Question

By what percent the energy of satallite has to be increased to shift it from an orbit of radius R to 3/2R
Ans 33.3%

Answer 1

The energy of satellite in the first case:

$$E_1=\frac{GMm}{2R}$$

In the second case:

$$E_2=\frac{GMm}{2(1.5R)}=\frac{GMm}{3R}$$

$$\Delta E=-\frac{GMm}{3R}-(-\frac{GMm}{2R})=\frac{GMm}{6R}$$

% increase:

$$\frac{\frac{GMm}{6R}}{\frac{GMm}{2R}} 100 \%=33.3 \%$$