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Find radial velocity of star from orbiting body

  1. Jun 29, 2010 #1
    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,

    [tex]R = \frac{m_1 p_1}{M} + \frac{m_2 p_2}{M} [/tex]

    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,


    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 [tex]\frac{d (1/2 r^2 \theta)}{dt} = 0[/tex] somehow?

    That's it, just a bunch of disconnected thoughts and no connected method. Help me out, would love to solve this :p
  2. jcsd
  3. Jun 30, 2010 #2
    dun dun
  4. Jul 5, 2010 #3
    dun dun
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