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The gravitational binding energy of a system is the minimum energy which must be added to it in order for the system to cease being in a gravitationally bound state. A gravitationally bound system has a lower gravitational potential energy than the sum of the energies of its parts when these are completely separated—this is what keeps the system aggregated in accordance with the minimum total potential energy principle.
For a spherical body of uniform density, the gravitational binding energy U is given by the formula
Assuming that the Earth is a sphere of uniform density with M = 5.97×10 kg and r = 6.37×10 m, then U = 2.24×10 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 , is given in the Preliminary Reference Earth Model. Using this, the real gravitational binding energy of Earth can be calculated numerically as U = 2.49×10 J.