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Originally Posted by Luna2uno
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Originally Posted by papageno
I explained it to Lunatik.
If G depended on positions, the mass of an object would not be affected, but the gravitational force would be.
A different force would give a different acceleration, because the inertial mass has not changed.
But this problem is no more exotic than a variable dielectric constant in electromagnetism (which gives us refraction, and lenses).
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I see this really as a question referring to our units of measure, what we call kilograms. Can the same kilograms be used if G is different from what we know it to be as a universal constant? |
The definition of the unit
kilogram has nothing to do with
G.
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Originally Posted by Luna2uno
In yours you said: "The Equivalence Principle says that the gravitational mass equals dynamical (a.k.a. inertial) mass. It has nothing to do with the value of G."
Granted, given that G is universally the same, it has nothing to do with it,...
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No, it has nothing to do with
G, whether it is constant or not.
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Originally Posted by Luna2uno
... though G is part of the function describing Newton's formula for gravitation, as per yours above:
F = G * (m*M) / r^2 , which is related to Newton's second law:
F = M * a
Now, this equivalence can be also shown as:
F = M * a = M * (G*m) / r^2, where by default a = (G*m) / r^2
which also means: G = (r^2 * a) / m
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As you can see,
G does not affect
M, which is the mass the Equivalence has been applied to, but affects the acceleration
a the mass
M is subjected to.
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Originally Posted by Luna2uno
Now assume that both a and r^2 are fixed, same values, but G is greater, viz. G1 = 10G. So we have:
G1 = (r^2 * a) / m1, except now of necessity, m1 = 1/10th of m, if G1 = 10G.
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But we applied the Equivalence principle to
M.
By changing the value of
G, you changed the force
M and
m are subjected to.
If the only mean we had to measure the mass
m, was from the acceleration of
M due to its gravitational interaction with
m, then changing
G would affect our measured
m because the acceleration is different (assuming that we did not know that
G has a different value).
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Originally Posted by Luna2uno
However the mass had not changed, same mass (same atomic composition and volume), so the mass did not suddenly shrink to a tenth of its original form. What changed instead was that the measures in kilograms had changed,...
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No. What changed is the gravitational force between the two masses, and hence the acceleration changed.
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Originally Posted by Luna2uno
...to where now the kilograms are 10 times greater than the kilograms used earlier, to match up with G ten times Newton's G.
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This has nothing to do with the units.
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Originally Posted by Luna2uno
Can you see how this could be a problem? Though for now, given that G is universal, we don't have a problem. But if it were discovered that G is different, something might have to be adjusted in the measure of our (Earth derived) kilograms.
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No. The units would not need to be adjusted.
We don't need to change the unit of electric charge because the dielectric constant is not universal in materials.
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Originally Posted by Luna2uno
(That said, I still think that the answer above, kg1 = 10kg is wrong, but I'm not sure of what the right answer is. I suspect a is in fact not fixed as assumed, for a variable G.
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This is the point.
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Originally Posted by Luna2uno
Hypothetically, the real answer may be more like kg1 = 100 kg, if G1 = 10G, or its squared. It may take 10 times as much acceleration to move the same mass in 10G, so a is not fixed, but rather a1 = 10X a. But I don't know this.)
So you can see why I am frustrated, and I don't like my own answers!  There must be a better way to see this. |
You just need to realize that the value of the constant
G does not affect the mass of an object.
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Originally Posted by Luna2uno
Interesting if this might not apply as well to a " variable dielectric constant in electromagnetism", since it might impact how light bends around stars, which would impact gravitational lensing. :-?
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Refraction is very common phenomenon, which is due to a change in dielectric constant: this is why lenses work.
A
G dependent on position would not be more exotic than refraction.