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The gravitational constant appears in the Einstein field equations of general relativity, [4] [5] + =, where G μν is the Einstein tensor (not the gravitational constant despite the use of G), Λ is the cosmological constant, g μν is the metric tensor, T μν is the stress–energy tensor, and κ is the Einstein gravitational constant, a ...
The Einstein field equations (EFE) may be written in the form: [5] [1] + = EFE on the wall of the Rijksmuseum Boerhaave in Leiden, Netherlands. where is the Einstein tensor, is the metric tensor, is the stress–energy tensor, is the cosmological constant and is the Einstein gravitational constant.
The Planck energy E P is approximately equal to the energy released in the combustion of the fuel in an automobile fuel tank (57.2 L at 34.2 MJ/L of chemical energy). The ultra-high-energy cosmic ray observed in 1991 had a measured energy of about 50 J, equivalent to about 2.5 × 10 −8 E P .
The Einstein tensor allows the Einstein field equations to be written in the concise form: + =, where is the cosmological constant and is the Einstein gravitational constant. From the explicit form of the Einstein tensor , the Einstein tensor is a nonlinear function of the metric tensor, but is linear in the second partial derivatives of the ...
The equation for universal gravitation thus takes the form: =, where F is the gravitational force acting between two objects, m 1 and m 2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant.
A common misconception occurs between centre of mass and centre of gravity.They are defined in similar ways but are not exactly the same quantity. Centre of mass is the mathematical description of placing all the mass in the region considered to one position, centre of gravity is a real physical quantity, the point of a body where the gravitational force acts.
The sources of any gravitational field (matter and energy) is represented in relativity by a type (0, 2) symmetric tensor called the energy–momentum tensor. It is closely related to the Ricci tensor. Being a second rank tensor in four dimensions, the energy–momentum tensor may be viewed as a 4 by 4 matrix.
A geometrized unit system [1] or geometrodynamic unit system is a system of natural units in which the base physical units are chosen so that the speed of light in vacuum, c, and the gravitational constant, G, are set equal to unity. = = The geometrized unit system is not a completely defined system.