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 (i.e., more negative) 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 where G is the gravitational constant, M is the mass of the sphere, and R is its radius. Assuming that the Earth is a sphere of uniform density (which it is not, but is close enough to get an order-of-magnitude estimate) with M = 5.97×1024 kg and r = 6.37×106 m, then U = 2.24×1032 J. This is roughly equal to...