Ratio of Periods of Revolution

Two satellites S and S' revolve around the earth at distances \(3R\) and \(6R\) from the centre of earth. Their periods of revolution will be in the ratio

1 : 2

2 : 1

1 : \(2^{1.5}\)

1 : \(2^{0.67}\)

Solution:

Using Kepler's Third Law, \(T^2 \propto r^3 \Rightarrow \frac{T_1}{T_2} = \left(\frac{r_1}{r_2}\right)^{3/2} = \left(\frac{3R}{6R}\right)^{3/2} = \left(\frac{1}{2}\right)^{1.5} = \frac{1}{2^{1.5}}\). Hence, the ratio is 1 : \(2^{1.5}\).

Ratio of Periods of Revolution

Solution:

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