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Volume 32, Number 2, pages 125-128 (2021)
https://doi.org/10.26830/symmetry_2021_2_125
THE STRUCTURE OF THE SOLUTION SPACE IN THE DIRECT AND INVERSE KEPLER PROBLEMS
Takeshi Sugimoto*
* Kanagawa University, Yokohama 221-8686, Japan
E-mail: sugimt01@kanagawa-u.ac.jp
Abstract: The direct Kepler problem, which Newton solved for the first time in the human history, is the task to induce physics behind Kepler’s first and second laws. That is the inverse-squre law of the unversal gravitation. The inverse Kepler problem is the task to look for the orbit of the planet by deducing from the law of the gravitation. This was solved in an incomplete manner by Jakob Hermann. The present study is to visualise the structure of the solution space in the direct and inverse Kepler problems by use of modern vector analysis. This novel result is summarised as a roadmap (Fig. 2).
Keywords: Conic Sections, Inverse Square Law of Gravitation, Kepler’s Laws.
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