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Note: I'm not talking about a star orbiting around a single or lonely planet :)

I know a star orbiting a planet is almost impossible because if a planet is more massive than a star, that "planet" would probably be a star. But how about if the planet is not lonely like:

  1. A multiple planetary system which consists of free floating planets only but the planets are so massive so that their total mass is larger than a star

  2. A planet itself is not more massive than a star but it has so many massive moons

Is it possible for a very small star to orbit around planets in such situations?

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There's theoretical ways to do it but it's so unlikely as to probably not exist. Assuming you want a system where the planets are in stable orbits around each other. The basic difficulty is the 3 body problem or n body problem. More on it here and here.

For example, a massive planet could (in theory) have a single super-massive moon of similar mass to the planet, though that would probably be considered a 2 planet system. It's not possible for one planet to have two super-massive moons because that wouldn't be stable. In general, planets are many times the mass of all their moons combined, similarly stars are many times the mass of all their planets combined and when that stops being true the system is no longer stable. It's very difficult to generate sufficient mass by adding moons to a system, or by adding enough planets to get more massive than the sun, unless the planets crash into each other but past a certain mass, they'd stop being planets and become a kind of star when enough planets combined.

If we look at gravitational systems, like our solar System, something like 99.7% of the mass is in the sun, so the sun dominates and everything orbits the sun. A few of the larger objects have moons, and curiously, but only cause they're in relatively calm orbits far away from other planets, a few asteroids orbit each other, but the system is very structured around the sun with much smaller stable orbital zones around the planets.

Pluto also has a rather curious orbital system of it's own, likely caused by an impact, where Pluto and Charon are comparatively large and 4 tiny moons orbit around them.

enter image description here

Source:

But these kind of structured systems are only possible if you have a significant mass differential. When you have 3 or more bodies of similar mass and similar distance you get a high degree of mathematical chaos and instability. There are creative mathematical tricks to make it work, but none of them are stable or likely.

This is what 3 similar mass bodies look like, and in such a system, with constant changes, the most likely scenario is that one of the bodies eventually gets ejected. (source, N-body problem above)

enter image description here

There are star systems with several stars, but they are either unstable or contain significant differences in mass. The gravitational structure applies for large planets the same as it does for stars, and there's an article about that here.

You can create stability by having 2 objects orbiting each other and a 3rd massive object quite distant. (Alpha Centauri is that kind of set-up though Proxima Centauri is quite a bit smaller, but it's the same system).

You can even create the heirarchy where you have 2 objects orbiting each other and then 2 more, orbiting each other, but distant so the 2 co-orbitals orbit around each other, and if you do this enough times, you can kind of create enough planetary mass where a more massive star could distantly orbit the entire thing, but it gets very structured and very distant. It's not what I'd consider a normal orbit.

You could also cheat and have several planets in a wildly unstable general proximity orbit and have a star some distance away orbiting the chaotic mess in the middle, but it wouldn't be stable for long.

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Don't forget that there are brown dwarfs between planets and stars in mass. The heaviest planets are around a dozen Jupiter masses, and the lightest stars are a little over 80 Jupiter masses (from the Wikipedia article on brown dwarfs). This means you would need some kind of system of seven super-Jupiters for one red dwarf to orbit around. As userLTK made clear in the accepted answer, there's really no plausible stable configuration where this works.

I can propose an implausible stable configuration, though. In an empty universe, or deep intergalactic space, two objects can be very far apart and still stably orbit each other. So, imagine two super-Jupiters orbiting their common center of gravity. Far away from them, a third super-Jupiter orbits the pair. More accurately, it orbits the common center of gravity of the 3-planet system.

Because the system is so isolated, we can, unless I am mistaken, repeat the process indefinitely. You can always move far enough from a cluster so that it is nearly a point from your perspective, and then orbit the center of gravity between you and that point. Using that process, you build a system with seven or more super-Jupiters and one red dwarf orbiting very far away.

If such a system existed, I would consider it evidence of intentional stellar engineering. Such a chain of perfect orbits is just too big a coincidence.

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