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I've tried to find answers online but surprisingly couldn't find any.

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    $\begingroup$ I’m voting to close this question because this is purely a Physics question $\endgroup$ – Carl Witthoft May 20 '20 at 12:03
  • $\begingroup$ Work out the force vectors for yourself! Just look at the instantaneous velocity vector and the direction of acceleration required to stay on the elliptical path. $\endgroup$ – Carl Witthoft May 20 '20 at 12:04
  • $\begingroup$ It's not even a physics question. It's purely mathematics. $\endgroup$ – David Hammen May 20 '20 at 12:12
  • $\begingroup$ I suggest to re-ask your question on the physics.stackexchange.com . This site is only for space exploration things. $\endgroup$ – peterh May 20 '20 at 13:16
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    $\begingroup$ It's a cool exercise but it's not on-topic here. You could consider asking in Math SE or Physics SE as mentioned above (may be a better fit) but no matter where you ask it you'll need to make some effort to solve it yourself and explain where and why you are stuck. $\endgroup$ – uhoh May 20 '20 at 13:19

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