Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 400 km above the earth's surface; at the high point, or apogee, it is 4000 km above the earth's surface.
(a) What is the period of the spacecraft's orbit?
(b) Using conservation of angular momentum, find the ratio of the spacecraft's speed at perigee to its speed at apogee.
(c) Using conservation of energy, find the speed at perigee and the speed at apogee.
(d) 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? What if the rockets were fired at apogee? Which point in the orbit is more efficient to use?