Campare universal gravitational constant (G) Perimitivity (E)and permeability in four points
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Answer:
We wonder the origin of Universal Gravitational constant and existence of vacuum permittivity and permeability in the space. These all seems, somehow related to the Space-time and physical dimensions of whole Universe. The relation between gravity and speed of light also reveals the origin of vacuum permittivity and permeability. Recently there was a discussion on Young's modulus Y of space-time [1, 2]. The question raised was, what is the Young's modulus Y of space-time as experienced by a gravitational wave (GW), originally discussed at 2018 Hamilton Lecture at Princeton "Exploring the Universe with Gravitational Waves". One response was that Y space−time is frequency dependent and given by − = 2 2 (1) where f is the frequency of the gravitational wave, and G the Newtonian Gravitational constant. Above equation reveals interesting relation between Gravitational constant and speed of light. In a way this is also clear explanation for the existence of vacuum permittivity and permeability in space. Using the same analogy of matching dimensions Newton's gravitational constant is G = 6.67 × 10-11 Kg-1 m 3 s-2 , speed of light in vacuum is c = 3× 10 8 m/s, diameter of Universe D u = 8.8× 10 26 m and total mass of the Universe M u = 1.5 × 10 53 Kg. Then, we can write (by dimensional analysis), = 2 (2) equation 2 also can be written in terms of Mass of Universe. = 2 (3)
