Is our galaxy rotating about the supermassive black hole at its centre?

Whilst it is true we cannot (by definition) see a black hole at the centre of our galaxy, that doesn’t mean we cannot detect one. There are several lines of evidence that indicate strongly that this is the case.

(i) the motion of stars very close to our galactic centre (specifically S2, see here) shows there is something at the centre of S2’s orbit, of approx. 4 million solar masses that occupies considerably less volume than the orbit of Neptune whilst emitting no visible light itself. According to our current understanding that can only be a black hole.

(ii) other galaxies similar to our own show evidence of jets, radio emissions (radio waves are largely unaffected by the dust/gas that intervenes) and shock waves in surrounding gas/dust consistent with supermassive black holes.

Finally, a video of the data collected over 20+ years ...

The Milky Way galaxy is massive. It is estimated to have a mass of more than #6*10^11# solar masses.

There is strong evidence that there is a supermassive black hole near the centre of the galaxy known as Sagittarius A*. There are stars, such as S2, which are orbiting a small massive object. The orbital calculations show that these stars are orbiting a small body which is smaller than the orbit of Neptune but has a mass of over #4*10^6# solar masses.

Now any bodies in orbit such as in a planetary system, a solar system or a galaxy orbit the centre of mass of the system which is called a barycentre.

In the case of our solar system, the Sun, planets and everything else orbit the Solar System Barycentre (SSB) which is in constant motion and is often outside of the Sun's surface.

Likewise, the galactic barycentre will be in constant motion and won't be inside the supermassive black hole.

So, the galaxy orbits its barycentre, not its central supermassive black hole.