We’ve done this already, sort of. We’ve calculated our Sun’s orbital period (the amount of time the Sun takes to fully rotate the supermassive black hole holding our galaxy together). We have calculations predicting this, as well as rough predictions for other nearby galaxies. Alas, never have we precisely measured the movement of several stars in all different regions and distances to get a firm figure of a galaxy’s spin.. not one that could 100% hold water. Never one so precise and thorough.
These calculations that were just released are of a galactic neighbor, the Large Magellanic Cloud. First, though, being I am writing from the northern hemisphere, I’ll give quick facts. The southern hemisphere has this dwarf galaxy, along with the smaller (duh) Small Magellanic Cloud all to themselves. The LMC (Lg Mag Cloud, SMC for smll Mag Cloud etc) will sometimes be visible, but only 5 or so degrees north of the equator. It appears similarly to what a distant, giant globular star cluster may look like. Over a large area, it shines at a magnitude 0.9 (the lower the better.. example being currently, Jupiter is a -2.5 and Venus, a -4.0. Most stars in the Big Dipper around between a +1 and +2). It appears dimmer than +0.9 because it is spread over a larger area. Like the Andromeda Galaxy which is spread over an area 6 times larger than the full Moon, when a visible magnitude is larger, it appears dimmer once closer to us.
However, this is a very naked eye visible treat, along with the SMC that follows it. It is the third closest satellite galaxy of the Milky Way. The LHC is the only visible one, other than the SMC. However, they have company. There are 14 confirmed satellite galaxies of the Milky Way, along with another 12 possible/probable others.
The reason doing these measurements is hard is, because even with some stars moving at hundreds of miles a second, the vast distances of ones, even nearby ones, makes it so in a human lifetime, they appear almost fixed to the same spot. So because dust and stars blocks a lot of the Milky Way from being seen, as well as our view of a lot of the cosmos outside of our own solar systems. So the target had to be near, and at 160k light years from Earth, it doesn’t get much closer than that in terms of visible galaxies. Andromeda, the nearest non-dwarf galaxy, is slightly larger than the Milky Way and it is still 2.3 million light years away. It will appear identical minus any new novas etc, in 100 years.
So it is found it takes the entire LMC the same amount of time as our galaxy to rotate, 250 million years. Quite coincidental being it is so much smaller. Most of the stars would need to go exponentially slower than our Sun and solar system orbits the Milky Way in the same amount time, except we go around 500,000mph.
“This precision is crucial, because the apparent stellar motions are so small because of the galaxy’s distance,” lead author Roeland van der Marel, of the Space Telescope Science Institute in Baltimore, said in a statement. “You can think of the LMC as a clock in the sky, on which the hands take 250 million years to make one revolution. We know the clock’s hands move, but even with Hubble we need to stare at them for several years to see any movement.”