This is a relatively important question for anyone who can answer it. I am trying to find the equation that accurately solves for Earth's Gravitational Binding Energy. The information below is from the wikipedia page:
Assuming that the Earth is a uniform sphere (which is not correct, but is close enough to get an order-of-magnitude estimate) with M = 5.97 x 10^24 kg and r = 6.37 x 10^6 m, U is 2.24 x 10^32 J. This is roughly equal to one week of the Sun's total energy output. It is 37.5 MJ/kg, 60% of the absolute value of the potential energy per kilogram at the surface.
The actual depth-dependence of density, inferred from seismic travel times (see Adams–Williamson equation), is given in the Preliminary Reference Earth Model (PREM). Using this, the real gravitational binding energy of Earth can be calculated numerically as U = 2.487 x 10^32 J.
So what I wish to not for the latter results (2.487e+32 J) is what is the actual equation is used to get this result.
And I do not mean the standard GBE equation which gave the other result above.