How Can Doppler Shifts Resolve Binary Star Orbital Inclination Ambiguity?

[joriarty]

This question has been bugging me... I've rephrased the question a bit so it shouldn't require much astrophysics knowledge to understand, just a bit of regular physics.

Consider a binary star system. By doing some geometry based on visual observations of the positions of the two stars over time, we can figure out the inclination of the orbit of the secondary star around the primary. However we can't tell from micrometer eyepiece measurements alone whether this orbit is tilted towards or away from us. How do you think this ambiguity could be resolved?

I'm thinking we could analyse the redshifts and blueshifts of the secondary star. I am imagining a system in the sky where the secondary star orbits clockwise around the primary and the top of this elliptical orbit as we observe it is tilted away from us, but I can't think how the measured redshifts or blueshifts would change if the orbit was tilted the other way. Perhaps I am on the wrong track...

Thoughts?

Thanks

 

[zhermes]

It depends on how much information you have available. If the binary system is so close that you can't resolve the two stars (e.g. you can only see one 'spot' of light, and you are 'seeing' the orbit via other measurments) then there is no way to tell.

If you can resolve the stars, you could do exactly as you say: measure the Doppler shifts. If the star moving downwards (relative to your view) is also blue-shifted, then the closer star is lower (i.e. the orbital plane is inclined relative to your line of sight), if the star moving downwards is redshifted, then the closer star is higher (i.e. the orbital plane is declined [negative inclined] relative to your line of sight).