Most stars in the Galaxy are members of binary pairs, or double stars. And they are not necessarily just doubles; triples, quadruples, and higher order multiple stars are also common. It appears to be a natural result of the process of star formation that stars often condense from their primordial nebulosities as gravitationally connected groups.

These stars circle in elliptical orbits around a common center of gravity, in the same plane, located at one of the foci of each ellipse, that is, the two ellipses share one focus. A mathematical property of an ellipse is that it is defined by two points contained within the ellipse, and residing on the line defining the ellipse’s major axis. For the most part, when a small body orbits a more massive one, we tend to say the lighter orbits the heavier, but in truth they share a common center of mass, always located proportionally closer to the more massive one. For example, the earth is much more massive than the moon, and the center of mass of the earth-moon system is actually inside the earth (although not at earth’s geometrical center). The distance between each body’s center of mass and the binary’s center of mass is inversely proportional to the masses of the two bodies.

There appears to be little or no correlation between the masses of the individual components of binary stars. Very often very massive stars have very lightweight companions. Also, the variation in separation between members of different binary pairs can be vast. Some are so close they are in actual physical contact. Others are so far apart it is not even obvious they are binaries, only a shared proper motion and similar parallax allows us to infer their connection to one another. Due to Newton’s laws, the orbital periods of binaries are a function of their masses and separations, so the periods can vary between hours and centuries, and their true separations between zero and hundreds, even thousands of Astronomical Units. Because of Newton, the orbital dynamics of binaries are well understood; this is important because it gives us the only direct way of calculating their individual stellar masses once the orbital elements are determined precisely. This is how we weigh the stars.

Because they form at the same time from the same nebula, members of a binary pair are identical in initial chemical composition and age, but because they may be of highly varied mass, they may have evolved very differently. Their size, brightness, temperature, color and other physical properties may be totally different.

Binaries are very common, so it must be relatively easy for them to form. Multiple stars, however, exhibit a hierarchical taxonomy. A binary pair is dynamically very stable, but higher order combinations are not. They only form under specific circumstances which yield dynamically stable configurations. For example, a binary star may have several other stars orbiting it, the way our sun has multiple planets, or planets have multiple satellites. But you will never see more than two stars orbiting each other. This combination is allowed by Newtonian dynamics, but is highly unstable and even the slightest perturbation will disrupt it.

Normally each binary pair forms a gravitational center of mass, and a third star, (or even another pair) may orbit at a great distance from that. Alpha Centauri is a triple star, the A and B components separated by 4.87 seconds of arc, at a Position Angle of 266 degrees (2013). Next year, the separation will be 4.42″, PA 276. (Remember, these are a pair orbiting a common center of mass with a period of 80 years). The C component, Proxima, is the closest known star to the sun, and lies about 2.2 degrees (four full moons) from A and B. Many binary stars are situated so that you can actually watch the members dance about each other through a small telescope–provided you wait a sufficiently long time between observations. If the orbital period is short (the components are very close together), or the star too far away, the stars appear too close together to resolve telescopically into their individual components. But for some stars the geometry works in our favor and we can actually see motion over a human lifetime.

There are a variety of different types of binary systems, defined by both their physical nature and by how they manifest themselves observationally. I’ll go through the list here because these are terms that often turn up in the astronomical literature.

Visual binary – An accidental juxtaposition of two stars that appear close together in the sky, but are not gravitationally connected. They may be at vastly different distances from us, but they lie along the same line of sight.

Eclipsing binary – A double star whose orbital plane is so oriented that one passes in front of the other as seen from our position in space. Timing the light variation allows us to determine the size and shape of at least one, perhaps both, of the stars (depending on the shape and orientation of the orbits to our line of sight). This technique is also used to search for extrasolar planets.

Interacting binary – A binary pair so close the stars are capable of physically affecting each other, either by tidal distortions, or surface heating of one star by the other.

Contact binary – An interacting pair in actual physical contact, sharing a common envelope, experiencing gravitational transfer of material from one to the other, or even merging together into one object. One type of supernova occurs when matter transferred from one star causes the other to exceed the Chandrasekhar Limit, causing it to become unstable and explode. The Limit is several solar masses. Stars heavier than that will not go quietly when their time comes.

Spectroscopic binary – a pair which cannot be optically resolved into two components, but which shows the superimposed spectra of two separate stars. If the orbital plane is close to our line of sight, we may even be able to detect the Doppler separation of individual spectral lines as one star approaches us and the other recedes.

Astrometric binary – A star orbiting an unseen companion (it may be too faint to detect) will sometimes display a sinusoidal shift of position, that is, its proper motion vector will be a wavy line. This technique is also used to search for extrasolar planets.