My equation have nothing with yours manipulated equation to do camrade Sensation_of_physics
We are still waiting for Bjarne to point out exactly where I have manipulated his equations.
And finally comrade Sensation_of_physics had begun to see that both equation are direct proportional . It took him 1/2 year.
And his own mistake is now claimed to have been caused by a "Skinner-constant Q"
No, I can't have, because my conclusions are based on manipulated equations and faulty math, Right?
anyway seriously, they are
not "directly proportional". They are approximately proportional in a limit of large r, which explains why Bjarne seems to get this "exact equlity" he's so worked up about. Everyone else seems to get this point.
But lets take it one more time, just for Bjarne, and lets see if we can reproduce his results:
Bjarne is comparing the two sides of the equation
[latex]$$\omega\frac{M}{Qr}=a_{0}\left(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1\right)$$[/latex]
But with the little twist that he's using already known orbital data to get v; to boot, Keplers Law. Thus we
substitute v for Keplers Law:
[latex]$$\omega\frac{M}{Qr}=a_{0}\left(\frac{1}{\sqrt{1-\frac{\frac{MG}{r}}{c^2}}}-1\right)$$[/latex]
(This is what Bjarne himself is doing, although he doesn't quite realize it, being oblivious to algebra, so I expect some more accusations of manipulations coming this way)
This is the onset of the circular reasoning; because we knew that the equation would already reduce to Keplers Law, i a large-r limit.
Bjarnes Claim is now that the above equlity holds
exactly for each planet distance, r, in the solar system and that a slight discrepancy would mean that said planet is in an unstable orbit.
But a little more Algebra reveals that the equation can have at most
one exact solution for r - it may even have none. All comes down to the constant Q, which Bjarne seems to have pulled out from one of the nether orifices of his body.
But if there is only one point where the equlity holds exactly then
all planets not at this exact distance should be in unstable orbits!
In principle we are done here. But Bjarne seems obsesed with numbers so let do a few:
Constants (from Bjarnes webpage):
M=2 10
30omega=2Pi/2.592.000
Q=6.52 10
21c=2.99 10
8
(yes I omitted the units - including them would cause major incompatibility)
And The Gravitational constant:
G=6.67428 10
-11
Mercury:
r=5.8 10
10
[latex]$$\omega\frac{M}{Qr}=1.28203 \times 10^{-8}$$[/latex]
[latex]$$\left(\frac{1}{\sqrt{1-\frac{\frac{MG}{r}}{c^2}}}-1\right)=1.28716 \times 10^{-8}$$[/latex]
Whoops! Discrepancy already on third decimal place... So much for the "exact equlity" - perhaps this goes to explain why Bjarne chose to stop at second decimal place.
I hope this serves to illuminate that Bjarnes equation is not exactly equal, at least not from a mathematical viewpoint.
But all this fuzz about numbers is a bit bizare. After all, I my self have statet that the agreement will be better and better with increasing r. That is true, and when including measurement uncertainties and such, you might argue that from a physical viewpoint, the equation hold. But Bjarne
still hits the snag that his idea
doesn't explain anything new, it merely restates what we already know. And thus he is simply
incorrect in his statement that this idea "solves numerous mysteries" - It doesn't! It predicts the exact same mysteries!
