Re: precession of mercury

On Sun, 14 Dec 2008 17:22:16 +0100, "Paul B. Andersen"
<paul.b.andersen@xxxxxxxxxxxxxxx> wrote:

Jerry wrote:
On Dec 14, 3:43 am, hw@..(Dr. Henri Wilson) wrote:
On Sat, 13 Dec 2008 20:24:41 +0100, "Paul B. Andersen"

<paul.b.ander...@xxxxxxxxxxxxxxx> wrote:
Dr. Henri Wilson wrote:
On Fri, 12 Dec 2008 12:19:35 +0100, "Paul B. Andersen"
<paul.b.ander...@xxxxxxxxxxxxxxxx> wrote:
When you measure stellar aberration, you don't assume
anything about anything.
All you do is to see how the direction to the star changes
throughout the year. (In which direction must
the telescope be pointed to see the star at the centre?)
'The direction to the star' is called the 'apparent position',
and _all_ stars appear to follow an ellipse where the major
axis _always_ is 2v/c radians.
And it is an irrefutable fact that spectroscopic binaries
_always_ will be seen as a single star, even if the magnitude
of the velocity difference between the components may be
_much_ higher than the orbital speed of the Earth.
The different velocities of the components do _not_
affect the direction in which we see them.
:).....:).......:)
I hope you can see the arguments against this without my having to tell you.
Please tell me.
How large is a point in the night sky?

You are, of course, asking whether differences in v/c radians
for the SEMImajor axis are resolvable.

I can't understand why you call this the SEMImajor axis.
Which ellipse is it the semi-major axis of?

Let us look at Algol. The orbital velocity of the primary star,
projected on our line of sight, is 44 km/s, while that of the
secondary star is 198 km/s. The maximum difference in orbital
velocities between the two components relative to our line of
sight is therefore 242 km/s.

So the difference in aberration due to the different speeds of
light should be (v/c - v/(c+u)) rad ~= (v/c)(u/c) rad
where u = 242km/s and v = 30km/s.
So the difference is 8E-8 rad = 0.0165"

Unification and extinction takes care of that.
It can't be reolved anyway.

The speed of Earth in its orbit around the sun is approximately
30 km/sec, so the maximum separation (equals the difference in
semimajor axis) of the two stars due to differences in aberration
would be 0.00000008 rad which equals 0.017 seconds of arc.

We seem to agree, even if I still don't understand what you
mean by the semimajor axis. :-)

This means that during the 3.8 days period, the two components
should appear to move away from each other till they are 17 mas
apart, then move together, pass each other, and move away till
they are 17 mas apart the other way, move together again, etc.

This
is outside the capabilities of an Earthbound telescope not
equipped with active optics, but within the capabilities of large
Earthbound telescopes equipped with adaptive optics such as the
Keck or Gemini instruments as well as the HST, which should
detect the differences as highly distorted stellar images.

Hardly. Even if all big telescopes now have adaptive optics,
no single telescope (including HST) can resolve 17mas.
But see below!

There are many binary stars with orbial motions considerably
faster than those of the Algol system, so highly distorted
stellar images from spectroscopic binary systems should have
been noticed a long, long time ago.

Jerry

The resolution which can be achieved with interferometry vastly
exceeds what can be achieved with single telescopes.

Let us look at another eclipsing close binary, beta Lyrae.
The radial velocity can be seen here.
http://vizier.hia.nrc.ca/viz-bin/vizExec/Vgraph?J/A%2bA/463/233/./table3&;

A difference of 242km/s is close enough, so we can use the same numbers
as calculated above.

Here are spectroscopic measurements of the binary.
http://arxiv.org/pdf/0808.0932v1

Look at Fig. 2 and Fig. 3 on pages 12 and 13

Where did the 17 mas go? :-)

I think this puts a rather low limit on the change in the speed of light.

Binary pairs with periods this short have overlapping 'EM spheres of
influence'...so all light leaves their 'vicinity' at around the same speed,
which should be approximately c wrt their barycentre.
Doppler shift will still give a true reading of individual star speeds, wrt
earth, since photons shrink and extend during speed changes.


Henri Wilson. ASTC,BSc,DSc(T)

www.users.bigpond.com/hewn/index.htm.

......
.

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