Kepler's Goat Herd: An Exact Solution for Elliptical Orbit Evolution

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sbank
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Kepler's Goat Herd: An Exact Solution for Elliptical Orbit Evolution

Post by sbank » Thu Apr 01, 2021 2:29 pm

https://arxiv.org/abs/2103.15829

“A fundamental relation in celestial mechanics is Kepler's equation, linking an orbit's mean anomaly to its eccentric anomaly and eccentricity. Being transcendental, the equation cannot be directly solved for eccentric anomaly by conventional treatments; much work has been devoted to approximate methods. Here, we give an explicit integral solution, utilizing methods recently applied to the 'geometric goat problem' and to the dynamics of spherical collapse. The solution is given as a ratio of contour integrals; these can be efficiently computed via numerical integration for arbitrary eccentricities. The method is found to be highly accurate in practice, with our C++ implementation outperforming conventional root-finding and series approaches by a factor greater than two.

David
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Re: Kepler's Goat Herd: An Exact Solution for Elliptical Orbit Evolution

Post by David » Sun May 30, 2021 4:36 pm

sbank,

go on, this is interesting. If it was not for Kepler to figure all 3 laws then it was never to be discovered to begin with.

The manner in which Kepler figured out the 3 laws, and the personal nature in which he did it, by making personal observations, cannot be described.
17 years it took him. One of the most impressive men in the history of mankind? :roll:

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