Welcome back. Today I want to talk about the formation of the sun and the earth. We're going to begin by talking about conservation of angular momentum and apply that idea to star formation and see how that explains the formation of disks. Then look at how the proto-planetary disk evolves. How particles are accumulated into planetesimals. And then into planets. And then we'll turn and look at the diversity of planetary systems, and see how this process produces planets as varied as Mercury and Jupiter. So, let's start where stars form. Stars form in molecular clouds. Molecular clouds are very large collections of molecules and dust. Typical molecular cloud might have a mass of a million times the mass of the sun and be a nursery in which about 1% or 2% of that molecular gas is converted into new stars. And we can see here, in this Spitzer telescope image, young stars forming out of molecular cloud. Now these molecular clouds themselves primarily lie in the spiral arms of galaxies. And here's a nearby galaxy, NGC 35, 3559, one that looks broadly like our own, and most of the star formation is taking place in the spiral arms. I should show you a picture of our own galaxy, and since we live in our galaxy, this, we see an image of our galaxy that looks like this. This is an infrared image. Of our galaxy. What we see here are the old stars and the galaxy's bulge, and this orange region is where there's a lot of dust. And we're seeing the dust and also, this is where the molecular gas is in the thin disk of our galaxy. And that's where star formation takes place. Here is a face on model of our galaxy. Our galaxy in the center is actually bar shaped and then there are spiral arms coming off the bar and we live here between some of the spiral arms. Our sun likely formed out of molecular cloud in one of the nearby spiral arms. So what happens when we form a star out of molecular cloud? Well, stars don't form in isolation, stars tend to form in what are called open clusters. And this is one of the nearby open clusters. A cluster called the Pleiades. And the Pleiades are a collection of young stars very close to the sun. And if you live in the Northern Hemisphere, you can go out and look at the Pleiades. Here's the Orion constellation. There's Orion's belt. This is Taurus the bull, that V-shape constellation here. Look from Orion's belt up towards Aldebaran, the bright star in Taurus, and above it you'll see the Pleiades. Now the Pleiades looks like a collection of about six or seven stars, when you look at them with your naked eye, that are very close together. But when you look at them with a pair of binoculars, you'll start to see there are tens, when we look with the telescope, hundreds of stars forming, that are formed in the Pleiades. And this is the kind of environment where our sun formed. Now what happens when star formation takes place? What happens when we take this molecular gas and we assemble it to form a star? To explain what happens I'm go, going to do a potentially dangerous demonstration to show the conservation of angular momentum. So let's see how this works. Imagine, I'm a dense molecular cloud filled with gas and dust. And this dense molecular cloud is slowly spinning. But as it collapses, it starts to spin faster and faster. So, angular momentum conservation means when the mass is way out here, I spin slowly, but when it comes in, I spin more rapidly. Let's try that experiment again, see how well we can do this. We'll start out spinning slowly, and then like an ice skater we spin more quickly. As we pull it up. The drag on the chair slows you down a bit. Those of you with, who are more ambitious, and willing to risk getting injured, you could try doing this yourself at home, and check whether angular momentum is indeed conserved. This works even better if you're an ice skater and you try this on ice. And you bring the weights in or just even bring your arms in. And you can find yourself spinning faster and faster. So, let's put the weights away. And write down an equation to describe what's going on. This equation describes angular momentum. And the angular momentum of the spinning man, or alternatively, the angular momentum with the molecular cloud or the protoplanetary disk, depends upon the mass times the radius squared, how far out the weights are, times the angular speed. And when I decrease the radius, in order to keep angular momentum conserved, omega goes up. So, one of the fundamental properties of nature, is that angular momentum is conserved. This is something that actually arises because the laws of physics are the same as I rotate around and as [INAUDIBLE] showed over 100 years ago, if the laws of physics are unchanged under rotation, then angular momentum will be conserved. So that, what do we mean by conservation? We mean that as this quantity here stays constant. So, if the r gets smaller, omega must increase. If we pull our arms in we start spinning faster. These laws apply not just to a foolish professor spinning around on a chair, they also apply to clouds of gas collapsing to form stars. So if we have a gas cloud that's slowly rotating when it's large, as it comes in and starts to collapse, it will spin faster and faster. Eventually, as it gets, the cloud gets smaller and smaller and collapses to form a star, the material will end up spinning quite rapidly and settle into a disk. So an inevitable by-product of angular momentum conservation and forming stars out of collapsing clouds, is that the star will be surrounded by a disk after it collapses. So now, we're applying this to stars. Here's a law of angular momentum conservation. And here's our slowly rotating cloud. And as that slowly rotating cloud collapses, it will form a disk of gas and dust around the collapsing proto-star, and this picture here is the basic picture you should have of a young forming star. And here is a visualization of what a system might actually look like with a bright star in the center surrounded by gas and dust. And, what's often seen is, as the material flows in this way, along the disk, a jet forms and we seem in some young star, stellar systems, jets, flowing outward from the center of the system. So now let's think about this idea of angular momentum conservation and apply it our own solar system. I'd like you to look up the mass of the sun, the mass of Jupiter, stick in the radius of the sun and the diameter of Jupiter's orbit, not Jupiter's radius, because Jupiter's moving around the whole system. Plug in those numbers and compare the angular momentum in Jupiter's orbit to the angular momentum in the sun. Work through those numbers and we'll be back in a moment.
