Question

Two satellites of mass m and 9m are orbiting a planet in orbits of radius R. Their periods of revolution will be in the ratio of [KCET 2011]

Easy

Solution

As we know,
From Kepler's law, time period of satellite is $T^{2} = \frac{4 π^{2} R^{3}}{G M}$
$T_{sat} = 2 π \sqrt{\frac{(R + h)^{2}}{G M_{e}}}$
As two satellites of masses m and 9m are orbiting a planet of radius R, their time periods will remain same, i.e. in the ratio 1 : 1, because time period of satellite does not depend on its mass.

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