Question

The gravitational potential energy of a two-particle system is derived in this chapter as U=Gm1m2r. Does it follow from this equation that the potential energy for r=[infinity] must be zero? Can we choose the potential energy for r=[infinity] to be 20 J and still use this formula? If no, what formula should be used to calculate the gravitational potential energy at separation r?

Answer 1

Explanation:

• (a)  No, the given gravitational potential energy relation of two particle system, $U=-\frac{G m_{1} m_{2}}{r}$, does not convey that the gravitational potential energy for r = infinity must be zero.  
• Only for calculation purposes, we have taken the gravitational potential energies of the two particles to be zero when they are separated infinitely.
• (b)  No, we cannot use the same formula,$U=-\frac{G m_{1} m_{2}}{r}$ when we choose the potential energy for r = infinity to be 20 J and we need to change the formula.
• (c) The formula to be used for gravitational potential energy at separation r is, $U\left(r^{\prime}\right)=U(r)-U(\infty)$. When $U(\infty)=20 J, \cup(r)=-G \frac{m_{1} m_{2}}{r^{2}}-20$.