Re: The Physics Behind 'Contractions'.

On Thu, 01 Jan 2009 23:00:04 +0100, "Paul B. Andersen"
<paul.b.andersen@xxxxxxxxxxxxxxx> wrote:

Dr. Henri Wilson wrote:
On Wed, 31 Dec 2008 15:44:45 +0100, "Paul B. Andersen"
<paul.b.andersen@xxxxxxxxxxxxxxx> wrote:

Dr. Henri Wilson wrote:
On Tue, 30 Dec 2008 22:41:00 +0100, "Paul B. Andersen"
<paul.b.andersen@xxxxxxxxxxxxxxx> wrote:

Strich.9 wrote:
Paul, to a fool, everything looks trivial doesn't it? Have you
figured out aberration yet?
No, I need to have someone with superior intelligence to teach me about it.
So would you be so kind as to explain where I am wrong here?
http://home.c2i.net/pb_andersen/pdf/Stellar_aberration.pdf
This is totally inadequate. You haven't stressed the importance of the
telescope's orientation when the readings are taken.
Very funny indeed, Henri. :-)
It _was_ a joke, right?

Well, we know that the whole of relativity is a joke but maybe that's not what
you meant.

I mean that when you know the direction of the light from a star
in an inertial frame, then it is a joke to ask in which the direction
a telescope which is stationary in that frame must be pointed to see the star.

So in the context of this:
http://home.c2i.net/pb_andersen/pdf/Stellar_aberration.pdf
your statement:
<<
This is totally inadequate. You haven't stressed the importance of the
telescope's orientation when the readings are taken.
>>
is indeed a joke.

What you write in the following is utterly irrelevant to the paper
you commented, but I will comment on it anyway.

Let me explain again..... read carefully.
If a space telescope is sent into a circular ecliptic orbit and is accurately
aligned with a star that lies right on the ecliptic polar axis and if that
telescope spins on a similarly aligned axis once per its orbit period, the
image of that star will remain exactly in the viewing centre.

But to make the telescope always be aligned with the star (the star is
always at the exact centre of the viewing field), the pointing of
the telescope must be moved along a small circle synchronous with it's
orbital motion, the radius of this circle must be u/c radians where
u is the orbital speed of the telescope.

You didn't follow what I wrote.

For example, if the telescope
is in geosynchronous orbit, u = 3km/s, u/c = 10^-5 radians = 2 arc-seconds.
At the same time it must be moved along a bigger circle once a year,
the radius of this circle is 20.5 arc-seconds.
Hard to do, but possible; its done in the HST with reaction wheels.
So let's assume it's done.

(A suspicion creeps in - have you still not understood stellar aberration?
Do you really think the star would stay in the centre if the axis of
the telescope always is pointing in the same direction? )

If you read what I said properly you would know the answer to that.

If all the other stars in view happened to be located at exacty the same
distance from Earth as the central star then they will appear to rotate around
the central star in parallel circles, the radius of which is just their
distance from the central star. In other words, aberration is the same for all
objects and doesn't affect their relative motions.

Sure. But only if the telescope is steered as explained above.

The telescope is in an ecliptic orbit (nothing to do with planet Earth). It
spins around an axis parallel with the ecliptic axis once every orbit period.
Get it now?

However, since they lie at vastly different distances, the sizes of those
circles will vary due to parallax....

Right.
One circle per orbit around the Earth, the radius will will change
one cycle per year.
The amplitude in the change in the radii will be equal the difference
in parallax of the reference star and the star in question.

the earth is not involved in my experiment.

and so will the positions of the CENTRES of those circles.

No. Why do you think it would?
The parallax due the orbit around the Earth is of course negligible,
so the angular distance between the stars doesn't change significantly
during one orbit, and the centre will remain at the reference star.

The offset of those centres can be used to estimate distances, using parallax.

No, but the differences in radii could.

You didn't follow what I wrote.

If instead the same telescope is pointed exactly parallel to the ecliptic polar
axis,

(Suspicion strengthened - but I will pretend you understand stellar aberration.)

You didn't follow what I wrote.

This is not what you meant, is it?
If it was pointed like that, and the telescope is not rotating, all the stars
would once per orbit move along the aberration circles with radius 2 arc-secs
(or bigger for lower orbits than geosync).
(And the centre of these circles would yearly move along the 20.5" circles.)
If the telescope was rotating as described above, the stars would move
in circles where the radius would change by 2", resulting in ellipses
where the difference between the semi-major and semi-minor axes would be 2".
Superimposed would be a yearly change in the axes of 20.5".

The parallax would only have the influence of a yearly tiny change in
the 20.5". The parallax acts in the opposite direction of the aberration,
so it would only have the effect that the yearly change in the radius
would be slightly less than 20.5".

Wrong. It is 90 out of phase.

(all stars have parallax < 1", most very much less).

So what you must mean is that it is pointed such that an infinitely
distant star at the ecliptic pole would always be at the centre.

RIGHT.

So it would have to be steered the same (complicated) way as above,
only with a slight change of reference.

It is not at all complicated. It just has to rotate once per (its) orbit around
the sun.
Get it now?


then a star right on that axis will appear to move in a circle whose
radius subtends an angle 1AU/D.

Right. But only if the telescope is steered as explained above.

The whole fields of view will rotate and the
other stars in the window will also follow circular paths (in the rotating
frame) with the same kind of radii as above (1AU/Dx).

Not at all.
The centre of all the circles will be at the centre of the viewing field,
but the radii will change yearly with the amplitude (1AU/Dx).

If the same vertically pointing telescope DOES NOT SPIN as it orbits, then the
whole fields DOES NOT rotate around the window either. Rather it 'wobbles' as a
whole due to aberration with each star moving in an additional small circle
(subtending 1AU/Dx) due entirely to parallax. CMIIW

If the telescope doesn't rotate, and is steered as explained above, you
get an image as a normal star picture. The distances between the stars
changes slightly due to differences in parallax.
They move in yearly small circles.


I don't quite see your point with all this.
And my suspicion that you still haven't understood stellar aberration
has grown very strong. :-)


The situation is obviously much more complicated when the telescope is pointed
away from the ecliptic pole.

If you are referring to my paper:
Not really.
It is correct that I in my paper explained how a star at the ecliptic pole
would move due to stellar aberration - along circles with radii 20.5",
but it should be fairly simple to understand that a star at the ecliptic
will appear to move back and forth along a line which is 2 x 20.5".
In the general case, it will appear to move along an ellipse where
the semi-major axis always is 20.5", and the semi-minor axis is
sin(phi)x20.5", where phi is the ecliptic latitude.

That is true if the star is kept right in the viewing centre and the telescope
angle is plotted over the year. The Earth's tilt has to be taken into account.
The plot produces an ellipse.

I did address that point:
http://home.c2i.net/pb_andersen/pdf/Stellar_aberration.pdf
page

But you still didn't follow what I wrote.


Henri Wilson. ASTC,BSc,DSc(T)

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

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