 Greetings and welcome to the Introduction to Astronomy. In this lecture we are going to talk about solar energy generation or how the Sun goes about producing its energy. So how does our Sun produce energy? Well, there have been some thoughts about this, but even a hundred years ago this was something difficult to understand. So how was the Sun able to produce its energy? When we knew some things, first of all we knew that it could not be burning in the traditional sense that we associate here on Earth. And that would, because that would only last a few thousand years, and we already knew that the Earth was far older than that. However, what we do know, and we try to think about different ways that energy could be produced, and one thing we have to recall is that energy is conserved, and that means you cannot create or destroy energy. You can change the form of energy, however. So this was one of the early thoughts as to how the Sun might be powered, and that was by, in the mid-1800s, by Kelvin and Helmholtz. And what they did was to suggest that the Sun could convert gravitational energy and take that energy and convert it into heat. Now that happens all the time. If you take an object and you lift it up in the air and hold it up in the air, it has potential energy. If you drop it, it will lose potential energy and gain kinetic energy or energy of motion. When it strikes the ground, it will convert that energy of motion into heat and sound energy that have been released. So the same amount of energy is always conserved. Now this is not an unusual thing to think about. This is what we believe causes Saturn to have excess heat. What it would be is have to have the Sun contracting. And if the Sun contracted about 40 meters per year in diameter, this would be enough to account for the energy that is produced by the Sun. While this change in size seems significant, it would really be unnoticeable relative to the size of the Sun. And it could power the Sun for a hundred million years. Well, at the time this was sufficient. This could account for the age of Earth. However, we now know that the Sun and Earth are four and a half billion years old. Much older than this and gravitational contraction is not able to supply energy for that long of a time. So what can we do now? Well, Albert Einstein told us that matter and energy are just different forms of the same thing. You can convert matter to energy and you can convert energy back to matter. And one equation that most people have heard of is Einstein's E equals MC squared. And that is a relationship between energy and mass. And the relation, the constant C, is the speed of light. And what that means is that a very small amount of mass is converted to a large amount of energy. Because the speed of light is 300,000 kilometers per second. So very large, big, big numbers there in terms of the speed. And when we square that, that makes an even bigger number, 300,000 times 300,000. Multiply that by the mass and you get the amount of energy released. So for example, if you take a paper clip and you could convert that completely to energy, that's the equivalent of 15,000 barrels of oil in one paper clip. Now of course, the question is how can you do this? How can you convert a paper clip into energy or any other kind of mass directly into energy? And to do that, we have to think a little bit about elementary particles. So let's look at these a little bit. We have protons, neutrons and electrons. Now that's what atoms are made up of. Each of these also has an antiparticle. So we have antiprotons, anti-neutrons, and anti-electrons. Anti-electrons are actually known as positrons. And they are exactly the same as electrons, except they have the opposite charge. So they're just like electrons, but with a positive charge instead of a negative charge. When matter and antimatter meet, that is a complete conversion of matter to energy. So you can take a particle and its antiparticle, they come in and collide here, and you get a couple of gamma rays, two photons of energy, extremely high energy photons that will then travel outward. So the mass is gone, completely converted into energy. Another elementary particle you want to look at is the neutrino. The neutrino was proposed first because there were some nuclear reactions that looked like they lost energy. And believing in the conservation of energy, it was proposed that another particle was present that was not detected. These are very nearly massless particles. They are neutral, so they do not have any electrical charge. And they are weakly interacting. They do not interact with ordinary matter. So they travel right through everything. And we will come back and look at these later on when we try to understand how the sun works because they are one way that we can get a look into the interior of our sun. So what are...we want to look at nuclear reactions here and how they work. So we can have two types of nuclear reactions. We have nuclear fission, which splits large atoms, such as uranium here, by firing neutrons into it. It becomes an unstable isotope of uranium, which then splits into two parts and more neutrons. And these neutrons then have high energy and they go back and continue the chain reaction. They will strike other uranium nuclei and continue the process. This releases energy. We can use nuclear bombs, use something like this in an uncontrolled sense. A nuclear power plant uses similar, but in a controlled sense. And both will work for producing energy. This is not useful for stars. Why? What are stars made up of? Hydrogen. And helium. So since stars are made up of hydrogen and helium, it doesn't make much sense because there's not enough uranium there to get a concentration of uranium. The other thing we can do is nuclear fusion. Nuclear fusion fuses light atoms, hydrogen. There we go. That's the hydrogen that stars are made up of into heavier atoms. The problem is, how do you overcome the repulsive