# Chapter 8 - Exercises and Problems - Page 142: 45

2.79

#### Work Step by Step

We know that the kinetic energy is the result of a change in potential energy. Thus, in order to solve this problem, we use conservation of energy. Doing this, we find: $\frac{1}{2}mv_f^2 + U_f=\frac{1}{2}mv_0^2 +U_0$ $\frac{1}{2}mv_f^2 -\frac{GMm}{R_e+22,000}=\frac{1}{2}mv_0^2 -\frac{GMm}{r}$ Plugging in the known values, we find: $r = 4.185 \times10^{11}=2.79 \ AU$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.