GP E = − \frac{GM_{1}M_{2}}{R}

dE = \frac{GMdm}{R}

M = \frac{4}{3}πr^{3}ρ

dm = (volume)(density) = (4πr^{2}dr) (ρ)

GP E = − \frac{GMdm}{r}

GP E = ∫_{r=0}^{r=R} − \frac{G (\frac{4}{3}πr^{3}ρ) (4πr^{2}drρ)}{r}

GP E = − \frac{3}{5} (\frac{GM^{2}}{R} )

GP E = \frac{GM_{Sun}M_{Moon}}{R}

system is unbound when KE + GP E = 0