Question

A satellite is in a circular orbit round the earth at an altitude $R$ above the earth's surface, where $R$ is the radius of the earth. If $g$ is the acceleration due to gravity of the earth the speed of the satellite is

• A. $\sqrt{2Rg}$
• B. $\sqrt{Rg}$
• C. $\sqrt{Rg/2}$
• D. $\sqrt{Rg/4}$

Answer 1

The correct option is C $\sqrt{Rg/2}$

Let, a satellite of mass m goes around the earth in a circular orbit of radius $r=R+R=2R$. Here the centripetal force $m{v}^2/r$ necessary to keep the satellite in its circular orbit is provided by the gravitational force $GMm/r^2$ between the earth and the satellite.

Thus, $m{v}^2/r=GMm/r^2$ or $v=\sqrt{\frac{GM}{r}}=\sqrt{\frac{GM}{2R}}$

Acceleration at the earth's surface is $g=\frac{GM}{R^2}$

So, $v=\sqrt{\frac{g{R}^2}{2R}}=\sqrt{gR/2}$