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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 ...
So, to find the acceleration due to gravity at sea level, substitute the values of the gravitational constant, G, the Earth's mass (in kilograms), m 1, and the Earth's radius (in metres), r, to obtain the value of g: [20]
For example, the atomic mass constant is exactly known when expressed using the dalton (its value is exactly 1 Da), but the kilogram is not exactly known when using these units, the opposite of when expressing the same quantities using the kilogram.
The standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of that body. For two bodies, the parameter may be expressed as G ( m 1 + m 2 ) , or as GM when one body is much larger than the other: μ = G ( M + m ) ≈ G M . {\displaystyle \mu =G(M+m)\approx GM.}
In SI units, the values of c, h, e and k B are exact and the values of ε 0 and G in SI units respectively have relative uncertainties of 1.6 × 10 −10 [16] and 2.2 × 10 −5. [17] Hence, the uncertainties in the SI values of the Planck units derive almost entirely from uncertainty in the SI value of G.
The constants that Stoney used to define his set of units is the following: [1] [2] c, the speed of light in vacuum, G, the gravitational constant, k e, the Coulomb constant, e, the charge on the electron. Later authors typically replace the Coulomb constant with 1 / 4πε 0 . [3] [4]
The refined value of the WGS 84 gravitational constant (mass of Earth's atmosphere included) is GM = 3.986 004 418 × 10 14 m 3 /s 2. The angular velocity of the Earth is defined to be ω = 72.921 15 × 10 −6 rad/s. [11]
The "mass of the earth in gravitational measure" is stated as "9.81996×6370980 2" in The New Volumes of the Encyclopaedia Britannica (Vol. 25, 1902) with a "logarithm of earth's mass" given as "14.600522" [3.985 86 × 10 14]. This is the gravitational parameter in m 3 ·s −2 (modern value 3.986 00 × 10 14) and not the absolute mass.