Close Binary Stars
Close Binary Castor BaBb
Image from Steve Bowers
Close Binary pair Castor Ba and Bb

Generally, a binary pair close enough that they can have a planetary system orbiting both stars as if they were a single star. The closest stable orbit for a planet orbiting such a pair is approximately 3 x the separation of the stars.
P and S type orbits
Image from Wiki Commons - Copyright Phillip D Hall
Planets in P-Type orbits orbit both stars in a binary system, while planets in S-Type orbits orbit only one star of the pair. The separation and eccentricities of the stars have a significant effect on the stability of planetary orbits in systems like this.
From the perspective of a planet orbiting a close binary, the two suns appear very close in the sky, usually as a single shining glare in the sky during the day, usually with a noticeable elongation and maybe even two disks if observed briefly. During sunset both stars will be separated more easily, especially when one of them sets before the other. If there is any colour difference then their mutual light will be mixed, varying as they orbit each other. Shadows tend to be tinted by this. Tides can occasionally be quite remarkable.

When the stars and planet align, the tides get bigger; likely not much more than usual (the two stars are pulling roughly the same way all the time), but it might make the difference when combined with a moon from a strong tide to a very strong once-in-a-century tide. At certain times one star will eclipse the other, and when the two suns appear as a single one, the combined sunlight gets dimmer as a result, and cooler.

Double star system
The binary suns of Gillbank, capital of the Disarchy, as seen at maximum elongation when they are nearly thirty degrees apart in the sky. As they orbit each other the two suns come closer together until they briefly overlap and appear to be a single star
The life history of close binary systems is quite complicated; variations arise from the initial masses and separation of the components, and from the transfer of mass from one component to the other.

Contrast with contact binary.
Close Binary YY Gem
Image from Steve Bowers
YY Geminorum, a close binary pair of red dwarf stars (part of the Castor system)
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Development Notes
Text by Anders Sandberg - additional notes by Chris Clowes and Steve Bowers
Initially published on 31 December 2007.