(II) $(a)$ Suppose we have three masses, $m_{1}, m_{2},$ and $m_{3},$ that

initially are infinitely far apart from each other. Show that the work needed to bring them to the positions shown in Fig. 39 is

$$W=-G\left(\frac{m_{1} m_{2}}{r_{12}}+\frac{m_{1} m_{3}}{r_{13}}+\frac{m_{2} m_{3}}{r_{23}}\right)$$

(b) Can we say that this formula also gives the potential energy

of the system, or the potential energy of one or two of the objects? $(c)$ Is $W$ equal to

the binding energy of the system-that is, equal to the energy required to separate the components by an infinite distance? Explain.