Do the stars of irregular galaxies (such as the Magellanic clouds) orbit a more precise point or are they just, I don't know, flying around? If they orbit, how stable would such orbits be, considering the overlapping of many different stellar orbits without any main ecliptic? This post doesn't mention irregular galaxies.
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Although the answer you link to doesn't mention irregulars, the answer applies to those as well: Star move around in the common gravitational potential created by everything in the galaxy, i.e. gas, stars, and, in particular, dark matter.
This potential has a center, but there isn't necessarily anything exactly at this center. The stars then move on elliptical orbits around the center, but are perturbed by local irregularities.
In spirals and elliptical, the potential is rather symmetric, whereas in irregulars it is quite… irregular. That means that, if you were to take two images of a galaxy, separated by a period of order the dynamical time scale ($t_\mathrm{dyn} \sim \sqrt{R^3/GM} \sim 100$ million years), a spiral and an elliptical would look more or less the same, while the irregular would probably have changed its shape notably.
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$\begingroup$ But dark matter isn't proven as yet, it's hypothetical. $\endgroup$– JohnNov 2, 2020 at 15:54
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1$\begingroup$ @John The existence or non-existence of dark matter doesn't change the conclusion, i.e. that stars move on more or less elliptical orbits around the center of mass, perturbed by local irregularities. That said, DM is not hypothetical in the sense that its existence is a hypothesis. In physics, we have a rather clear distinction between conjectures, hypotheses, and theories, and the existence of DM is most definitely a theory. That doesn't mean that it's "proven" (nothing ever is in physics), but it does mean that it's not just "something we conjure to explain results we don't understand". $\endgroup$– pelaNov 2, 2020 at 20:45
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1$\begingroup$ There are other theories than DM that can explain our observations, but as more and more evidence is found, most physicist tend to believe in DM, I'd say. The other theories (e.g. MOND, f(R) gravity, entropic gravity, and what have you) eventually begin to look somewhat like DM theories, I think. The reason most people believe in DM is that so many mutually independent observations can be explained by this. See this answer for a description :) $\endgroup$– pelaNov 2, 2020 at 20:51
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$\begingroup$ Thank you. Yeah I was just stating that DM is not proven but I also think something like that exists. $\endgroup$– JohnNov 2, 2020 at 20:58
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