Final answer:
Using a modified version of Kepler's third law, which relates orbital period and separation, one can calculate the total mass of a binary star system. To obtain individual stellar masses, further data on the visible star and orbit orientation are required. Kepler's law aids in identifying not only binary stars but also black holes in such systems.
Step-by-step explanation:
When the period (P) and separation (semimajor axis, D) of a binary star system are known, it is possible to determine the system's total mass. This is achieved by using a modified version of Kepler's third law, which relates the period of orbit to the distance of the objects: D³ = (M₁ + M₂) P². The variables M₁ and M₂ represent the masses of the binary stars. By measuring the speed of the stars and utilizing the Doppler effect, astronomers can determine the period of the orbit. Coupling this information with the separation of the stars grants us the capability to calculate their combined masses.
Kepler's work initially described the motion of planets around the Sun, but it is similarly applied to binary star systems to determine their masses. However, to get individual masses of stars in the binary system, additional information is necessary about the visible star and the orientation of their orbit relative to Earth. Even when considering complexities such as neutron stars with accretion disks, astronomers can still find black holes within these systems by employing Kepler's third law.