prove that the value of G(gravitational constant) is 6.23×10
Answers
Just use Newton’s equation.
F = (G*M*m)/r^2
By experiment, you can determine the magnitudes of F, M, m, and r.
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Now, perform the operation
(M*m)/r^2; and,
compare this to F.
It’s not going to match; ergo, it’s not an equation.
You must introduce a constant; that happens to be G.
That answers why G = <insert that long string of digits>.
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Now, perhaps you meant is G = G’? Does G vary across space? → Experiments show it does not.
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Is it possible that there is a different ‘G’ out there? Sure. We’d have, almost certainly, reason to call a region of space that has a G’ not equal to G → a different universe.
If the definition of universe is to be considered a causally connected region where the laws of physics are the same, then some G’ (G-prime) not equal to G would designate a new universe had been found.
Even though it’s possible that G changes with temperatures. We have some reason to think that the coupling constants for EM, weak, and strong equalize at some energy scale (somewhat) just below the Planck scale → it is at least possible that gravity’s ‘G’ also unifies at a scale immediately before the Planck scale or at the Planck scale itself.
Of course, it’s easy to speculate about anything when we have no way to test it! The only thing that has been tested is the equivalence of G in experiments to-date.