We know there is another massive galaxy a bit like the Milky Way a relatively large 2.2 million light years away, and also that there are dozens of very small dwarf galaxies surrounding (and mostly falling into) the Milky Way. But where is the edge of our own Galaxy, or to put another way, can one define an edge to it as one does by cutting into a piece of rolled dough with a cookie cutter?
We can try to find the edge of our Galaxy by calculating how fast the stars orbit around it. As we learn from basic physics principles, the farther away an object is from the center, the slower it should move in its orbit.
Thus we would expect that the stars closer to the center of our Galaxy should have the greatest speeds, stars about mid-way should have smaller speeds, and stars at the outer 'edge' should have the slowest speeds of all. The first measurements made to test this hypothesis took place in the 1970s.
To our great surprise then as now, the stars near to the center are not moving faster than stars at about the middle, and additionally stars near to the middle of the pack are not moving faster than stars near to the edges! Only very recently, with measurements taken in the 21st century, do we find hints of a downturn in stellar speeds.
This strange behavior does not at all describe how planets orbit the Sun, or how planets orbit any other stars or how stars are supposed to orbit any galaxy. What is going on here? Why are the stars misbehaving?
Well, there are two possibilities: 1) there is a substantial amount of "stuff" in the outer parts of the Galaxy that ramp up the speeds of the stars or 2) we do not yet have a complete understanding of how gravity works. Both options are being explored. It does appear that at least part of the problem arises as a result of option #1. This "stuff" is what astronomers now call "dark matter."
We cannot see dark matter, yet we see the effects of it on the motions of stars that pass through it. In this picture the stars would not be misbehaving at all, but rather following the rules of the visible AND of the dark matter.