Question

A 1000kg satellite orbits the Earth at a constant altitude of 100km.
(a) How much energy must be added to the system to move the satellite into a circular orbit with altitude 200km?

Answer 1

$$\Delta E=\frac{GmM}{r^2}-\frac{GmM}{r'^2}\\ \Delta E=\frac{(6.67\cdot10^{-11})(10^3)(5.97\cdot10^{24})}{(10^5)^2}\\-\frac{(6.67\cdot10^{-11})(10^3)(5.97\cdot10^{24})}{(2\cdot10^5)^2}=3.00\cdot10^{7}\ J$$