Consider a star and two planet system. The star has mass M. The planet A and B are identical and they revolve around the star in circular orbits according to Bohr model in first and second orbit ( $s_{1}$ and $s_{2}$ are small geostationary satellites of A and B respectively). Planet A and B have no natural satellite and if a planet does not have natural satellite then time to revolve around star is same the time taken to revolve around its own axis. The potential is taken as zero at infinity.

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If the time period of the satellite $s_{1}$ is T, then time period of $s_{2}$ is 8T.

If the radius of $s_{1}$ is R, then the radius of $s_{2}$ is 4R.

If the radius of $s_{1}$ is R, then the radius of $s_{2}$ is 2R.

If the time period of the satellite $s_{1}$ is T, then time period of $s_{2}$ is 2T.

answer is A, B.

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Detailed Solution

$T \propto n^{3}$

$R \propto n^{2}$

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