The total energy of a circularly orbiting sat | vedclass

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(B) For a satellite of mass $m$ orbiting a planet of mass $M$ at a distance $r$,the potential energy is $U = -\frac{GMm}{r}$.The kinetic energy requir

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half the potential energy of the satellite.

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(B) For a satellite of mass $m$ orbiting a planet of mass $M$ at a distance $r$,the potential energy is $U = -\frac{GMm}{r}$.The kinetic energy required for a circular orbit is $K = \frac{GMm}{2r}$.The total energy $E$ is the sum of kinetic and potential energy: $E = K + U = \frac{GMm}{2r} - \frac{GMm}{r} = -\frac{GMm}{2r}$.Comparing $E$ with $K$: $E = -K$,which means the total energy is the negative of the kinetic energy.Comparing $E$ with $U$: $E = \frac{1}{2} U$,which means the total energy is half the potential energy.

The total energy of a circularly orbiting satellite is

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