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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 ...
Thus, the gravitational acceleration at this radius is [14] = (). where G is the gravitational constant and M(r) is the total mass enclosed within radius r. If the Earth had a constant density ρ, the mass would be M(r) = (4/3)πρr 3 and the dependence of gravity on depth would be
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.}
What is the gravitational constant, how do scientists measure it, and is it really constant or can it change across time and space?
where F g is the gravitational force acting between two objects, M E is the mass of the Earth, 5.9736 × 10 24 kg, m s is the mass of the satellite, r is the distance between the centers of their masses, and G is the gravitational constant, (6.674 28 ± 0.000 67) × 10 −11 m 3 kg −1 s −2. [68]
The standard acceleration of gravity or standard acceleration of free fall, often called simply standard gravity and denoted by ɡ 0 or ɡ n, is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is a constant defined by standard as 9.806 65 m/s 2 (about 32.174 05 ft/s 2).
G, the gravitational constant, ħ, the reduced Planck constant, and; k B, the Boltzmann constant. Variants of the basic idea of Planck units exist, such as alternate choices of normalization that give other numeric values to one or more of the four constants above.
G is the universal gravitational constant (G ≈ 6.67×10 −11 m 3 ·kg −1 ·s −2) g = GM/d 2 is the local gravitational acceleration (or the surface gravity, when d = r). The value GM is called the standard gravitational parameter, or μ, and is often known more accurately than either G or M separately.