Extension of the solution of Kepler's equation to high eccentricities
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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 wordsKepler's equation Lagrange's series
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