# For how many bodies can there be a stable orbit with no very heavy central body?

The question is a bit vague, but let me explain:

Take for example 2 bodies of the same mass. They can orbit around their centre of mass/gravity. Is something like this possible with multiple bodies of varying mass and distance from the centre of gravity without a relatively extremely massive body there? i.e. would it be possible to have a planetary system that orbited around the centre of mass without there being a massive star (roughly) in the middle?

I know that the Sun also has an orbit around the centre of gravity of the solar system, but that orbit is very small compared to its size, which puts it roughly in the centre.

• Klemperer rosette. But stability is suspect, and creating one is not natural (the configuration would have to be designed). – David Hammen May 23 '15 at 17:02
• Stability would need a mathematical proof, which we can already do for the 3-body-problem only in special cases. For arbitrary N-body that's impossible. – AtmosphericPrisonEscape Jun 10 '15 at 17:26
• I think Ed Shaya's answer is pretty much spot on. For 3 objects near each other and all a similar size, you get an unstable orbit, but for 2 objects near each other and a 3rd one distant but still in the same system. That's the simplest 3 body system of 3 similar masses and that would be stable for a long time - the distant object orbits the 2 as if they are just 1 object. Now if the 2 inner bodies become tidally locked you might get gradual instability cause the outer object would then steal energy from them. Not tidally locked, there could be more balance and it's stable longer. – userLTK Jun 11 '15 at 5:03

It is not unusual to have pairs of pairs or even more complex stellar systems. Two stars make a stable pair. A pair of these make a stable system and a pair of these would also make a stable system. It is, however, necessary for stability for each pair to be separated by roughly 10 or more times the separation of the previous level. This could continue ad infinitum were it not for the tidal field of neighboring systems or the Galactic potential limiting the overall size.

• I like your answer, but shouldn't that be pairs of pairs (4 stars). I think the most number of stars in a system so far discovered is 7. - en.wikipedia.org/wiki/Star_system and granted, 7 stars doesn't mean 7 similarly sized stars, going back to the original question. – userLTK Jun 11 '15 at 4:57
• @userLTK: OK. I rephrased pairs of pairs etc. – eshaya Jun 15 '15 at 19:19

Two star systems: http://en.wikipedia.org/wiki/Circumbinary_planet - not exactly what you asked, but I think it's as close as real systems will get.

The example you give, 2 planets orbiting each other is easy, two objects will tend to orbit each other but when you have 3 objects, it gets a bit more complicated, unless the 3rd one is distant and orbits the two from a distance. 3 body orbits tend to be unstable unless you have them kind of locked in (sun/earth/moon) with the moon around the earth and the earht-moon around the sun, or in synch (Sun/Neptune/Pluto) - where Pluto and Neptune are in orbital resonance. Neither of those would be stable if the sun wasn't so dominant.

There are exotic mathematical models for 3 object orbits but they are improbable in the actual universe cause they aren't very stable. http://www.ams.org/samplings/feature-column/fcarc-orbits1 and https://www.sciencenews.org/article/strange-orbits-1

At least a few hundred billion bodies can be in a stable orbit without the majority of the system mass at the center. Our own Milky Way Galaxy is in a stable orbit with hundreds of billions of bodies. The black hole at the center of our galaxy, Sagittarious A*, is estimated to have a mass of only $$2.6 \times 10^6 M_\odot$$, while the entire Milky Way has a mass of about $$1.5 \times 10^{12} M_\odot$$. So, while the mass of the black hole is substantial, it isn't a substantial part of the overall mass of our galaxy.

In fact, the spiral structure of the Milky Way is driven more by gravitational interactions between the stars, rather than interactions with the black hole center.

From Baba et al.:

The spiral arms of disk galaxies are the most prominent structures, and the arms are formed due to gravitationally driven variations in the surface density in the stellar disk

Michikoshi and Kokubo 2020 perform N-Body simulations of galactic spiral arms with N = 4000 stars.