I've been working on simulating orbits. I've found that, when solving Kepler's equation, $M = E - \varepsilon\sin{E}$, I'm unsure about the solution to use. For a true anomaly $< \pi$, using the first solution is correct, but for angles larger than that the second solution must be used. Is this a pattern that repeats indefinitely? I'm having trouble consistently being able to identify the solution I should use. Thanks for any help!
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1I don't know anything about your specific question, but in case you don't know of it, Peter Colwell published a historical survey book on Kepler's equation in 1993 -- Solving Kepler's Equation over Three Centuries. – Dave L. Renfro Jun 25 '15 at 15:40
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see https://math.stackexchange.com/questions/1053472/how-to-solve-keplers-equation-m-e-varepsilon-sin-e-for-e/4732665#4732665 – IV_ Jul 08 '23 at 11:32
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Does this answer your question? How to solve Kepler's equation $M=E-\varepsilon \sin E$ for $E$? – Тyma Gaidash Jun 19 '24 at 13:20