Gravitational binding energy Guide, Meaning , Facts, Information and Description

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.

It is equal to minus the gravitational potential energy, but should not be confused with the case of separating e.g. a celestial body and a satellite to infinite distance, keeping each intact.

For a spherical mass of uniform density, 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.

Thus it is 20 % more than the energy to separate to infinity two such spheres touching each other.

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. It is 37.5 MJ/kg, 60% of the absolute value of the potential energy per kg at the surface.

According to the virial theorem, the gravitational binding energy of a star is -2 times its internal thermal energy.

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