Consider three planets, $P_1$ , $P_2$ , and $P_3$ , each with masses $m_1$ , $m_2$ , and $m_3$, initially positioned infinitely far apart. The work required to bring them into a stable equilateral triangular configuration around their common center of mass, where each side of the triangle has the same distance r, is given by:

$W=-G\left(\frac{m_1m_2}{r}+\frac{m_1m_3}{r}+\frac{m_2m_3}{r}\right)$

Does this work W correspond to the gravitational binding energy of the planetary system? Explain.