Find radial velocity of star from orbiting body

[luma]

How do I get radial velocity of a star given a single body orbiting it in a 2-body system?

I have the mass of both objects and for the second object it's eccentricity. Assume everything else is default or zero like the mean eccentricity.

I compute the barycenter between the star and smaller star/planet by,

$$R = \frac{m_1 p_1}{M} + \frac{m_2 p_2}{M}$$

where M = m_1 + m_2 and p = position of body

But we don't know the orbit of the first body so how can I find this?

Let's say I have the orbit for the combined masses and then find the orbit for the star.

r(theta) = r(0) * (1 + e) / (1 + e cos theta)

I can then find the radial velocity over time by stepping through that equation in time by,

http://en.wikipedia.org/wiki/Keplers_laws#Position_as_a_function_of_time

And find it's offset from the origin, and compare small changes in position over time to numerically differentiate and hence find the velocity and then take the y component to find radial velocity...

Or could I use $$\frac{d (1/2 r^2 \theta)}{dt} = 0$$ somehow?

That's it, just a bunch of disconnected thoughts and no connected method. Help me out, would love to solve this :p

 

[luma]

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[luma]

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