- #1
luma
- 32
- 0
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
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