Sunday, 23 February 2020

newtonian mechanics - Is the gravitational potential of a planet in orbit always equal to minus the squared velocity?


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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