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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:

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.

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    $\begingroup$ You asked for hard science. Can we take it that you are looking for a numerical result listing the 3 masses of the 3 stars, the 3 dimentional positions and velocities of these 3 stars such that a simulation would result in the formation of a stable binary after 200-900 years? If not what are you looking for? $\endgroup$ – Slarty Oct 16 at 22:18
  • $\begingroup$ Are there upper limits on the separation between any two stars in the system? If, for instance, I have two Sun-like stars orbiting each other at 1 AU, and a third orbiting the pair at 1000 AU, I'm reasonably certain that they'll all remain stable for much longer than several hundred years; from the point of view of the outermost star, the inner two are essentially a point mass 1000 AU away, rather than a distinct pair of stars. $\endgroup$ – HDE 226868 Oct 17 at 18:41
  • $\begingroup$ @Slarty Yes, that is precisely what I'm looking for. I want to know whether such a system is possible, but I need a way of confirming the system's validity. $\endgroup$ – overlord - Reinstate Monica Oct 17 at 19:27
  • $\begingroup$ @HDE226868 The 3 stars all orbit each other in a rotating equilateral triangle shape, which is an unstable formation. I want that formation to last several hundred years until one of the stars gets flung out into space. $\endgroup$ – overlord - Reinstate Monica Oct 17 at 19:30
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    $\begingroup$ you might find it interesting to test out a gravity simulator snadbox like this one:testtubegames.com/gravity.html $\endgroup$ – Slarty Oct 17 at 20:59
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There are known binary, ternary, and larger systems with orbital periods measured in centuries. For an example, note Mizar and Alcor, the naked-eye binary at the bend in the handle of the Big Dipper.

Each of the two naked eye stars is easily resolved, by a modest telescope (or large binoculars, in my experience) into another binary (one of which is in fact two binary pairs). It is not known conclusively that Mizar (group) and Alcor (pair) are bound to either other, but they appear to be no more than 1.5 light years apart, so it seems likely. The two binaries have periods of several years, so the orbit of the two pairs around each other, if bounds, is more than a century.

Systems of three or more stars orbiting each other are not that uncommon -- ternary systems are less common than binaries, but are far from rare.

The ones that are unstable are those with closer orbits, and we don't see them, because they don't exist long enough for us to see them. Generally, an unstable system will eject or merge one or more of the elements before star formation has completed. Exceptions are open clusters like the Hyades, where the separations are large fractions of a light year or greater, the periods of individual stars around the cluster center of mass are centuries or even longer, and it takes millions of years for the interactions to eject stars (and they do, thinning such clusters over time).

So, we don't ever see unstable ternaries, because they degenerate before the individual stars have collapsed enough to ignite. They won't form after stellar ignition, either, because there's not a high-cross-section mechanism to temporarily capture a new star into a binary -- such interactions will lead to a single-pass encounter that may or may not disrupt the binary, but any capture will be unstable enough that one or two orbits is all you'll get. If those orbits are on the order of a century, then a space traveler might see such a system -- but that means separations large enough that such a traveler would need astronomical instruments and long term observation (decades, at least) to even be sure any of the stars are gravitationally bound.

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Some triple star systems hierarchical systems: the stars in the system can be divided into two smaller groups, each of which traverses a larger orbit around the system's centre of mass. Hierarchical triple star systems are known and can be stable for long periods. Triple star systems that are not hierarchical (where the gravitational attractions of all three bodies are significant upon each other) are all unstable.

The hierarchical system classification is not absolute there will be intermediate instances where triple star systems are only semi stable with small destabilising gravitational attractions from all three bodies. For example a binary star system might encounter a lone star and capture it. Depending on the circumstances the orbit of the new star might be such that the star orbits a little too close with small disturbing gravitational effects every orbit. Eventually the orbit would degenerate and become chaotic leading to expulsion, collision or transformation into a much further orbit that would be stable. Ref https://en.wikipedia.org/wiki/Star_system https://www.aanda.org/articles/aa/pdf/2018/11/aa33097-18.pdf

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