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Related questions have been raised before Is our central black hole actually at the CG of the galaxy? Orbiting supermassive black hole or galactic center of mass? , where explanations have been given that the black hole should be at the center of mass. These explanations implicitly lie within the framework of widely accepted theories and models, considering only the interaction of matter within the visible three dimensions of space. However, there are hypotheses of gravitational interaction with parallel universes attempting to explain dark matter (for example [1] [2] [3]). In this case, the placement of the supermassive black hole nearly at the galactic center of mass is not obvious.

With what precision do existing measurements of star orbits in the galaxy allow us to calculate the position of the galactic center of mass? Are there measurements of the black hole's proper motion (I'm not sure relative to what, especially considering that the Sun itself moves within the galaxy), somewhat similar to measuring the proper motion of other stars?

The galaxy is written in the singular form, assuming that sufficiently accurate measurements could only have been made for the Milky Way. But the question is not limited to our galaxy.

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    $\begingroup$ We directly imaged the SagA* accretion disc a couple years ago using the Event Horizon array... and we've measured the movements of super-speed stars like S4716 that are (as far as we can tell) directly orbiting it and swing as close as 100 AU at periapsis. Is that the sort of thing you're looking for? $\endgroup$
    – Darth Pseudonym
    Commented Apr 24 at 12:28
  • $\begingroup$ No, that's not it. The question concerns the center of mass of the entire galaxy and the orbits of the central supermassive black hole relative to the center. $\endgroup$
    – Imyaf
    Commented Apr 24 at 17:36
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    $\begingroup$ We cannot determine where the precise centre of mass of the Galaxy is. That would require detailed knowledge of the exact position and size of every mass. Why is this question not duplicating the first question you link to? $\endgroup$
    – ProfRob
    Commented Apr 24 at 20:09
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    $\begingroup$ It's hard to see a significant sector of the Milky Way opposite our position relative to the core. See upload.wikimedia.org/wikipedia/commons/4/40/… from en.wikipedia.org/wiki/Milky_Way $\endgroup$
    – PM 2Ring
    Commented Apr 25 at 7:44
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    $\begingroup$ Thinking about the galactic center of mass is really misleading. Not only can we not measure it, there is not even a unique way to define it, since there is not a unique criterion for whether a particle belongs to the galaxy. Anyway, if you define the galaxy to include its halo, the galactic disk is not even at the center of the halo, so there's no reason to expect the central black hole to be near the overall center of mass. $\endgroup$
    – Sten
    Commented Apr 25 at 7:44

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