So this is the image of Andromeda galaxy that is a 2.5 million light years away from us. But it's our closest neighbor so they as big as our own galaxy and we can observe the stars, individual stars in this Andromeda galaxy because it's actually pretty close to us. 2.5 million light years away is pretty close to us in the universe. And you can again study how quickly these stars move about. In the Andromeda galaxy you'll find that they're moving very fast. So even if you put the mass of all the stars combined, you can observe in your telescope together, that wouldn't provide enough force of gravity to keep these individual stars inside Andromeda galaxy. So there must be some mass that's providing extra force of gravity beyond the stars you can observe in your telescopes. So what could that be? So here is actually a data that shows that you do need more mass than that meets your eye in the telescopes. So the data points here shows how quickly the stars are moving as a function of the distance from the center of Andromeda galaxy. You really see that something is wrong with this, right? So, as we saw in the solar planet the solar system, the farther away you are, the speed has to go down. But, it looks, you know, it's more or less the same, no matter how far you’re away, you move out from the center of the Andromeda. And if the stars are the only source of gravity, you can, you know, count them up using telescope. You see that the curve has to fall down like this, just like what it was in our solar system. So there's the big difference between the speed the star's actually moving with, and the speed the stars can actually be supported by the force of gravity due to the other stars inside the galaxy this difference has to be explained by something else and we call that difference the dark matter there must be other form of mass or matter in a given galaxy that provides even stronger force of gravity but we don’t see it, so we call that dark. And as far as Andromeda goes, it's part of this system we call the local group, which consists of more than 40 galaxies. Most of them are very small, or dwarf galaxies. And Andromeda and our Milky Way galaxy are the biggest, twins in this local group. And because Andromeda at the 2.5 million light years away is just a neighbor from us, we're actually pulling with each other with also a gravity and we're going to actually probably collide in 4 .5 billion years from now. And that sounds like a really scary thing but it turns out if you look out into space, you see many galaxies actually colliding and merging. So this is a picture of two galaxies getting pretty close to each other, by the mutual pull of gravity. This is different pair of galaxies, which have started to merge. And this another picture that shows the two galaxies have pretty much merged already. One center, the other center, and they are now merging into a single galaxy. So this kind of collision and merger of galaxies actually happen all the time in the Universe. And, and it does, it sounds scary, but it's actually a good thing. So in this picture you see this blue, twinkling lights all over in this picture. And that's the way the new stars are born. So if you let the galaxy live on its own, then eventually would age. And then, just fades away. But if the two galaxies collide and merge, then gets rejuvenated. It gets young again. And new stars are born. So that's actually a very interesting lesson we may draw about a human life as well. But anyway, back to the discussion of how quickly the stars revolve around the center of galaxies. You can actually measure these things fairly precisely these days. So this is yet another galaxy which you can look, you know, fairly, fairly out there, edge on. And you can map out the velocity of individual stars again as a function of distance from the center. And just like in the solar system, you would expect that it will fall down like 1 over square root r, but it stays fairly flat. So this kind of plot is called rotation curve of galaxies and, and all the rotation curves we have measured today, basically look flat. That means there's extra mass than beyond we can see. Yet another galaxy, same deal. Flat rotation curve. It doesn't go down like one over square root of r So putting all this, this, data together, we came to understand, the real nature of galaxies. What you can see in telescopes, is only this disk, which is, sort of at the center of this whole thing. That this is the only thing you can see. But around it, you have this blob, or sea, of dark matter, you don't get to see. And, thanks to the gravity of this sea of dark matter, so you live in this ocean of dark matter, you are trapped inside, and that's how you can happily move about. Without this dark matter, the galaxies would just fly apart, and should have disappeared many billions of light, billions of years ago. And the galaxy may extend over, like, you know, a hundred thousand light years, but the, the dark matter will just keep going over millions of light years and, and that's the real nature of our galaxies. So now is the question to you, how do we know if this is the right picture, and what goes beyond this, this distance of millions of light years?