Chapter 12.7, Problem 3ES

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

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

Use the result in Exercise 1(d) to show that for a particle in an elliptical orbit with eccentricity e, the maximum and minimum speeds are related by ${\upsilon }_{\max }={\upsilon }_{\min }\frac{1+e}{1-e}$