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  4. A geostationary satellite is orbiting the earth at a height 6R above its surface, where R is the radius of the earth. What is the time period of another satellite at a height of 2.5R from the surface of earth in hours?

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Q. A geostationary satellite is orbiting the earth at a height $6R$ above its surface, where $R$ is the radius of the earth. What is the time period of another satellite at a height of $2.5R$ from the surface of earth in hours?

NTA AbhyasNTA Abhyas 2020

Solution:

Here, $r_{1}=6R+R=7R; \, T_{1} \, = \, 24 \, hours; \, r_{2}-2.5R \, + \, R \, = \, 3.5R; \, T_{2}= \, 1$
$T_{2}=\left[\frac{R_{2}}{R_{1}}\right]^{3 / 2}\times T_{2}=24\left[\frac{3.5 R}{7 R}\right]^{3 / 2}=\frac{24}{2 \sqrt{2}}=6\sqrt{2}h$ h