Consider a spaceship in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 400 kilometer above the earth's surface; at the high point, or apogee, it is 4000 kilometer above the earth's surface.
a) Find the period of the spaceship's orbit?
b) Using conservation of angular momentum, determine the ratio of the spaceship's speed at perigee to its speed at apogee.
c) Using conservation of energy, determine the speed at perigee and the speed at apogee.
d) It is necessary to have the spaceship escape from the earth completely. If the spaceship's rockets are fired at perigee, determine by how much would the speed have to be increased to achieve this?