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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,

    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 [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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