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  4. The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is v . For a satellite orbiting at an altitude of half of the earth's radius, the orbital velocity is

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Q. The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is $v$ . For a satellite orbiting at an altitude of half of the earth's radius, the orbital velocity is

NTA AbhyasNTA Abhyas 2022

Solution:

We know that $v_{0}=\sqrt{\frac{G M}{R}}$ for a satellite at at altitude $\frac{R}{2}$ ,
$v_{1}=\sqrt{\frac{G M}{\left(R + \frac{R}{2}\right)}}$
therefore $\frac{v_{1}}{v}=\sqrt{\frac{2}{3}}$