Binaries do not orbit each other, each orbits their CENTER OF MASS. Binary stars are always found opposite each other from the CENTER OF MASS point in space with the highest mass star nearest this point. The low mass star (shown as M₁) will have to travel a very large diameter path, a₁, moving quickly. The high mass star (shown as M₂) travels a very small diameter path, a₂, and does so slowly.

Different Kinds of Binaries

Visual Binaries
Some binary systems are sufficiently close to Earth and the stars are well enough separated that we can see the two stars individually in a telescope and track their motion over a period of time.

Spectroscopic Binaries (both single- and double-lined)
What appears to be a single star on the sky is actually two when seen spectroscopically and perhaps as witnessed by a varying (Doppler) shift in the lines from the binary motion. If the second star is very dim, one may only see one set of lines, but their periodic shifting indicates an unseen companion.

Eclipsing Binaries
Here the binary system is orientated such that they pass in front of each other as seen from Earth. The total light coming from the system will appear to 'dip' (this is called the light curve) as the stars block each other during eclipse.

Orbiting Binary Stars and Eclipsing Binary Stars Activity