Gravitational binding energy
The gravitational binding energy
of an object is the amount of energy
required to accelerate
every component of that object to the escape velocity
of every other component. It is also the amount of energy that is liberated (usually in the form of heat
) during the accretion
of such an object from material falling from infinity.
For a uniform, spherical mass, the gravitational binding energy is
Where G is the gravitational constant
, M is the mass of the sphere, and r is the radius of the sphere.
Assuming that Earth is uniform (which is not correct, but is close enough to get an order-of-magnitude estimate) with M = 5.97×1024kg and r = 6.37×106m, U is 2.24×1032J. This is roughly equal to one week of the Sun's total energy output.
According to the Virial theorem, the gravitational binding energy of a star is -2 times its internal thermal energy.