Common examples of binary systems are binary stars, binary black holes, binary galaxies, binary planets and binary asteroids.
The first three binary systems are classified based on brightness, orbit and observation.
Classification based on brightness:
the two objects are classified as primary and secondary objects respectively. Here, the brighter object is the primary object and the other object is the secondary object.
Astrometric binaries, a fourth class of binaries, are formed when the secondary object is invisible. Only one object is visible because the secondary object is either hidden or not bright enough. The secondary object cannot be identified and the primary object seems to move around nothing.
Classification based on orbit:
the binary system is classified into close binaries and wide binaries. In close binaries, the two objects are close to each other, such that mass is transferred from one object to another. In wide binaries, although the two objects orbit the same centre of mass, they are separate and independent of each other.
Classification based on observation:
the binary system is classified into visual and eclipsing binaries. Visual binaries are made up of two stars that can be viewed separately through the aid of a telescope or binoculars. Eclipsing binaries, when viewed from the earth, the two objects are at an angle such that they form an eclipse when one passes in front of the other.