The Masses of the Sun and Stars

The most reliable way in which to determine the masses of celestial objects is to study objects which are in binary systems. For example, the masses of the stars in the Algol system can be determined by studying the motion of the stars about each other; the stars do not fall together because of their orbital motion. The gravitational pull of Algol is counteracted by the centrifugal force generated by the orbital motion of its companion. The stronger the pull of gravity, the faster the stars must move in order to keep from falling together. Since the pull of gravity depends upon the mass of the stars and how far apart they are, we can use the orbital speeds of the stars to infer their masses. Formally, we use Newton's formulation of Kepler's Third Law of Planetary Motion, i.e.,

where P is the orbital period of the planet, pi = 3.14, a is the semi-major axis of the planet's orbit and G is the gravitational constant. (The value for G depends upon the unit system one chooses.) When applied to the Solar System, we find that the mass of the Sun is

This method is also used to determine the masses of nearby binary stars.