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  4. Two satellites of masses M and 9M are orbiting a planet in a circular orbit of radius r . Their frequency of revolution will be in the ratio of

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Q. Two satellites of masses $M$ and $9M$ are orbiting a planet in a circular orbit of radius $r$ . Their frequency of revolution will be in the ratio of

NTA AbhyasNTA Abhyas 2020Gravitation

Solution:

Using Kepler's IIIrd law of planetary motion,
$T=2\pi \sqrt{\frac{r^{3}}{GM}}$ or $T^{2} \propto r^{3}$
Frequency, $f=\frac{1}{T}=\frac{1}{2 \pi }\sqrt{\frac{GM}{r^{3}}}$
Frequency is independent of the mass of the satellite.
Hence, required ratio $= 1 : 1$