http://arxiv.org/abs/2101.00925
A class of bivariate infinite series solutions of the elliptic and hyperbolic Kepler equations is described, adding to the handful of 1-D series that have been found throughout the centuries. This result is based on the exact analytical computation of the partial derivatives of the eccentric anomaly with respect to the eccentricity $e$ and mean anomaly $M$ in a given base point $(e_c,M_c)$ of the $(e,M)$ plane. Explicit examples of such bivariate infinite series are provided, corresponding to different choices of $(e_c,M_c)$, and their convergence is studied. In particular, the polynomials that are obtained by truncating the infinite series up to the fifth degree reach high levels of accuracy in significantly large regions of the parameter space $(e,M)$.
D. Tommasini
Tue, 5 Jan 21
42/82
Comments: N/A
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