force? The nuclei are all positive. And what that means is that they want to repel each other. As they come close to each other, they come closer and closer together, you get a very strong repulsion between them because this is positively charged, this is positively charged, and they want to push each other away. So if you throw them toward each other at a slow velocity, they will push each other back and never fuse. What we need is to overcome this electrostatic repulsion, the electrostatic force. And we can do that if we push them close enough together. When you get very close, you see here the nuclear force takes over. So if you could somehow push them close enough, then the nuclear force takes over and binds the two together, and they would then fuse together. You need two things for this to happen. You need extremely high density, so there's got to be a lot of hydrogen there, and you need extremely high temperatures, at least 10 million Kelvin. If you recall, the surface of our Sun was about 6,000 Kelvin. This is 10 million Kelvin. And actually the center of our Sun is closer to about 15 million Kelvin. At those high temperatures and pressures, the particles are moving fast enough that they can get close enough together to stick before the electrostatic force would have pushed them away. Now it still doesn't happen in a single step, and let's look at what we call the proton-proton chain. This is how hydrogen is fused into helium. The net result is four hydrogen atoms into one helium nucleus. But you can't do this in one step. You'd have to have four hydrogen atoms come together all at once, which would not be very easy to do. So it happens in steps. The first step shown in the top here is you have two hydrogen nuclei. They're moving very fast. They fuse together. They give off energy. They give off a couple of other particles as well, and they form an isotope of hydrogen called deuterium. Deuterium is heavy hydrogen. It has one proton and one neutron, so it is still hydrogen because it has a proton and just one proton, but it's heavier because it has twice the weight because it also has a neutron present. In addition, a positron comes out. That's an anti-electron. What happens to an anti-electron in the middle of a bunch of ordinary matter? It finds an electron and annihilates it, producing energy. Then there is a neutrino, and we will come back and talk about neutrinos in another lecture and go over those in a little bit more detail because they travel right through the sun. It's formed at the core, and it just travels straight out and zips right out into space. It is not deterred by all that material in between us. It travels right through that constantly. That's step one. We form some deuterium. The next step, we take that deuterium and that deuterium fuses with another regular hydrogen atom. That gives off helium-3. Helium-3 is a lighter version of helium. Normal helium, helium that we fill up balloons with, is helium-4. That's the standard isotope. Helium-3 is a lighter version of this, so we do that twice and we've now formed two of these helium-3 nuclei. They combine together to fuse and make a helium-4 nucleus, sending two protons back off at high energy to continue this process. So this goes on and on continuously within the sun and begins the process again. And each of these gives off a little bit of energy, not a lot of energy, but a little bit, and that adds up over all of the different, of all of the reactions that occur. So how does this give us energy? Well, let's look at this in a little more detail. The mass of a helium nucleus is a little less than 1% less than the mass of four hydrogen nuclei. So if we add up the mass of the hydrogen that went into it and subtract the mass of the helium nucleus, there's a little bit of mass left over. What happened to that? Well, that goes back to our equation, E equals mc squared. So that little bit of mass here gets multiplied by the speed of light, our big number, and squared, and that gives us energy that is produced. In fact, 1 kilogram of hydrogen converted to helium would produce a tremendous amount of energy, 6.4 times 10 to the 14th joules of energy. What does that mean? Well, that's about the electric supply of the United States for two weeks. That is, two weeks of the United States electrical supply from 1 kilogram of hydrogen being converted to helium, and the sun converts a lot of hydrogen to helium every single second, far more than just 1 kilogram. Now there is another way to fuse these together. This is called the Carbon Nitrogen Oxygen, or CNO cycle. This is another way to diffuse hydrogen to helium, and it's not significant in the sun, but it does work for stars that are several times more massive than the sun. Essentially, it uses carbon as an intermediary. The carbon builds, you add atoms to the carbon, and that eventually forms a helium nucleus. So you'd add a proton to carbon, then you'd add another proton to that, you'd form nitrogen and then oxygen, and eventually you would pop off a helium nucleus and get back to carbon again. It's another way to build this up, but it doesn't really work except at much higher temperatures, much higher than we get in the sun. But it is important for our massive stars, which we will look at when we talk about stars. So let's go ahead and finish up with our summary, and what we've looked at here is we had that puzzle, that puzzle of energy generation. It was solved when we learned by Einstein that mass and energy were interchangeable, you convert mass to energy and energy to mass. The sun produces energy by the proton-proton chain, which really takes four hydrogen atoms and makes one helium atom. The mass difference between the hydrogen and helium is then converted into energy which powers our sun. So that concludes this lecture on solar energy generation. We'll be back again next time for another topic in astronomy. So until then, have a great day everyone, and I will see you in class!