Help with Doppler shift galaxy question

[failingTP]

Homework Statement

Hi, I'd really appreciate being pointed in the right direction with this past exam question, as I just have no idea how to approach it and can't find similar examples in my notes anywhere.
A nearby star has a spectrum similar to the sun, suggesting it has the same mass. The Doppler shift of lines in the stellar spectrum vary sinusoidally with a period of 10^6s and velocity amplitude of 90m/s

The question then asks for things like the mass of the 'invisible companion' to the star, and then lead onto finding the distance from one star to the other as they eclipse, etc.

What I'm really asking, is what information can I get using the period, velocity amplitude, and mass?

Any help appreciated!

Homework Equations

Can the Virial Theorem be used?
(1/2)I''=2U+Ω where I= Σmr^2, U is kinetic energy and Ω is potential energy.
v=(2pia)/P I could find the velocity of the galaxy if I knew the semi major axis, then maybe combine this with the doppler shift information given in the question?

The Attempt at a Solution

Some ideas above..

 

[Simon Bridge]

What I'm really asking, is what information can I get using the period, velocity amplitude, and mass?

The doppler shift tells you something about the speed of the star - the fact that the doppler shift is periodic tells you the star is orbiting something.
You may need to make some guesses about the orbit - but if you know the orbit-speed and you know the orbit period, then you should be able to figure out the likely mass of the primary. How would you normally do this?

What you don't want to do is try to guess the "right" equation to use.
Note: this is not a "doppler shift galaxy" question.

 

[Buzz Bloom]

Any help appreciated!

Hi @failingTP:

The following might be helpful:

https://en.wikipedia.org/wiki/Two-body_problem .​

Regards,
Buzz