Why are the 'Fixed Stars' so FIXED?

On Mon, 2 Apr 2007 22:27:46 +0100, "George Dishman"
wrote:


"Henri Wilson" HW@.... wrote in message
.. .
On Sun, 1 Apr 2007 14:54:22 +0100, "George Dishman"
wrote:
"Leonard Kellogg" wrote in message
egroups.com...

Henri Wilson wrote:

[grammatical errors corrected to improve readability]

Hold a circle (or an ellipse) in front of you at any angle.
Rotate your head until you find an axis in the plane of the
circle that is horizontal to the line between your eyes,
and is also perpendicular to the LOS. (one always exists)
ALL the radial velocities and the accelerations around the
orbit are then multiplied by the same factor, cos(pitch),
where the pitch angle refers to the rotation around the
above axis.

Rotating one's head is irrelevant. The rotation that you
describe (A "roll" of either the head or the projected
ellipse) simply puts the long axis of the projected ellipse
on the viewer's X axis. That is convienient but has no
effect on the process of multiplying radial velocities and
accelerations around the orbit by a factor of cos(pitch).

You said this previously and I do not understand why George
did not point out its irrelevancy at that time.

Do I understand your terminology correctly as saying that
the "pitch" of an orbit is zero when seen edge-on and 90
degrees when seen face-on?

If so, your term "pitch" means the same as "inclination",
which is the term everyone else uses in astronomy. Though
it is often measured as angular deviation from face-on
rather than from edge-on. That is how it is used in arXiv
astro-ph/0507420.pdf (Table 1, "Orbital inclination, i")

To double-check that we are talking about the same thing,
see the illustration of "yaw", "pitch", and "roll" near the
top of this page:

Leonard, I think Henry has just swapped some definitions
for convenience. His cos(pitch) is the same as the usual
sin(inclination). I'm less clear about his yaw but I'm
fairly sure it is directly related to the longitude of
the ascending node.

It is the angle between the LOS and the major axis, in the edge on
position.

Any edge on orbit can be rotated about the axis perpendicular to the LOS.
At
any particular angle, all RADIAL velocities and accelerations will be
multiplied by the same factor, my cos(pitch).

ALL POSSIBLE ORBIT CONFIGURATIONS (WRT EARTH) CAN BE CREATED IN THIS WAY.

Think about it.

I don't need to, I think there is a trivial relationship
between your angles and the conventional ones. For example

pitch = 90 - inclination

I haven't bothered working out the yaw but I'm sure something
similar will result.

My main point is to show why redefining yaw angle makes it legitimate to use
edge-on orbits.

Did you try holding up a paper cutout and rotating it around the LOS till you
find the axis I talked about?


George



Einstein's Relativity - the greatest HOAX since jesus christ's mother.