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I'm curious, are there any known STABLE triple systems in which a close inner binary pair is orbited by a more massive star, yet the total mass of the binary pair is greater than that single orbiting large star?

Something relatively compact, like this:

  • Close Inner Binary: Star A with mass of 1, Star B with mass of 0.8. Combined Mass: 1.8
  • Outer Star Orbiting Binary: Star C with mass of 1.2.
  • Inner Binary Orbital Period: months or a couple years.
  • Outer Star Orbital Period (orbiting binary): Decades to maybe a century or two.

Star A and B are both smaller than Star C, with the combined mass of A and B exceeding Star C. Star C orbits the barycenter of the close binary A+B.

I'm only aware of triple star systems in which the largest star is closest to the combined barycenter of the system. I don't know of any examples in which the largest star is also the star furthest from the system barycenter. Does this arrangement exist?

Thanks!

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Short Answer: Star sytem HD 188753 seems to be an example of the type of star system asked for.

Long Answer:

Part One of Two: The orbital characteristics.

In any multiple star system, all of the stars will orbit the combined barycenter of the system. Any pairs will orbit around the barycenter of the pair, and the barycenter of each pair will orbit around the barycenter of the whole system.

If there is a close pair of stars plus a third more distant star in the system, the close pair will act like a single star with their combined mass. If their combined mass is less than that of the single star, their barycenter will orbit farther from the barycenter of the system as a whole than the single star will. If their combined mass is greater than that of the single star, their barycenter will orbit closer to the barycenter of the system as a whole than the single star will orbit.

According to the formula found at: https://en.wikipedia.org/wiki/Barycenter[1] the barycenter of the pair of stars will be at a point closer to the more massive star than to the less massive star. It will be 0.444444 of the distance between the two stars, while the less massive star will orbit the barycenter at a distance of 0.55555 of the total distance between the two stars.

the more massive star should orbit at a distance at least a few times as large as the distance between the stars in the pair. Assume that if the distance between the two stars in the pair is 1, the distance to the more massive star is 5 or 5,000 as examples.

According to my calculations, if the third star orbits at a distance of 5, the distance between the barycenter of the pair and the the barycenter of the system as a whole should be 2 times the distance between the two stars in the pair. The third star will orbit the system barycenter at distance of 3.

According to my calculations, if the third star orbits at a distance of 5,000, the distance between the barycent of the pair and the the barycenter of the system as a whole should be 2,000 times the distance between the two stars in the pair. The third star will orbit the system barycenter at distance of 3,000 times the distance between the two stars in the pair.

So in star systems with a a pair of stars whith a total mass greater than that of the single star, the more massive pair of stars will orbit closer to the barycenter of the system tha tthe single star will, even if it is more massive than any one star in the pair.

So the question is are there any known trinary star systems with a pair of stars and asingle stars whose mass mass is slightly less than that of the pair, though slightly more than any one star of the pair.

I'm sure there are many trinary star systems where the single star is more massive than the pair of stars let alone one of hte stars in the pair.

I'm sure there are many trinary star systems where one or both stars in the pair, and thus the pair as a whole, are more massive than the third star.

The problem is finding a system with three stars of very similar masses.

Part Two of Two: An Example.

Using the list of trinary stars at: https://en.wikipedia.org/wiki/Star_system[2]

I found that one of the six trinary stars listed has a pair slightly more massive than the single star.

HD 188753 is a trinary system with a main star HD 188753 A with a mass of 1.06 plus or minus 0.007 that of the Sun, and a pair of stars HD 188753 B & C. B has amass 0.96 plus or minus 0.05 that of the Sun, and C has a mass of 0.67 plus or minus 0.05 that of the Sun. So A should be a lot more massive than C, and slightly more massive that B, but the pairr B & C together should have about 1.53 the mass of A. Although in this case the uncertainty in the masses of A & B makes a lsigh psosibility that B could be slightly more massive than A.

In a 1999 version of a catalog of multiple stars, 551 out of 728 systems listed were trinary stars.

https://en.wikipedia.org/wiki/Star_system#Multiple_star_systems[3]

So presumably seraching multiple star catalogs should find other examples of star systems satisfying the requirements of the question.

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  • $\begingroup$ I’ve been “toying” with HD 188753 for a few days for something unrelated, and it so happens that I was wondering if BC revolve around A, or the other way around? It seems to me like BC revolve around A… Mind you, maybe I misunderstood something somewhere. Also, keep in mind that in binary star systems, A and B orbit each other, so there are TWO ellipses/orbits—for a trinary, that means THREE ellipses/orbits. $\endgroup$
    – Pierre Paquette
    Jan 26, 2021 at 23:29
  • $\begingroup$ Oh! it even says in the Wikipedia article you refer to that “B and C orbit each other every 156 days, and, as a group, orbit A every 25.7 years.” $\endgroup$
    – Pierre Paquette
    Jan 26, 2021 at 23:30

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