Question

what is the binding engery prove with theorem
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Answer 1

Answer:

For a spherical mass of uniform density, the gravitational binding energy U is given by the formula[2][3]

{\displaystyle U={\frac {3GM^{2}}{5R}}} U={\frac {3GM^{2}}{5R}}

where G is the gravitational constant, M is the mass of the sphere, and R is its radius.

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 1024 kg and r = 6.37 x 106 m, U is 2.24 x 1032 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.