Stick your arm straight to your side, like half a bird. Now, swing it around in front of you, like half a superman. Unless you did this wrong, or you don't have any arms, your hand should have moved much faster than your shoulder. In the same amount of time, your fingertips moved much farther than your elbow, and your elbow moved faster than your shoulder. If you had recreated this in 360 degrees, this is a lot how a planet rotates, with the outside moving faster than the inside.
This is, however, the opposite of the way a planet revolves. Assuming that most of the mess in a planetary system is in the center, planets closer to the center move faster than planets further out. Sorry. There's no cool arm trick to go with this one.
Think about it this way. Mercury is the fastest planet, going about 48 km/s. Venus is slower than Mercury, Earth is slower than Venus, and so on, until we get to Neptune, which goes only (only!) 5.5 km/s. Remember those certain types of donation boxes, where you put a quarter into a slot, then watch it “circle the drain” until it fell into a hole in the middle. The analogy isn't perfect, but it helps. The quarter (a planet) circles the gravitational hole (the sun) faster and faster the closer it is to the middle. Eventually, it's just a metallic blur dropping into a hold to feed starving children in the middle of the sun (or something.)
But that's the solar system, let's go bigger and talk about the entire galaxy.
Just like the solar system, the Milky Way is mostly flat. It is (as far as we know) 100,000 lightyears across and usually 2,000 ly “tall” with a 6,000 ly “tall” bulge in the middle. (Think of it like a crumbled-up fruit roll up sitting on top of a spread-out fruit-by-the-foot.) So, (as far as we know!) most of the mass in the galaxy is concentrated in the center, just like the solar system. And, all the stuff in the galaxy revolves around the middle, just like the solar system, except that it's a lot faster, and gets up to speeds like 230,000 km/s.
But here's the problem, the sun does pretty much what it's supposed to, but nothing else does. Everything else is moving around the center of the galaxy, but it's either too fast or too slow, depending on how far away it is from the center of the galaxy. Actually, things move a little bit faster than they should further away from the center, so it's more like the half-bird/half-superman trick, instead of the quarter circling the drain.
But it's not even that “clean” of a problem. Overall, stuff is moving not even close to the speeds they should. For example, an object 50,000 ly away from the center (at the edge of the galaxy) should according to the rules of “quarter motion donation” moving at a speed of 100,000 km/s. Turns out, it's going about 2.5 times as fast as that. For comparison sake, if the Earth did this, we would move at 74 km/s (much faster than Mercury) and have a year only 146 days long. The stuff towards the middle should be moving cartoonishly fast, but instead, is nowhere close to as fast it should be. They move at about 230,000 km/s (remember, Mercury moves over 9 times as fast as Neptune). This is the modern-day Neptune/Uranus wiggle problem and the Mercury perihelion problem.
So how should we approach this problem? Well, first and foremost, is our data and observations correct? Do we correctly see stuff further out than the galaxy moving fast than some of the stuff closer to it? Let's assume that our observations are correct and this is actually what we're seeing.
The next thing we do is apply the Neptune method, that is, apply old theories to make predictions about observations to be made in the future. And the old theory states that there should be a lot of mass outside of the galaxy.
How much mass? Well, remember that the stuff inside the galaxy is behaving nowhere near how it should; it is not a little wiggle. So it's going to take a lot of mass to set it right.
The hypotheses differ on how much mass, but they all agree on a lot. Some say five times as much, but for that extra wow-factor, we're going with the liberal estimate that there is nine times as much mass on the outside of the galaxy as there is on the inside. That's like saying that when you see Uranus move a little bit, it's not Neptune, but instead is nine more suns.
So, alright, we have now mathed our way into figuring out what we're looking for, where is it, and how much of it there is. Now, all we have to do is point our peepers into the right direction and say, “aha,” right? But, just like Vulcan, we don't see it. This is where dark matter comes in.
The idea is that the reason we haven't seen all this matter (nine times the amount of all matter in the galaxy, if you recall) is because it can't be seen. It emits no radiation whatsoever, so the name “Dark Matter” is actually a misnomer, as it would, theoretically, be invisible. If you were holding a lump of it in your hand, it would feel heavy (perhaps even very, very heavy) but have no temperature and you could see right there it. That's right. Dark Matter does absolutely nothing except conveniently solve this problem that astronomers have.
Here, I would like to take a moment to explain a few things. For one, I have done my absolute best to explain everything as best as I can, while still keeping things relatively simple. There is some more evidence for dark matter (and dark energy) that I have left out, because it's not important to the point I'm making (next week). For two, I'm not saying for certain that dark matter doesn't exist or that it can't exist.
What I'm saying, at this point, is that we need to look at the most likely scenario of what's going on, which may very well be that only 10% of everything in the universe can be seen. (There is some pretty strange shit in the universe, so this one wouldn't surprise me.) Or, it could be something else completely different (like the Mercury deal.)
I'll be continuing and concluding this series next week, as well as answering the question, “Why the fuck did you waste my time talking about Neptune and dark matter?”