Chapter 6 - Problems - Page 234: 108

$U = -2K$

The gravitational force provides the centripetal force to keep an object of mass $m$ in circular orbit: $\frac{GMm}{r^2} = \frac{mv^2}{r}$ $\frac{GMm}{r} = mv^2$ $\frac{1}{2}\frac{GMm}{r} = \frac{1}{2}mv^2$ $(-\frac{1}{2})(-\frac{GMm}{r}) = K$ $(-\frac{1}{2})(U) = K$ $U = -2K$