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Picture below is from the Kepler's laws of Wiki. I fail to found its proof. I mean that how to use $$ F=G\frac{Mm}{r^2} ~~~~~~\text{and}~~~~~~~ F=ma $$ to prove the orbit of planet must be so.

I just be inquisitive mathematic student, and want to prove some familiar physical sense, for example, the orbit of planet is ellipse. Whether there is some book is talk about proof of familiar physical sense ? Thanks.

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    $\begingroup$ To start: en.wikipedia.org/wiki/Kepler_orbit $\endgroup$
    – Mark H
    Commented Oct 21, 2017 at 9:58
  • $\begingroup$ @MarkH Thanks very much. Do you know any book about the familiar physical sense ? $\endgroup$
    – Enhao Lan
    Commented Oct 21, 2017 at 11:41

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