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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 value of the constant G was first accurately determined from the results of the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798, although Cavendish did not himself calculate a numerical value for G. [5] This experiment was also the first test of Newton's theory of gravitation between masses in the laboratory.
1.438 776 877... × 10 −2 m⋅K: 0 [12] [e] Wien wavelength displacement law constant: 2.897 771 955... × 10 −3 m⋅K: 0 [13] ′ [f] Wien frequency displacement law constant: 5.878 925 757... × 10 10 Hz⋅K −1: 0 [14] Wien entropy displacement law constant 3.002 916 077... × 10 −3 m⋅K: 0
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 reason for this is that the choice of a system of units may arbitrarily select any physical constant as its basis, making the question of which constant is undergoing change an artefact of the choice of units. [5] [6] [7] For example, in SI units, the speed of light has been given a defined value in 1983. Thus, it was meaningful to ...
By making this assumption, g takes the following form: = (i.e., the direction of g is antiparallel to the direction of r, and the magnitude of g depends only on the magnitude, not direction, of r). Plugging this in, and using the fact that ∂ V is a spherical surface with constant r and area 4 π r 2 {\displaystyle 4\pi r^{2}} ,
In unit systems where force is a derived unit, like in SI units, g c is equal to 1. In unit systems where force is a primary unit, like in imperial and US customary measurement systems , g c may or may not equal 1 depending on the units used, and value other than 1 may be required to obtain correct results. [ 2 ]
A mass m attached to a spring of spring constant k exhibits simple harmonic motion in closed space. The equation for describing the period: T = 2 π m k {\displaystyle T=2\pi {\sqrt {\frac {m}{k}}}} shows the period of oscillation is independent of the amplitude, though in practice the amplitude should be small.