Classes of Sept 9,11,16,18, continued I. Laws of Gravity We didn't say a whole lot about gravity, except to give you a qualitative feel for how the laws of gravity allow us to derive masses of objects. Newton, around 225 years ago, showed that orbits can all be explained given his Law of Universal Gravity... F= G(M_1)(M_2) ---------- R**2 So any two objects which have mass attract each other. The strength of this attraction depends on G, which is the Gravitational Constant (the physics of gravity if you will) TIMES the mass of the first object TIMES the mass of the second object DIVIDED BY the distance-squared between the two objects . So, if you perform the thought experiment of increasing the mass of one of the objects, the strength of gravity increases. If you move the two objects father apart, the strength of the attraction goes down as the square of the distance. Let's imagine the Earth going around the Sun. Earth is at a distance of 1 AU. Plugging into the above equation, you get some number, which we won't write down. So, let's now imagine that we replace the Sun with a 2 solar-mass star, and keep the Earth at a distance of 1AU. The attractive force doubles. The Earth is being pulled harder, so it orbits more quickly. The point of this thought experiment is to show you that if you know the size of the orbit and the speed of the orbit, you can derive masses. What you're really doing is calculating how much force there is between the two objects. So, if you have two stars orbiting each other (more than half the stars in the sky are in binary systems), and if you derive speeds and orbital sizes, you get masses. That's how we discover that the main sequence is really a mass sequence. For now, that's all we need to know about gravity. We'll come back to it later in the course. II. Forces of Nature, and Atomic Nuclei One of the remarkable triumphs of Physics is its ability to explain all of what we see from a small number of ideas. We can explain the large scale structure of the Universe, the creation of the atomic elements, the structure of the atom, the structure of molecules and minerals, energy from fossil fuels, atomic energy, and many other things from experiments that have shown that there are only four forces in Nature: Electromagnetism Gravitation The Strong nuclear force The Weak Nuclear force Electromagnetism and gravitation are long-range forces. Gravity, although intrinsically the weakest force, turns out to control the structure of the Universe because it cannot be turned off. Electromagnetism, which binds together atoms into more complicated structures, can be either an attractive force or a repulsive force. Most things in everyday life, in fact, are electrically neutral. Particles of like electrical charge repel each other (another inverse-square force!). Particles of opposite charge attract each other. The strong nuclear force is a short-range attractive force, that only operates on a size scale of an atomic nucleus. It's what keeps a nucleus of many protons bound together even though the protons are electrically trying to move farther away from each other. We won't worry about this force except for this one-sentence explanation. The weak nuclear force controls how certain fundamental atomic particles interact. We won't really worry about this force in this class. In the mid-to-late 1800s the fact that matter was indeed bundled into tiny nuclei was proven. It was realized that the nuclei of atoms were positively electrically charged, and that a typical atom contains a number of low-mass electrons with opposite charge. One of the many mysteries, unexplained by 19th century physics, was why the electrons didn't crash into the protons, since they're electrically attracting. So a model of the atomic behavior, including how atoms make light, was incomplete or wrong using what we knew in the second half of the 1800s. We'll come to that story in the next section. For now, let's see what we know about atoms... Nuclei of atoms consiste of one or more positively charged protons. Some more complicated atoms also contain one or more electrically neutral protons. The number of protons in the atomic nucleus controls its identity, its place in the (chemical) Periodic Table of the Elements. So, for instance, Hydrogen has one proton in its atomic nucleus. Helium has two protons, along with two neutrons. Hydrogen and Helium have different chemical and atomic properties. And so on. Atoms can absorb or emit light. This absorption or emission comes from the electron. Again, the behavior of the electron is not predicted from our understanding of Nature before the year 1900. Atoms can interact electrically to form more complicated things, for instance, molecules. Water, H2O, is a molecule consisting of two hydrogen atoms and one oxygen atom bound together. The individual atoms still exist, but are connected together electrically. If you give water enough energy, you can separate it into hydrogen gas and oxygen gas. We'll come back to more facts about atoms later. III. Emission and Absorption of Light by Atoms Kirchoff's Laws, which are empirical laws discovered many years before the appropriate explanation existed, tell us that there's an important difference between light emission from a solid (it emits light of all colors), and from light emission from a thin gas (it emits light of only very special wavelengths). We now want to give you a qualitative understanding of how a thin gas behaves. Experiments done in the late 1800s showed