Period of revolution of a close satellite about a planet of radius R is T . The period of revolution

Question

Period of revolution of a close satellite about a planet of radius R is T . The period of revolution around another planet whose radius is 8 R and having same mean density is\

Professor PC Thomas Classes · Answer

For a close satellite\ $\mathrm{T}=\frac{2 \pi \mathrm{R}^{3 / 2}}{\sqrt{\mathrm{GM}}}$\ $\mathrm{T}^{1}=\frac{2 \pi(8 \mathrm{R})^{3 / 2}}{\sqrt{\mathrm{G} 	imes 8^{3} \mathrm{M}}}$\ $=\mathrm{T}$ itself\ Note:- When diameter is 8 times, volume will be $8^{3}$ times and mass will be $8^{3}$ times