[geocentrism] Outrages at Mathpages

From: "Robert Bennett" <robert.bennett@xxxxxxx>
To: "Geocentrism" <geocentrism@xxxxxxxxxxxxx>
Date: Wed, 18 Apr 2007 23:24:22 -0400
I've mentioned several times my admiration for Richard Feynman and tonight
while roaming freely, I chanced across this little gem.
http://www.mathpages.com/home/kmath320/kmath320.htm
<http://www.mathpages.com/home/kmath320/kmath320.htm>


Yes, Mathpages is one of my favorite comedy sites. The section on stellar
aberration attempts to validate mathematically that aberration proves the
earth is moving, using the MS paradigm of special relativity.
http://www.mathpages.com/rr/s2-05/2-05.htm
<http://www.mathpages.com/rr/s2-05/2-05.htm>
From within this section:

??.
For example, consider a binary star system in which one large central star
is roughly stationary (relative to our Sun), and a smaller companion star is
orbiting around the central star with a large angular velocity in a plane
normal to the direction to our Sun, as illustrated below.



It might seem that the periodic variations in the velocity of the smaller
star relative to our Sun would result in significantly different amounts of
aberration as viewed from the Earth, causing the two components of the
binary star system to appear in separate locations in the sky - which of
course is not what is observed. Fortunately, it's easy to show that the
correct application of the principles of special relativity, accounting for
the non-uniform variations in the orbiting star's velocity, leads to
prediction that agree perfectly with observation of binary star systems.

At any moment of observation on Earth we can consider ourselves to be at
rest at the point P0 in the momentarily co-moving inertial frame, with
respect to which our coordinates are



Notice anything wrong? The first error:
 This is a GC system, when it should be HC, to be MainStream.  The Earth
should be in polar coordinates centered on the Sun, representing the earth
in orbit while light is in transit from the binary stars.  As set up, the
earth never moves; at any time t,  it?s at the origin!
Suppose the large central star of a binary pair is at point P1 at a distance
L from the Earth with the coordinates



V is the speed of stellar rotation as seen from earth  - again, the GC view.

The fundamental assertion of special relativity is that light travels along
null paths, so if a pulse of light is emitted from the star at time t = T
and arrives at Earth at time t = 0, we have



This is derived from the null space-time interval for light:   r2 ?(ct)2 = 0
.     Units are being used in which c = 1, so r2 ? t2 = 0

So  r02 ? t02  = 0     and r12 ? t12 = 0    and thus     r02 ? t02  =  r12 ?
t12
Plug in the initial values to obtain the equation above.

Now the second error:  Light is emitted from the star at a time T  AFTER it
arrives at Earth at time zero!. Light is traveling backwards in time,
received before emitted.  The MS trademark ? contradictions.
The correction: set t = 0 in the star system #1 and t= T on earth ? system
#0.
Inserting these values into the last equation,

0 ? T2  = L2 ?0  ;     ? T2  = L2

Since the left side is always negative and the right side always positive,
we have found another MS trademark contradiction!   Error 3, and counting.

But why the error, if GC was used (albeit under disguised pretenses)?
Suppose  r02 ? t02  = k     and r12 ? t12 = k, where k is constant and
non-zero.  Then it would also be true that   r02 ? t02  =  r12 ? t12  , but
they are not each equal to zero !!
The equation is degenerate, folks, because the value of the constant k has
been removed??.
Error # 4.

This site is the reference of many other MS sites for explanations of
relativity math?.
God help us all.

There are more errors below, but if you get the point - what?s the point ??


Robert

and so


from which it follows that x1/z1 at time T is . Thus, for the central star
we have the aberration angle



Now, what about the aberration of the other star in the binary pair, the one
that is assumed to be much smaller and revolving at a radius R and angular
speed w around the larger star in a plane perpendicular to the Earth? The
coordinates of that revolving star at point P2 are



where q = wt is the angular position of the smaller star in its orbit. The
fundamental principle of special relativity is that light travels along null
paths, so a pulse of light arriving on Earth at time t = 0 was emitted at
time t = T satisfying the relation



Solving this quadratic for T (and noting that the phase q depends entirely
on the arbitrary initial conditions of the orbit) gives



If the radius R of the binary star's orbit is extremely small in comparison
with the distance L from those stars to the Earth, and assuming v is not
very close to the speed of light, then the quantity inside the square root
is essentially equal to 1. Therefore, the tangents of the angles of
incidence in the x and y directions are



The leading terms in these tangents are obviously just the inherent "static"
angular separation between the two stars viewed from the Earth, and the
first term in the x tangent is completely negligible (assuming R/L and v are
both small compared with 1), so the aberration angle is essentially



which of course is the same as the aberration of the central star. Indeed,
binary stars have been carefully studied for over a century, and the
aberrations of the components are consistent with the relativistic
predictions for reasonable Keplerian orbits. (Incidentally, recall that
Bradley's original formula for aberration was tan(a) = v, whereas the
corresponding relativistic equation is sin(a) = v. The actual aberration
angles for stars seen from Earth are small enough that the sine and tangent
are virtually indistinguishable.)
[geocentrism] Outrages at Mathpages

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