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

Answer: (C)

0.667

Answer 2

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 $=\frac{\Delta E}{{{U}_{1}}}\times 100$ $=\frac{GMm/3r}{GMm/2r}\times 100$ $=66.7$%