Abstract
Power series solutions of Kepler's Equation associated with Lagrange, Levi-Civita and Stumpff may be obtained by Newton's method as an algorithm for formal power series.
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References
Fleckenstein, J.O.: 1941, Notiz zur Lagrangeschen Lösung des Keplerschen Problems, Comm. Math. Helv. 13, 83–89.
Kaminskii, B.I.: 1982, Expansion of coordinates of elliptical motion with respect to the Levi-Civita parameter, Soviet Asir. 26, 478–480.
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Stumpff, K.: 1968, On the application of Lie-series to the problems of celestial mechanics, NASA Technical Note D-4460.
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Colwell, P. Kepler's Equation and Newton's method. Celestial Mech Dyn Astr 52, 203–204 (1991). https://doi.org/10.1007/BF00049450
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DOI: https://doi.org/10.1007/BF00049450