Gravitational Binding Energy
The gravitational binding energy 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. 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.
The gravitational binding energy of a system is equal to the negative of the total gravitational potential energy, considering the system as a set of small particles. For a system consisting of a celestial body and a satellite, the gravitational binding energy will have a larger absolute value than the potential energy of the satellite with respect to the celestial body, because for the latter quantity, only the separation of the two components is taken into account, keeping each intact.
For a spherical mass 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. This is 80% greater than the energy required to separate to infinity the two hemispheres of the spherical mass.
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 · 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 kilogram at the surface.
The actual depth-dependence of density, inferred from seismic travel times (see Adams–Williamson equation), is given in the Preliminary Reference Earth Model (PREM). Using this, the real gravitational binding energy of Earth can be calculated numerically to U = 2.487 · 1032 J
According to the virial theorem, the gravitational binding energy of a star is about two times its internal thermal energy.
Other articles related to "energy, gravitational binding energy, gravitational":
... List of orders of magnitude for energy Factor (Joules) SI prefix Value Item 10−33 2×10−33 J average kinetic energy of translational motion of a molecule at the lowest temperature reached, 100 picokelvins as of. 3-7×10−21 J energy of a van der Waals interaction between atoms (0.02-0.04 eV) 4.1×10−21 J "kT" at 25 °C, a common rough approximation for the total thermal energy of each molecule in a system (0.03 eV) 7-22 ... firing a.458 Winchester Magnum 9×103 J energy in an alkaline AA battery 104 1.7×104 J energy released by the metabolism of 1 gram of carbohydrates or protein ...
... Dave Typinski demonstrates iron-cored Earth's homogeneous average density gravitational binding energy value is 31% larger than its more accurate integrated-over-density vs ... The moon's homogeneous average density gravitational binding energy value is 1.8% higher than its more accurate mantle plus core radial density value ... BE is the ratio of gravitational binding energy mass equivalent to observed neutron star gravitational mass of "M" kilograms with radius "R" meters, Given ...
... The gravitational field at the star's surface is about 2×1011 times stronger than on Earth ... Such a strong gravitational field acts as a gravitational lens and bends the radiation emitted by the star such that parts of the normally invisible rear surface become visible ... supernova explosion from which it forms (from the law of mass-energy equivalence, E = mc2) ...
... and the general mathematical definition of work to determine gravitational potential energy ... For the computation of the potential energy we can integrate the gravitational force, whose magnitude is given by Newton's law of gravitation, with respect to ... Using that definition, the gravitational potential energy of a system of masses m1 and M2 at a distance r using gravitational constant G is , where K is the constant of integration ...
Famous quotes containing the words energy and/or binding:
“A great number of the disappointments and mishaps of the troubled world are the direct result of literature and the allied arts. It is our belief that no human being who devotes his life and energy to the manufacture of fantasies can be anything but fundamentally inadequate”
—Christopher Hampton (b. 1946)
“With a binding like youve got, people are gonna want to know whats in the book.”
—Alan Jay Lerner (19181986)