A satellite $X$ moves round the earth in a circular orbit of radius $R$ . If another satellite $Y$ of the same mass moves round the earth in a circular orbit of radius $4 R$ , then the speed of $X$ is ________ times that of $Y$ .

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Solution

When an artificial satellite moves around a planet. Its orbital velocity is given by $V = \sqrt{\frac{G M}{R_{1}}}$
where $R_{T}$ is the distance of satellite from the centre of planet.
$\frac{V_{x}}{V_{y}} = \sqrt{\frac{R_{T (Y)}}{R_{T (X)}}}$ [masses are same]
$\frac{V_{X}}{V_{Y}} = 2$
So, the speed of $X$ is $2$ times that of $Y$ .

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