After reading the following question, I know that there are not that many solutions to the 3-body problem, and I know that a ternary system is unstable. The 3 stars all orbit each other in a rotating equilateral triangle shape, which is an unstable formation due to perturbations.

Doing research elsewhere, I've discovered that one of the following things will occur in such a system:

• Two of the stars will orbit each other, and the third star will orbit around both of them. The result is a binary star system and a singular star that are orbiting each other, like this stable ternary star system.
• A collision will occur between two of the stars.
• The third star will be ejected from the system.

For my story, I will need to know the amount of time that a ternary system as described in the linked question can stay in place before being disrupted by perturbations and becoming stable in one of the ways described above.

The amount of time is highly variant. We can't answer this question without specifics. Voting to close as too broad. -Average comment that makes me sad

Okay, fair point. Therefore for this question I will place the following constraints:

1. The system must become stable by ejecting one of the stars. (no collisions, and no pairs becoming binary without ejecting a star)
2. After ejecting the third star, the remaining two stars must become a binary system (rather than all 3 stars flying away from each other forever)
3. The unstable system (before ejecting the star) must be able to continue for several hundred years
4. The three stars are all Sun-like in mass, volume, and spectral class. (can be changed as needed)

The purpose of this is because in my story, there were astronomical observations of an unstable ternary star system and I'd like to know how long I can have the observations have been ongoing, historically.

Hopefully, I can have the people of my world observe the system for at least several hundred years (if not longer) before observing a star being suddenly ejected from the system.

Can a system like this last several hundred years before a star is ejected from the system?

I don't know the orbital distances that would be necessary between stars in order for the instability to last several hundred years, so if someone could help me calculate that, that'd be great.

If such a system would eject a star much more quickly than that, please help me correct my model. I simply need a ternary system that lasts several hundred years before ejecting a star and becoming stable as a binary system.

NOTE: For this question, 'years' refers to Earth years.

_{Please help me adjust the question title to reflect the content, if necessary. I was struggling to find a good way to summarize what I'm asking for.}

posted about 5 years ago

overlord - Reinstate Monica‭

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