Henri Wilson wrote:

How does the light know that it should adjust its speed
relative to the barycentre rather than something else?

In actual fact light only 'knows' of one object, its own
source. ...

How does the light determine its speed relative to the
barycentre of the system it has left?

It leaves at between c+v and c-v in the observer direction,
wrt the orbit centre. I'm saying, that in time, it unifies
to something like c wrt that centre. Don't ask me how or
why... but this seems to happen in varying amounts according
to the BaTh.

It is most astonishing. Light from the star adjusts its
speed relative to something with which it has no connection.

If the light came only from the far side of the orbit,
would it unify relative to the mean radial speed during
that half-orbit, instead of unifying relative to the mean
radial speed over the full orbit?

I presume it unifies to the mean, rather than the median.
Is that correct?

No, you don't seem to understand this properly.
The suggestion is that all light emitted in any particular
direction unifies towards c in the barycentre frame. For
circular orbits, it starts out with velocities in the range
c+v to c-v wrt the barycentre in that direction. For
elliptical orbits the range will be biased somewhat,
depending on the eccentricity and yaw angle.

The example I used was a bad choice, but your reply tells
me that it doesn't matter: The light doesn't unify relative
to either the mean or the median of the emission speeds,
but to the speed of the barycentre. I was speculating that
perhaps the whole beam of light averaged its speed over
time. Instead, you say the light adjusts its speed relative
to the barycentre of the system from which it was emitted.

Does light readjust its speed relative to the barycentre
of a system that it passes through? For example, if the
speed of light emitted from the Moon is first unified
(or partially unified) relative to the barycentre of the
Earth-Moon system, does the light then change speed if it
happens to pass through the Saturn-Titan system, to unify
relative to the barycentre of the Saturn-Titan system?
And does the light again readjust its speed to unify
relative to the barycentre of the Galaxy?

As you say in your first reply quoted above, the light
should only 'know' of one object, its own source. So it
is most puzzling how it can also be aware of the various
barycentres, know which barycentre it must unify its speed
relative to, and know the amount of adjustment required.

The only explanation I can suggest is that all large mass
centres are surrounded by some kind of weak EM reference
frame....and these extend well away from the objects
themselves.

I gather that what you meant was some kind of weak EM
*field* which changes the speed of light passing through
it closer to c. The strength of such a field would have
to be nearly constant with distance, so that light speed
can eventually unify yet not unify too rapidly. If the
strength of the EM field fell off at the same rate as the
gravitational field, light from the far side of the orbit
which passes close to the primary body would be unified
much more rapidly than light which does not pass close to
the primary.

Would light leaving the Moon toward a distant viewer unify
its speed to c relative to the Earth-Moon barycentre or to
the Moon-Sun barycentre?

For a three body system, The radial velocity would be
something like c+Acos(xt)+Bcos(yt).

The max amd min are c+A+B and c-A-B.

That seems reasonable.

So I presume there would be two separate unification
processes occuring simultaneously at different rates.
The A would go towards zero over relatively short
distances followed by the B over larger distances.

So light from the Moon would tend to unify relative to the
Earth-Moon barycentre, and then tend to unify relative to
the Moon-Sun barycentre.

It is a puzzle how the light could seem to know that it
was emitted from a body which is orbiting other bodies.
And it is a puzzle how the light could seem to know its
speed relative to the different barycentres.

Like I said above, there must be some kind of reference
frame surrounding large masses.

I say this because unification rate appears to be dependent
on orbit period. Don't ask me why. There could be an entirely
different explanation as to why the hipparcos distances are
generally longer than those I need to match brightness curves.

The obvious relationship is that the shorter the orbit
period, the higher the radial speed, and thus the greater
the initial bunching effect, so the unification distance
needs to be shorter in order to prevent excessive bunching
during transit.

That is true...but it doesn't explain why the actual
unification rate itself should be period dependent.
What could make space around short period binaries
different from that around longer period ones?

I think that if you look at the numbers for a few stars,
you will find that the unification rate depends directly
on the maximum speed, rather than period.

I know there could be an entirely different explanation
for this....but I cannot see it.

The things which are closest at hand can sometimes be the
most difficult to see.

Leonard