What refined physical law governs the direct calculation of mass in binary star systems?

Newton's version of Kepler's Third Law

The most reliable method for determining stellar mass involves observing two stars orbiting a common center of mass within a binary system. This scenario transitions the complex problem into a direct application of classical mechanics, specifically Kepler's Third Law of Planetary Motion as refined by Isaac Newton. This formulation explicitly relates the square of the orbital period ($P^2$) to the cube of the semi-major axis ($a^3$) and the sum of the masses of the two bodies ($M_1 + M_2$). The equation mathematically codifies the gravitational interaction between the two objects, allowing astronomers to solve for the combined mass if the orbital period and separation distance can be accurately measured. This application of Newtonian mechanics forms the bedrock for calibrating all other, less direct, stellar mass measurements.