Sensation_of_physics
Student
- Joined
- Oct 15, 2009
- Messages
- 41
Hello again
I must confess to a slight error on my part. It seems that Bjarne had gotten me confused as to whether his "space drag" should be
[latex]$$a_\mathrm{sd} = a_0 \left(1-\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\right)$$[/latex]
or
[latex]$$a_\mathrm{sd} = a_0 \left(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1\right)$$[/latex]
Turns out, he's consistently using the latter, so for the sake of honorsty, I shall repeat the calculation (and no, it hardly gets any better for Bjarne).
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The argument goes as before, the result is the same, save for a few changed signs:
[latex]$$v=\frac{c \sqrt{M \omega } \sqrt{2-\frac{M \omega }{a_0 Q r+M \omega }}}{\sqrt{a_0 Q r+M \omega }}$$[/latex]
However, this solution is valid for the whole r-range. So is Bjarne perhaps onto something after all?
Well no... lets examine: The generic form of the above expression is:
[latex]$$\frac{\sqrt{2-\frac{1}{1+r}}}{\sqrt{1+r}}$$[/latex]
which, when r gets large, converges asymptotically to
[latex]$$\sqrt{\frac{2}{r}}$$[/latex]
But that is the exact same generic form as Kepler's law for orbital velocity:
[latex]$$v=\sqrt{\frac{MG}{r}}$$[/latex]
So Bjarne has by some weird luck managed to reproduce Kepler's Law, save for a constant (Which is exactly the purpose served by the Skinner-constant Q)
But wait a second: Bjarne claimed that these thoughts provided a solution to some discrepancies from Kepler's Law, most notably the Pioneer anomaly and "the Galaxy Rotation Problem". However, since he merely reproduces Kepler's Law, he also reproduces these discrepancies and has thus not taken us anywhere further.
So, a little better than predicting that orbital motion should not exist, but still no cigar.
Sensation of Physics.
I must confess to a slight error on my part. It seems that Bjarne had gotten me confused as to whether his "space drag" should be
[latex]$$a_\mathrm{sd} = a_0 \left(1-\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\right)$$[/latex]
or
[latex]$$a_\mathrm{sd} = a_0 \left(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1\right)$$[/latex]
Turns out, he's consistently using the latter, so for the sake of honorsty, I shall repeat the calculation (and no, it hardly gets any better for Bjarne).
-------
The argument goes as before, the result is the same, save for a few changed signs:
[latex]$$v=\frac{c \sqrt{M \omega } \sqrt{2-\frac{M \omega }{a_0 Q r+M \omega }}}{\sqrt{a_0 Q r+M \omega }}$$[/latex]
However, this solution is valid for the whole r-range. So is Bjarne perhaps onto something after all?
Well no... lets examine: The generic form of the above expression is:
[latex]$$\frac{\sqrt{2-\frac{1}{1+r}}}{\sqrt{1+r}}$$[/latex]
which, when r gets large, converges asymptotically to
[latex]$$\sqrt{\frac{2}{r}}$$[/latex]
But that is the exact same generic form as Kepler's law for orbital velocity:
[latex]$$v=\sqrt{\frac{MG}{r}}$$[/latex]
So Bjarne has by some weird luck managed to reproduce Kepler's Law, save for a constant (Which is exactly the purpose served by the Skinner-constant Q)
But wait a second: Bjarne claimed that these thoughts provided a solution to some discrepancies from Kepler's Law, most notably the Pioneer anomaly and "the Galaxy Rotation Problem". However, since he merely reproduces Kepler's Law, he also reproduces these discrepancies and has thus not taken us anywhere further.
So, a little better than predicting that orbital motion should not exist, but still no cigar.
Sensation of Physics.
): Essentially, Bjarne inserts +n and -m in the formula, where n=m. And then he claims that proof of his thesis is that the results match. As if they could do otherwise.
