Chapter 3.5, Problem 32E

To determine

To find: the effect on $U$ as it moves farther and farther away from the Earth.

Answer to Problem 32E

  $U\left(r\right)\to 0\text{ as }r\to \infty$

Explanation of Solution

Given information:

  $U\left(r\right)=-\frac{Gm{M}_e}{r}$

Here the gravitational potential energy of the object is U, Newton’s gravitational constant is G, the mass of object is m, and the mass of earth is $M_e$ .

  $r=\infty$

Calculation:

Put the value of r in the given function and evaluate U as follows:

  $\begin{array}{c}U\left(r\right)=-\frac{Gm{M}_e}{r}\\ =-\frac{Gm{M}_e}{\infty }\\ =0\end{array}$

As r approaches infinity, the denominator will equal infinity, so the potential energy will equal 0.

Thus, the $U$ will become zero if the r becomes greater and greater.