There is no single "period" for a binary star system. The period of a binary star system is the time it takes for the two stars to complete one orbit around their common center of mass. This period can vary greatly depending on:

* The masses of the stars: More massive stars exert a stronger gravitational pull, resulting in faster orbital speeds and shorter periods.

* The distance between the stars: Closer stars orbit each other faster and have shorter periods.

Examples:

* Sirius A and Sirius B: This famous binary system has a period of about 50 years.

* Alpha Centauri A and Alpha Centauri B: This system has a period of about 80 years.

* Cygnus X-1: This system, containing a black hole and a blue supergiant, has a period of only 5.6 days.

Therefore, to know the period of a specific binary star system, you need to know the masses of the stars and the distance between them. Astronomers use observations of the stars' motions to determine their orbits and calculate the period.