Chapter 12.7, Problem 12ES

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) Vanguard I was launched in March 1958 with perigee and apogee altitudes above the Earth of 649 km and 4340 km, respectively. Find the length of the semimajor axis of its orbit.

(b) Use the result in part (a) of Exercise 16 in Section 10.6 to find the eccentricity of its orbit.

(c) Find the period of Vanguard $l$ in minutes.