On 28 Mar, 11:40, HW@....(Henri Wilson) wrote:
On 28 Mar 2007 02:16:59 -0700, "George Dishman" wrote:
On 28 Mar, 08:10, HW@....(Henri Wilson) wrote:
On Sun, 25 Mar 2007 23:34:03 +0100, "George Dishman" wrote:
"Henri Wilson" HW@.... wrote in message

George, when you can, have a look at

http://www.users.bigpond.com/hewn/ellip_circle.jpg

This shows how an elliptical orbit can produce a near perfect sine wave under
certain condition whilst the circular orbit produces nothing like one for
exactly the same parameter values.

Yaw angle is -90 (periastron closest to observer).

The white curve is an exact sinewave.

You might like to consider how the elliptical orbit's
curve will change with distance.

For small changes in magnitude I cannot tell the difference between the output
for a circular orbit and one with a small eccentricity.

What I expect is that as the distance changes, the ratio
of VDoppler to ADoppler changes giving a change in phase.
To compensate for that, you might need to alter the yaw
or a change of eccerntricity might do it.

The shape of the 'sinewave' produced for an elliptical orbit certainly changes
with distance, as expected. However it is certainly interseting to note that a
perfect sine wave 'bunching curve' can be produced by a star in an elliptical
orbit.

There is probably an algebraic reason for this ...but I don't think I'll bother
to find out what it is.

That is what I was alluding to a couple of weeks ago. For
small values you can probably get a match by eye but the
equation for an ellipse and those for Kepler's Laws are
quite different from the effect of ballistic theory. It
would be a curious though unimportant coincidence if they
exactly matched. Just as Ptolemy was able to get a good but
imperfect match with combined circles, I think if you did
the analytical investigation, you would find there was a
small difference but perhaps third or fourth order. That
is what would show up as the shape of a pattern in your
residuals.
theory

For example can you
do the same at a distance where VDoppler and ADoppler
are of equat magnitude (the 45 degree case for a
circular orbit).

George, I think what you are calling VDoppler is what you would get if you
placed a large number of equally spaced lights around a spinning wheel (Edge
on). Those on the sides would be 'VDoppler bunched' or separated.

I'm not sure I follow that but it is certainly not
what I am doing.

This is not the situation we are examining. The pulses are emitted in sequence
and not all at the same instant..and not at exactly the same point.
....
I have finally realised there is no VDoppler in the classical sense (as in the
case of the spinning wheel, above)

What the program measures is the rate at which pulses arrive. The ones on the
edge are emitted under constant velocity conditions and arrive at *very nearly*
the rate at which they are emitted. There is a very small difference due to the
fact that consecutive pulses are not emitted at the same point.

Right, that is the cause of classical VDoppler. Two
pulses emitted 2.295 ms apart travel slightly different
distances due to the motion of the source. At an orbital
speed of 27983 m/s when the pulsar is moving directly
towards us, the second pulse would travel 64.22 m less
than the first which corresponds to about 214 ns. The
VDoppler would be about 93 parts per million.

The diagram would be like this:

g h --- O


+
B

The pulsar sends one pulse from g and the next from h,
it is orbiting round the barycentre B and the observer
is at O. Obviously there is a v*cos(theta) term for
other parts of the orbit, it is the distance change
in the direction of the line of sight that matters.

I have
incorporated that by adding an Rsin(x) term to the star distance. It is
generally negligible.

It will certainly be small but it is not negligible, it
will produce a 45 degree phase shift when the ADoppler
is about 93 parts per million too and in fact we know
that the VDoppler is probably larger than the ADoppler
_except_that_ the phase can be changed by the effect you
describe at the top of the post regarding an elliptical
orbit looking circular.

I have held off replying to
see if you would clarify that (and also I was out last
night and we had visitors at the weekend). I've also
been tinkering with a GUI and might do a simulation for
comparison with yours but I have a couple of other
projects I'm working on too so I may not spend too much
time duplicating what you've already done. Does your
program actually include VDoppler or not?

George, I think your model is something like a spinning wheel with many lights
equally spaced around its rim.

No, it is what you describe above. You say you have
an R*sin(x) factor in the distance to address it,
though whether that works or not depends on your
code obviously.

VDoppler shift will occur in that model, if you
assume constant light speed to the observer from all sources. The correct model
is a spinning wheel that has one *flashing* light on its rim. There is a subtle
difference. Conventional VDoppler does not occur in this case.

You seem to have an odd idea of "conventional VDoppler",
the single flashing light on the rim of the wheel is how
I would think of it.

The shift in the former is (c+v)/c. In the latter it is something like
(D-Rsin(xt))/D and very soon disappears.

Do you see what I'm getting at?

Not really. The classical Doppler is c/(c-v) for a single source
that moves which is how the pulsar behaves. Balistic theory
changes the speed so it becomes (c+v)/c where v is the component
along the line of sight and includes the sin(theta) term.

I don't know where you get this idea of multiple sources.

George