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For a general orbit, how can I write its energy function? And how would I solve...

For a general orbit, how can I write its energy function? And how would I solve for important components of that equation? Thanks!
Science   Advanced-Physics   
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Considering motion under central force with a generalized potential ,U(r) as a function of distance only we deduce the equation of orbit in plane polar coordinate,as angular momentum is conserved.

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