The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M to transfer it from a circular orbit of radius R, to another of radius R₂ (R₂ > R₁ ) is

GmM $(\frac{1}{R_{1}^{2}} - \frac{1}{R_{2}^{2}})$

GmM $(\frac{1}{R_{1}} - \frac{1}{R_{2}})$

2 GmM $(\frac{1}{R_{1}} - \frac{1}{R_{2}})$

$\frac{1}{2}$ GmM $(\frac{1}{R_{1}} - \frac{1}{R_{2}})$

Solution

$\frac{1}{2}$ GmM $(\frac{1}{R_{1}} - \frac{1}{R_{2}})$

Additional kinetic energy provided to satelite

$- \frac{GmM}{2 R_{1}} + KE = \frac{- GMm}{2 R_{2}}$

KE = $\frac{- G Mm}{2 R_{2}} + \frac{G Mm}{2 R_{1}}$

∴ KE = $\frac{1}{2} GMm (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

Some More Questions From Gravitation Chapter

For Daily Free Study Material Join wiredfaculty