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Theoretical Radial Velocity Curves

  1. Nov 5, 2006 #1
    Okay... so here's the problem I'm working on. Suppose you're observing a celestial body in space that is following a (relatively small) elliptical orbit around a larger distant celestial body (let's say it's at a distance d such that d>>a, where a is the semi-major axis of the orbit). For simplicity let's treat both the earth and the larger celestial body as fixed, so the only moving object is the smaller body.

    I would like to find a way of expressing the radial velocity (i.e. the component of the object's velocity that lies along the line of sight from the earth) as a function of time, expressed in terms of the angle of inclination i, the semi-major axis a (or perhaps a sin i as one parameter), the eccentricity e, the period P, the longitude of the ascending node capital omega, and the argument of the perihelion lower-case omega.

    I am relatively familiar with all of the equations relating each of the parameters to each other, and I can even calculate for a specific time t what you would expect the radial velocity to be (with given initial conditions), but if it's possible I would like some kind of an equation for it (again, "it" being the radial velocity) even if it contains inverse trig functions, so that I can plot my own radial velocity curves to look at, without a large amount (or rather, any amount) of programming knowledge. In other words, I'd like to be able to do it with Mathmematica, if possible.

    I don't expect anyone to hand me an equation or anything, but any information, insight, references, etc. relating to this matter would help.

    I've been reading some literature on binary star systems, which seems to include some of this kind of stuff. It's been helpful, and I've seen a number of places where people have plotted these kinds of curves, but they don't do the greatest job of explaining how it was done...

    Thanks to anyone who has read this far!
  2. jcsd
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