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.

• A. W is too high as it ignores energy lost as heat or radiation.
• B. W doesn't include motion energy, so it can't be the binding energy.
• C. W is not the binding energy because it represents the system's kinetic energy.
• D. W equals the gravitational binding energy, showing the energy needed to assemble the system.

Answer: (D)