Chapter 12.7, Problem 4ES

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 Formula (22) and the result in Exercise 1(d) to show that the speed $\upsilon$ of a particle in a circular orbit of radius $r_0$ is constant and is given by $\upsilon =\sqrt{\frac{GM}{r_0}}$