View Single Post
  #6  
Old March 12th 11, 09:15 AM posted to sci.astro
Henry Wilson DSc
external usenet poster
 
Posts: 264
Default Most 'Variable Stars' are not Varying at all..

On Fri, 11 Mar 2011 22:15:32 -0000, "Androcles"
wrote:


"Henry Wilson DSc" Hw@.. wrote in message
.. .
| On Fri, 11 Mar 2011 02:37:54 -0000, "Androcles"
| wrote:


| Even if the orbit were perfectly circular (which in most cases it is not)
| the function would give an initial velocity of c+v.sin(t/period modulo
2pi),
| you need to convert t/period to a pure number for dimensional analysis
| and then convert to radians to become the argument of the function sin()
| (or cos(), depending on your arbitrary choice of axes).
|
| t/T IS already a pure number. The 2pi turns it into a phase angle, in
| radians....also a pure number...I usually leave out the 2pi because it is
| understood.

What you call T is the period, P.
When I wrote Doolin'sStar I used T for the APPARENT time interval.
http://www.androcles01.pwp.blueyonder.co.uk/Doolin'sStar.GIF
You are not helping by changing the definition of variables.


Let's not argue about trivialities, chief. When you adjust your time axis for
arrival time of each sample 'bunch' your program will produce the same curves
that mine does.

| So T must be the
| period (symbol P) and t must lie between 0 and 2pi.
|
| We know the correct equation is c + v(cos(2pi.t/T), where v is the radial
| velocity. That means it already includes cos(pitch)

*I* know that v is your sqrt(vellx^2 + velly^2), see sheet 2 of
http://www.androcles01.pwp.blueyonde...lsonMethod.xls
because Wilson's Wobbly Worbits are Wedge-on and v does not
include cos(pitch).


Cos pitch is included in my velocity value. that should be obvious.

| If the orbit is inclined the light moves at
| c+v.cos(inclination).sin(t/P mod 2pi), again for a circular orbit.
| If a starting point is defined for periapsis (not relevant for circular
| orbits,
| but needed for elliptical orbits) then the equation becomes
| c+v.cos(inclination).sin( [phi + t/P] mod 2pi), where phi is the angle
| of periapsis to the line of sight. For elliptical orbits the sin function
| cannot be used except as an approximation.
|
| Of course...

Ok, so v isn't the radial velocity, it is the orbital velocity composed
of vellx and velly, and P is the period, not T.


The usual convention for period in for instance, the traveling wave equation is
the agreek letter Tor, which is replaced by T in ascii.

I'm not saying you are wrong, I'm saying we need to be consistent
and clear. When writing a paper or a program, the first thing is to
list definitions so that we all know what they mean.
Radial velocity = c+v.cos(psi).sin([phi + t/P] mod 2pi).
psi = 0 for edge on. psi and phi are constants.


I have explained how all orbit configurations can be accomodated by using edge
on ones. I also expect my readers to be able to understand what my (few)
equations imply.