Binary System in circular orbit: Separation distance between stars

[Thomas Smith]

Homework Statement

The binary system has a parallax of 0.07 arc seconds. This system consists of two identical stars in circular orbits.

An absorption line at a wavelength of 512nm is seen in the spectra of both stars. This line is split into two components by the orbital motion and has a maximum separation of 0.04nm, which occurs every 26 years.

What's the separation distance between both stars?

Relevant Equations

Distance to Star System from parallax d=1/p

Doppler Shift Δλ = λ - λ_0

Radical Velocity v_r=Δλ/λ_0 c

Distance is d=1/0.07 = 14.3 parsecs

The Doppler shift of one star is, Δλ = 512 - 512.04 = -0.04

So the radical of the velocity of the star is = (-0.04/512) x (3.00 x 10^5 km/s) = 23.4km/s which is the same for both stars because they have the same mass.
This is as far as I've got.

 

[jbriggs444]

From the information provided, can you determine the orbital period of the binary system?

 

[Thomas Smith]

From the information provided, can you determine the orbital period of the binary system?

Well considering the separation of 0.04nm every 26 years, I believe the full orbit period is 52 years.

 

[jbriggs444]

If you make an assumption about orientation, you have tangential velocity and period...

 

[Thomas Smith]

If you make an assumption about orientation, you have tangential velocity and period...

Ah sorry, i missed out the inclination. It says the orbital plane is inclined to the plane of the sky by 90 degrees

 

[jbriggs444]

Ah sorry, i missed out the inclination. It says the orbital plane is inclined to the plane of the sky by 90 degrees

That was the assumption I'd needed for the problem to make sense. So we are looking at the binary system, "edge on". Does that give you everything you need to finish the exercise?