Is it possible to have a trinary star system with a planet that orbits their barycenter? I am trying to model a 3-star system with a planet. The three stars have the same mass. I have gotten the stars (Yellow, Pink, Blue) into a stable orbit. However, I am wondering if a &quot;free-floating&quot; planet can exist in this system. By &quot;free-floating,&quot; I mean a planet that does not orbit any star; it orbits the barycenter.
Currently, I only know of metastable orbits that work for a while, but then the planet crashes into a star or gets ejected. Here are my setups:


Is there such a system that satisfies these conditions? If yes, is there a real-life example that astronomers know of?

There are 3 stars of the same mass.
There is a planet that orbits the barycenter of these three masses.
The planet is orbiting in a &quot;Hot Jupiter&quot; setup (the planet orbits close to the barycenter)
This configuration should be possible if the planet is located sufficiently far from the barycentre (i.e. sufficiently far outside the outermost orbit of the triple): close-in orbits will end up being destabilised.
So far there are no confirmed exoplanets orbiting the common barycentre of three (or more) stars: while planets are known in triple star systems, they are usually found orbiting just one of the stars. There might be a triple star containing a circumbinary planet but can't find it right now (there's definitely a quadruple with a circumbinary planet though).
If you're willing to consider candidate planets, and to relax your requirement that the stars have the same masses and that the planet is as close to the barycentre as possible, Phuong et al. (2020) suggest the presence of a protoplanet located outside the dust ring of the system GG Tauri A, at a separation of ~290 au. GG Tauri A is a T Tauri triple system, comprising the primary GG Tau Aa (~0.6 solar masses) separated at ~35 au from a close (~4.5 au) binary GG Tau Ab1/Ab2 (~0.38 and ~0.3 solar masses).
The configuration is as follows (apologies to users of assistive technology):
            ┌ GG Tau Aa (~0.6 Msun)
            │
      ┌35 au┤
      │     │      ┌ GG Tau Ab1 (~0.38 Msun)
      │     └4.5 au┤
      │            └ GG Tau Ab2 (~0.3 Msun)
290 au┤
      │
      │
      │
      └ GG Tau Ac (candidate protoplanet)

Masses for Aa, Ab1 and Ab2 from Di Folco et al. (2014)
The protoplanet is inferred from spiral structure observed in the disc. The paper suggests that other spiral structures may be induced by additional protoplanets (GG Tau Ad and Ae) located even further out. As mentioned before, these protoplanets are not currently considered confirmed.
GG Tauri A is itself a member of a quintuple system, the binary GG Tauri B is located at a projected separation of ~1500 au from GG Tau A. GG Tau Ba is a ~0.12 solar mass star, while GG Tau Bb is a ~46 Jupiter mass brown dwarf (White et al. 1999).