How Do You Calculate the Center of Mass in a Three-Body Celestial System?

[Ertosthnes]

Homework Statement

A space system consists of two visible stars, one is a blue giant with a mass of 11M and the other is a red dwarf with a mass of 0.5M. The system also has a black hole with a mass of 2M but we don't know where it is located. The blue giant is 700 gigameters away from you along the x-axis and the red dwarf is 825 gigameters away from you 14 degrees below the x axis. The blue giant is moving in the +y direction and the dwarf moves 45 degrees clockwise of the +y direction.

We're looking for the system's center of mass, and the location of the black hole.

We also assume the following about the system:
1) Orbits are approximately circular about the system's center of mass
2) All lie in the same plane
3) All orbit in the same direction (e.g., clockwise or counterclockwise)

Homework Equations

The relevant equations are uses of algebra, trigonometry, and the center of mass equation, as far as I can tell.

The Attempt at a Solution

So far I've mapped out the locations of the two planets; the blue giant's coordinates are (700, 0) and the red dwarf's coordinates are (800,-200). I have no idea how to continue.

 

[D H]

Given that the stars have circular orbits about the system center of mass, what is the angle between the vector from the center of mass to a star and the star's velocity vector? What does this mean in terms of the inner product between vector from the center of mass to a star and star's velocity vector?