Absolute Orbits and Mass Ratios

Abstract

The relative orbit as discussed in the preceding sections adopts one component as the reference point for the motion of the other star. The determination of the actual motion of both stars with respect to their center of mass (center of gravity = c.g.) requires one or more external reference points which do not partake in the orbital motion. Let M _A , M _B be the component masses. f = M _B /(M _A +M _B ) is the fractional mass (often thought less precisely termed ‘mass ration’). If d = (x,y) is the vector of the relative position (A → B), the vectors with respect to c.g. are

$$c.g. \to A = - fd and c.g. \to B = (1 - f)d$$