Binary Star Systems

Binary Star Systems
All the relations for Kepler's Law's assumed that the central star was massive compared to the orbiting object. In fact, any two objects will orbit about their common center of mass. Two body problems can be reduced to one object orbiting another provided:

1. We change to a frame of reference attached to the center of mass of one of the stars. Either one will work.

2. We replace this star's mass with the total mass of both stars.

3. We replace the mass of the orbiting body with the reduced mass of the system.

Note that when one of the star's masses becomes large relative to the other, the reduced mass m is approximately equal to the mass of the smaller body, and the total mass M is approximately equal to the mass of the larger object. The problem reverts to described in Kepler's law section.

Reduced Mass Frame:
* A body of mass m orbits a larger body of mass M.

Center of Mass Frame:
* Both stars orbit about their center-of-mass with the same eccentricity.

Each star has its own orbit with a different, but related semimajor axis.
The stars are always opposite each other about the center-of-mass. Both stars will reach peristron (closest approach) at same time.

Binary Star Orbits
The stable orbits of two stars about each other is displaced by specifying their masses, their initial separation, and the eccentricity of their orbits. The resulting action can also be observed from different frames of reference: star 1, star 2, center of mass, and a rocket moving at a constant speed. (IP 3.0 Simulation of Binary Star Orbits - The center of mass frame does work correctly in IP2.5)