The gravitationalbinding 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.
Gravitational potential energy is the energy that would be released if an object in a gravitational field (such as the earth'sgravitational field) were allowed to fall from its current position to a given reference level (such as the surface of the earth).
The gravitationalbindingenergy of an object consisting of loose material, held together by gravity alone, is the amount of energy required to pull all of the material apart, to infinity.
Gravitational potential is the potential energy per unit mass of an object due to its position in a gravitational field.
In general, bindingenergy represents the mechanical work which must be done in acting against the forces which hold an object together, while disassembling the object into component parts separated by such sufficient distance that further separation requires negligible additional work.
Since all forms of energy in a system (which has no net momentum) have mass, the question of where the missing mass of the bindingenergy goes is of interest.
The region of increasing bindingenergy is followed by a region of relative stability (saturation) in the sequence from magnesium through xenon.
Feeds |
Contact