The time period of revolution of a satellite | vedclass

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(A) The time period $T$ of a satellite orbiting very close to a planet is given by the formula:$T = 2\pi \sqrt{\frac{R^3}{GM}}$Since the mass of the p

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$T$

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(A) The time period $T$ of a satellite orbiting very close to a planet is given by the formula:$T = 2\pi \sqrt{\frac{R^3}{GM}}$Since the mass of the planet $M = \rho V = \rho \left( \frac{4}{3}\pi R^3 \right)$,we substitute this into the formula:$T = 2\pi \sqrt{\frac{R^3}{G \cdot \rho \cdot \frac{4}{3}\pi R^3}}$$T = 2\pi \sqrt{\frac{3}{4\pi G \rho}}$From this expression,it is clear that the time period $T$ depends only on the density $\rho$ of the planet and is independent of the radius $R$ of the planet.Since both planets have the same density $\rho$,the time period of the satellite will remain the same,i.e.,$T$.

The time period of revolution of a satellite orbiting very close to a planet of radius $R$ is $T$. What is the period of revolution around another planet,whose radius is $3R$ but having the same density?

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