Say a planet (mass m) is orbiting a star (mass M) in a perfect circle, so it is in circular motion.
F=ma and the gravitational force between two masses F=GMmr2 so
GMmr2=ma
GMr2=a
And in circular motion a=v2r so
GMr2=v2r
GMr=v2
And gravitational potential V=−GMr
So v2=−V
Is there a (qualitative/less math/wordy) reason why this is the case? (or have I got this wrong?) and is this limited to the specific case of perfect circular motion?
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