One of the ways they measure the (supposed?) supermassive black hole at the galactic center of the milky way is to measure those tens of stars right at the galactic center that are orbiting what appears to be nothing, but what is said to be a supermassive black hole.
My question is why there is a distinction between all other stars in the galaxy orbiting (for instance, our own sun) and those few right near the galactic center orbiting. My point is, if you ask what our solar system orbits, an astronomer wouldn't say "the supermassive black hole at the center," he would say "the galactic center of mass." My assumption is that you couldn't even calculate the mass of the supermassive black hole by knowing our sun's mass and orbit - people would probably say we are too far out, or we are orbiting the galactic center of mass rather than the black hole, yadda yadda.
1) Why the distinction? How do we know that the stars right at the galactic center aren't also orbiting the galactic center of mass vs. the supermassive black hole?
2) What would happen if you magically removed the supermassive black hole in an instant? Would the stars right at the center continue to orbit the center? If so, how is that different than what they were originally doing?
Note that I know that center of mass of the galaxy and the supermassive black hole are two different things. I also know that the center of mass of the galaxy is either superimposed on the supermassive black hole, or quite close to it. I just want to know how or why some objects feel the center of mass of the galaxy and respond to it, while others feel the pull of the supermassive black hole and respond to it. How far away do you have to be to be considered "orbiting the center of mass" rather than "orbiting the supermassive black hole?"