e,M) of Kepler's equation in powers of eccentricity is extended to highly eccentric orbits, 0.6627... less than e less than 1. The solution E(e,M) is developed in powers of (e - e*), where e* is a fixed value of the eccentricity. The coefficients of the expansion are given in terms of the derivatives of the Bessel functions Jn (ne). The expansion is convergent for values of the eccentricity such that the absolute value of e - e* is less than rho(e*), where the radius of convergence rho(e*) is a positive real number, which is calculated numerically.

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