I was looking at the wikipedia page for the gravitational binding energy of a sphere, but let's say that there was a toroidal planet. What would its gravitational binding energy be? I have attempted the solution similar to what they did on wikipedia and obtained: [tex]U = -4 G \pi^5 R^2 r^4 \rho^2 [/tex]https://lh3.googleusercontent.com/fPHuQ6I0NONuFyo7tz0OBkPVGWVW6kVChq_TjWU05B-jQRFqvMmnVLfPN7Q9OMCPe3qTMw=s95 R and r are shown in the diagram to be the total radius of the torus and the radius of the tube of the torus respectively. I believe with a substitution for [itex]\rho[/itex] as density, this simplifies to: [tex]U = -G M^2 \pi[/tex] But this seems to simple. Any ideas?