Consider a spacecraft in an elliptical orbit around the Earth. At the low point, or perigee, of its orbit, it is 450 km above the Earth's surface; at the high point, or apogee, it is 2000 km above the Earth's surface.
a) Using conservation of energy, find the speed at perigee and the speed at apogee.
b) It is necessary to have the spacecraft escape from the Earth completely. If the spacecraft's rockets are fired at perigee, by how much would the speed have to be increased to achieve this?
c) What if the rockets were fired at apogee?
d) Which point in the orbit is more efficient to use?