Chapter 8, Problem 96GP

(II) (a) Suppose we have three masses, m₁, m₂, and m₃, that initially are infinitely far apart from each other. Show that the work needed to bring them to the positions shown in Fig. 8–39 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 object? (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.

FIGURE 8–39

Problem 58.