Chapter 12.7, Problem 13ES

In exercises that require numerical values, use Table 12.7.1 and the following values, where needed:

$\begin{array}{l}\text{radius}\text{of}\text{Earth}=4000\text{mi}=6440\text{km}\\ \text{radius}\text{of}\text{Moon}=1080\text{mi}=1740\text{km}\\ \text{1year (Earth Year)}=365\text{days}\end{array}$

(a) Suppose that a space probe is in a circular orbit at an altitude of 180 mi above the surface of the Earth. Use the result in Exercise 4 to find its speed.

(b) During a very short period of time, a thruster rocket on the space probe is fired to increase the speed of the probe by $600\text{mi}/\text{h}$ in its direction of motion. Find the eccentricity of the resulting elliptical orbit and use result in part (a) of Exercise 5 to find the apogee altitude.