"This means that the system in question could have planets with small orbits (like the earth's for example) orbiting that system's centre of mass despite the stars being many AUs away from it. It may be unlikely but it's certainly possible, right?"

No, this does not mean that at all! An orbit asks for a centripetal force. In heliocentric systems this force is the gravity of the star (considering the gravity of the orbiting body to be negligible). Here, pairs of stars are kept into orbits and for each star the force that keeps it around is not only the force of gravity of the other star, but also that of its own (since it's not negligible any more). A third body can not have a stable motion around the "centre of mass" between those stars because there does not exist any force to keep it there. Any body between the orbiting stars will be under forces that will pull it towards the stars. It may at most stay "stable" in the middle, where the gravity forces of the around-orbiting stars cancel each other.

..and if there were inhabitants, they'd be suffering unpredictable chaotic seasonality like the aliens in https://en.wikipedia.org/wiki/The_Three-Body_Problem

Could a planet maintain an atmosphere for any length of time under such variable attraction?

Dammit, I knew it sounded way too cool to be possible :(

Thanks!

Orbiting around the center of gravity only can be applied for two body systems. For many body systems it can be applied too as a careful approximation (like in the article). The movement of a small planet in the middle couldn't be described by this however, since it's an approximate three body system now (the two pairs and the planet)-

There could be stable point's in the middle, I don't know about that. Most certainly it can't be described by this approximation.

Looking into it, couldn't a planet orbit one of the two stable Lagrange points between the two groups, L4 and L5? That wouldn't be "inside" the orbit though :(

Yeah, I would think that the quasi stable orbits would be L4, L5 or orbiting around any of the pairs. If you have a symmetric situation isn't the middle point exactly L1? That would be unstable.

Edit: From Wikipedia:

>The triangular points (L4 and L5) are stable equilibria, provided that the ratio of M1/M2 is greater than 24.96.

So with a symmetric situation, where M1/M2=1 they wouldn't be stable either.

Depends on the details of the system, but in general it is highly unlikely. Usually already a binary star system does not really have nice orbits, since a too close encounter between a planet and a star basically acts like a fly-by-maneuver, so that it transfers energy to the planet and potentially kicks it out of the system.

A example for a triple star system would be Alpha Centauri and Proxima Centauri, the closest star system to the Solar System. Alpha Centauri is a double star and Proxima Centauri orbits it at a huge distance, such that the seperation between the components of Alpha Centauri is no longer important for the orbit.

So it is certainly possible to find stable orbits, even in a very unusual star system like this one. But they are ( except in very rare cases), just elliptical orbits at huge distances.

I wonder is there can be a small planet at the gravitational centre of this system, of if it's be ripped apart by the stars on each side.