"Henry Wilson DSc" Hw@.. wrote in message
...
| On Fri, 11 Mar 2011 02:37:54 -0000, "Androcles"
| wrote:
|
| .
| "Henry Wilson DSc" Hw@.. wrote in message
| .. .
| | They are ordinary stars that have a large orbiting planet.
| | Their light moves at c+vsin(t/T)
|
| 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.


| 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).


|
| 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.

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.



|
| | towards Earth, causing the photon stream to
| | spatially bunch up and separate as it travels. This gives the
impression
| of a
| | periodic brightness variation when it reaches an Earth observer.
| |
| | For a complete discription of the process see:
| |
| The word you seek is "description".
|
|