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Originally Posted by pghnative
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Originally Posted by nutant gene 71
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Originally Posted by Tassel
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Originally Posted by nutant gene 71
"Nough said. I've given you all the information you need to show how this works. I will reply only to specific errors in my math, or my reasoning.
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What about actually providing some math that shows the necessity/correctness of your "variable mass" idea? In spite of your efforts, there hasn't been a single calculation (using correct equations...) in this thread that shows "constant mass" failing in a variable G scenario.
And I suppose I'm not going to get an answer to my questions as to how you would suggest we measure 1kg of mass in 10G on Titan in your "variable G/variable mass" universe.
We've gone over every conceivable "hypothetical" variation of location and value for G in the solar system, and yet we have never had to redefine the kilogram to model what you say we should observe in a variable G universe...even when you've changed your mind on what you think we'd observe!  |
See this post, July 9, 2005, pg. 2 of this thread. |
Yes, I can see that post. That post is effectively debunked by
a) my analogous post regarding Saturn above, which demonstrates that you need G to be = 1G at Saturn's orbit to correctly calculate its orbital velocity.
b) Tassel's subsequent post on pg. 2 showing that you used the wrong mass in the equation "GM = rv2". You used M = mass of jupiter; in reality, M=mass of sun in that equation.
Note that we've pointed out an error in your mathematics, as per:
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Originally Posted by nutant gene
I will reply only to specific errors in my math, or my reasoning.
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So would you now be able to answer my questions about Saturn's orbit? If you do, it will be patently obvious where your mathematical errors are. |
RE: GM = Rv^2 for Saturn, it would be the same methodology
as worked out for Jupiter here, July 11, 2005, pg. 3 of this thread.
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Originally Posted by nutant gene
We know GM = rv^2 is a short form, a reduced simplified equation. We also know that what's on the left has to be equivalent to what's on the right, which is what an equation equals. One way to see this is to reconstruct from whence this simplified equation came from. We know the following:
F = GMm/ r^2, and we know F = ma, which is also F = M*(Gm/r^2), where a = (Gm)/ r^2, but we can also see Newton's orbital equation one more way, as:
F = M*(Gm)/r^2 = mv^2/ r.
I showed the M separate, since it represents the Sun, a fixed value of mass, unaffected by G. The (Gm) is together because these are the variables, hypothetically, that need to be addressed. And on the right (mv^2/r) is a version of the same equation. When M*(Gm)/r^2 = mv^2/r is netted out, it gives us:
GM = rv^2
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Please note that in the "short form", big M is now the planet, since the Sun's mass drops out from the "long form".) --
this is wrong, M remains Sun's mass, will redo below to correct error. GM=rv^2 cannot be used for variable G, since Sun's G and M are invariable.--n.g.71
Taking Saturn's mass and distance from the Sun, adjusted for hypo 10G at Saturn:
Remember (critical point) neither Saturn's orbit nor its mass are changed, only how we
measure the mass in terms of an
increased G. So let's plug in some numbers for Saturn as we know them in (Earth's) 'universal constant' G, where G = 6.67E-11 m^3 kg^-1 s^-2 and Saturn's m = 5.685E+26 kg:
M * (Gm)/r^2 = mv^2/r, so that M*(6.67E-11 m^3 kg^-1 s^-2)(5.685E+26 kg)/ r^2 = m v^2/r, which is M*(37.92E+15 m^3 s^-2)/r^2 = m v^2/r
(Remember the right side is in Earth units, so does not change.)
Now let's plug in the new Saturn's G', tenfold, approxmately G' = ~66.7E-11 Nm^2 kg^-2:
M*[(~66.7E-11 m^3 kg^-1 s^-2) * m'] /r^2 = m v^2/r, and to conserve the product (G'm') = 37.92E+15 m^3 s^-2, divided by 66.7E-11 kg,
m' becomes =
0.5685E+26 kg (which is one tenth the mass of what Saturn
was in a G = 6.67E-11 N.. equation).
M, r^2, and mv^2/r remain the same as before. So we don't see any difference in Saturn's orbit with a different G. You cannot tell from the orbital "short form" GM=rv^2 because adjusted G' and m' are not shown, as they were canceled out in a 1G universal constant scenario. If you want to continue and plug in the M, r, r^2, in the "long form" you'll still get the same results as before.
The same applies to all the other values, since they are all derived from Earth's observations, so M and mv^2/r remain the same, figured in Earth units. Only (G*m) are adjusted for each other, while the Sun's "m" on the right side remains the same as it had been figured in the original. Why? Because all our math is derived from Earth based units of kilogram mass (as well as meters and seconds). If you were using Saturn based "kilograms", then you would not need to adjust (G*m) since it would all be figured "as if" that was the "universal constant" in its own kilograms. The orbital equation would still yield same, given the new units for G' and m'. It's just we seem to like Earth's G units for mass better, for better or worse. Consequently, our inherent "terracentrism" has given us a bias to believe G is a universal constant.
So the new orbital would be, for Saturn at hypo 10G:
GM = rv^2, plugging in the adjusted G and M (which is now Saturn):
(66.7E-11 m^3 kg^-1 s^-2)(0.5685E+26 kg) = rv^2
37.92E+15 m^3 s^-2 = rv^2.
Like I said before, you have all you need to figure this out. Whether or not you do, or whether you believe it, is up to you.
[Edited, for explanation of M vs. m, as Sun's mass, cannot use short form of G*M, also typo errors.]