Chapter 13.2, Problem 13.117P

Using the answers obtained in Prob. 13.108, show that the intended circular orbit and the resulting elliptic orbit intersect at the ends of the minor axis of the elliptic orbit.

13.108 A satellite is projected into space with a velocity v₀ at a distance r₀ from the center of the earth by the last stage of its launching rocket. The velocity v₀ was designed to send the satellite into a circular orbit of radius r₀. However, owing to a malfunction of control, the satellite is not projected horizontally but at an angle α with the horizontal and, as a result, is propelled into an elliptic orbit. Determine the maximum and minimum values of the distance from the center of the earth to the satellite.

Fig. P13.108