Question

A satellite of mass $m$ revolves around the earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

• A. $gx$
• B. $\frac{gR}{R-x}$
• C. $\frac{gR^{2}}{R+x}$
• D. $\left(\frac{gR^{2}}{R+x}\right)^{1/ 2}$

Answer 1

Answer: (D)

$\left(\frac{gR^{2}}{R+x}\right)^{1/ 2}$

Answer 2

For the satellite, the gravitational force provides the necessary centripetal force i.e. $\frac{GM_{o}m}{\left(R+X\right)^{2}} = \frac{Mv^{2}_{o}}{\left(R+X\right)}$ and $\frac{GM_{o}}{R^{2}} = g$ $\therefore \, v_{0} =\left(\frac{gR^{2}}{R+x}\right)^{1/ 2}$