I'm trying to find some data that I can use to derive dark matter (in a loosey-goosey sort of way, I won't be too rigorous). I'm helping a friend out with a final project for his astronomy course and I'm tasked with doing the maths. Any idea where I can find a table of various stars distance from the center of our galaxy and their speed (how fast they are going around the center of the galaxy)? This does not need to be comprehensive but would ideally contain several data sources from various representative radii. Also some sort of formatted text would be SUPER cool so I could just tell my computer to do the calculations!
It is very difficult to measure Galactic orbital speeds of stars in our galaxy for several reasons. We are moving with them and do not have a reliable measurement yet of even our own orbital motion. We only get one component of motion, the radial component (although Gaia is about to change that). Dust in the galactic plane prevents us from seeing very far in our own galaxy. So, when we measure Dark Matter in galaxies, it usually done in other galaxies where we can see both sides of the galaxy and, except for inclination angle, directly measure the orbital motion.
I don't know of any sources for the data you're looking for, however, I did something like this a year ago in one of my classes. An option would be (keeping in mind that you don't want to be too rigorous) to get an image of a good enough galaxy, i.e a fits file released to the public like M83. Under the assumption that wherever there's light there's mass (mass = $kL$, where $k$ is a constant and $L$ luminosity), you can equate forces and solve for velocity. This would get you values for "expected virtual velocities" at each radii, so you could plot the data and get a curve with a certain shape. What you expect to find is that as you increase radii, the values for velocity drop under the initial assumption. Then you go and compare with different and more rigorous measurements, like this one (page 18). Here you notice that the curve doesn't quite agree with the shape of the curve you got from the image, since it peaks and stays approximately constant (as opposed to dropping). Why is that? Maybe there's something that light can't show you. Note: as I said, this isn't rigorous. I've skipped conversion from counts per pixel, relationship between flux and luminosity and some other things. I've also assumed that you can work with something like astropy to process the data. Hope it helps