Question

By what percent the energy of a satellite has to be increased to shift it from an orbit of radius r to 3r?

• A. 0.223
• B. 0.333
• C. 0.667
• D. 1

Answer 1

The Correct Option is C

Binding energy of satellite in 1st case $ {{U}_{1}}=-\left( -\frac{GMm}{r}+\frac{1}{2}\frac{GMm}{r} \right) $ $ =\frac{GMm}{2r} $ Binding energy of satellite in 2nd case $ {{U}_{2}}=-\left[ -\frac{GMm}{3r}+\frac{1}{2}\frac{GMm}{3r} \right] $ $ =\frac{GMm}{6r} $ Energy increased $ \Delta E={{U}_{1}}-{{U}_{2}} $ $ =\frac{GMm}{r}\left[ \frac{1}{2}-\frac{1}{6} \right] $ $ =\frac{GMm}{3r} $ % increase in energy $ =\frac{\Delta E}{{{U}_{1}}}\times 100 $ $ =\frac{GMm/3r}{GMm/2r}\times 100 $ $ =66.7 $%