The period of a satellite in a circular orbit | vedclass

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Question

(C) The orbital period $T$ of a satellite is given by the ratio of the circumference of the orbit to the orbital velocity:$T = \frac{2 \pi r}{v_o}$Sin

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the mass of the satellite

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(C) The orbital period $T$ of a satellite is given by the ratio of the circumference of the orbit to the orbital velocity:$T = \frac{2 \pi r}{v_o}$Since the orbital velocity $v_o = \sqrt{\frac{GM}{r}}$,we substitute this into the equation:$T = \frac{2 \pi r}{\sqrt{\frac{GM}{r}}} = 2 \pi \sqrt{\frac{r^3}{GM}}$Here,$M$ is the mass of the planet,$r$ is the radius of the orbit,and $G$ is the gravitational constant.From the formula,it is clear that $T$ depends on the radius of the orbit $(r)$ and the mass of the planet $(M)$,but it does not depend on the mass of the satellite $(m)$.Therefore,the period is independent of the mass of the satellite.

The period of a satellite in a circular orbit around a planet is independent of

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