Question

A satellite of mass m is in an elliptical orbit around the earth. The speed of the satellite at its nearest position is $\left(6GM\right)/\left(5r\right)$ where r is the perigee(nearest point) distance from the centre of the earth. It is desired to transfer the satellite to the circular orbit of radius equal to its apogee (farthest point) distance from the centre of the earth. The change in orbital speed required for this purpose is?

• A. $0.35\sqrt{\frac{G{M}_e}{r}}$
• B. $0.085\sqrt{\frac{G{M}_e}{r}}$
• C. $\sqrt{\frac{2G{M}_e}{r}}$
• D. Zero

Answer 1

The correct option is B $0.085\sqrt{\frac{G{M}_e}{r}}$

$\Delta v=\sqrt{\frac{6GM}{5R}}\times \sqrt{\frac{GM}{R}}$

$R=\frac{3r}{2}$

$\Delta v=\sqrt{\frac{GM}{r}}[\sqrt{\frac{2}{3}}-\sqrt{\frac{8}{15}}]$

$\Delta v=0.086\sqrt{\frac{GM}{r}}$