that the atomic nuclei in a thin foil of gold, for instance, are quite small and far apart. It was then natural to invent an analogy to a solar system, and to be anachronistic, to an artificial satellite orbiting the Earth. In the case of the satellite orbiting the Earth, you can change the size of the orbit by firing the rocket motor. Firing it in one direction adds energy, firing it while pointed in the other direction removes energy. The orbit changes in response to this change of energy. All orbits are allowed as long as you give the satellite the right amount of energy. Well, this isn't how this miniature solar system, the atom, works! In the atomic realm only certain orbits are allowed. This is a testable idea, no matter how weird it sounds. Words are not ideal for describing these circumstances, but we can get a little bit of insight by reminding ourselves that light behaves, sometimes, like a particle, and that it behaves, sometimes, like a wave. Particles, like electrons, also behave sometimes like a particle and sometimes like a wave. We didn't give the following example in class, but let's try it anyway. If electrons were particles ONLY, we could shoot them at targets and they'd end up exactly where we shot them. BUT THAT'S NOT WHAT NATURE DOES. If you shoot electrons through a slit, and shoot them one at a time, it turns out that they don't always end up at the bullseye, they end up in a distribution around the center of the target. This distribution is exactly what you expect for waves interfering with each other. (Think of throwing two rocks in a pond and watching how the waves interfere with each other) Even weirder, if you shoot ONLY ONE electron through a slit, it interferes with itself! So the electron does not behave like a miniature bowling ball. Our expectations form the world of footballs and bowling balls and racecars and rockets GIVE THE WRONG ANSWER. Let me give one more example where the electron behaves like a particle, but it still doesn't behave the way you expect. We did talk about this example in class, at least part of it. Think about pushing a car whose engine has died. If you're not strong enough to push the car, you can get a bunch of friends, and eventually you muster together enough energy to push the car. Well, remember, photons of light, these little particles, carry energy. So when light snashes into a solid, it deposits energy. There is something called the PHOTOELECTRIC EFFECT, where you shine light at a solid and it emits electrons (electricity). This photoelectric effect is used every time you enter a door of a store and you hear a "ding ding" as you cross into the store. It takes a certain amount of energy to liberate an electron. So light has to be a certain color. Well, in the auto analogy, two lower energy photons would work just as well as one higher energy photon. BUT THEY DON'T. So Nature doesn't behave according to our car rules. Anyway, this is just to give you a flavor of the problem. So, everything we knew in the late 1800s (and everything we know from ordinary life) doesn't work when we try to explain atoms. It took the seemingly weird ideas in QUANTUM MECHANICS to explain how light works. In trying to explain how light is emitted from an atom, the difference between the quantum mewchanical model and the classical model is that quantum claims that only certain orbits are allowed. We said in class that we could get a bit closer to an understanding by thinking of how one would packwaves into a circular orbit. If the orbit is just right so that the beginning of one wave can hook onto the end of the wave, ie, that there are an integral number of wavelengths in the size of the orbit, then things are good. If not, the orbit is forbidden. So the Bohr model of the atom claims that only certain orbits are allowed. Electrons can change orbits by gaining or losing energy. One way that they gain energy is to absorb light (there are other ways!). But since there are a finite number of allowed orbits, they can only absorb special colors of light. So we say that absorption of light allows the electron to move from a lower-energy orbit to a higher energy orbit. If the electron then goes back to the lower orbit, which it really really wants to do, it emits light. But it can only absorb or emit special wavelengths of light. This is not what we expect from "everyday life." But you saw in the lab last week that this is exactly what goes on. We'll finish talking about these ideas on Sept 23. So these seemingly weird ideas explain how light is emitted. This fact alone doesn't mean that quantum mechanics is right, BUT every experiment made in the past 100 years to test quantum is consistent with the predictions of quantum. Experiments un-thought-about by the inventors of quantum, made after they were dead, get the right answer! If you want to predict the results of an experiment, you'd better use the rpedictions of quantum. IV. What we can learn from spectra Well, as you're seeing in the lab, you can learn the chemical composition. I don't know if we'll talk about it right now, but you can also learn the temperature. You can learn how fast the gas is moving towards you or away from you. These are all incredibly useful things. V. Stars So we now know the structure of stars, the luminosities of stars, the temperatures of stars, and their chemical composition. Once we learn the source of the vast energy leaking from stars for extended periods of time, we'll be ready to tackle stellar evolution.