The Center of Mass for a Binary System

In a binary star system the two stars revolve around their common center of mass, as illustrated in the following figure.

This requires that Kepler's original laws for orbital motion (which apply to stars as well as planets) be modified. Only in the limit that one mass is much larger than the other does one recover Kepler's original picture in which the less massive object orbits the more massive one on an ellipse.

Recall that in terms of the diagram shown on the left, the center of mass between two objects is defined through the equations

m₁d₁ = m₂d₂

d₁ + d₂ = R

where R is the total separation between the centers of the two objects. This animation illustrates the center of mass. Here is a center of mass calculator that will help you to make and visualize calculations concerning the center of mass.