WEBVTT 00:00.860 --> 00:02.350 Prof: Some things about this course. 00:02.350 --> 00:05.320 This is a course for non-scientists. 00:05.320 --> 00:11.390 That portion of the enrollment policies is not a suggestion. 00:11.390 --> 00:13.700 I really don't want science majors in this class. 00:13.700 --> 00:16.000 If you are a science major, I'm going to notice because 00:16.004 --> 00:18.484 that's one of the things that appears on the class list; 00:18.480 --> 00:19.940 what your major is. 00:19.940 --> 00:23.310 So, don't take the course if you're a science major. 00:23.310 --> 00:27.220 Let me point out that freshmen don't have major, 00:27.218 --> 00:32.038 so it doesn't matter if you intend to be a science major if 00:32.040 --> 00:33.870 you're a freshman. 00:33.870 --> 00:36.780 If you are a science major I recommend Astro 210, 00:36.779 --> 00:38.779 which is being given this term. 00:38.780 --> 00:42.470 I have a little handout on all the different introductory 00:42.470 --> 00:45.830 astronomy courses at the front of the room if you're 00:45.831 --> 00:46.821 interested. 00:46.820 --> 00:52.840 Let's see, it is also true that this course is kind of intended 00:52.839 --> 00:58.469 for non-science majors who have a certain basic high school 00:58.471 --> 01:03.521 level comfort with tenth-grade science and math. 01:03.520 --> 01:07.300 If you're extremely phobic about these kinds of things, 01:07.299 --> 01:11.659 I would say that Astronomy 120, while it has a similar level of 01:11.656 --> 01:15.546 math, has a somewhat shallower learning curve and a somewhat 01:15.552 --> 01:16.942 deeper safety net. 01:16.938 --> 01:20.788 So, if you're the kind of person who breaks into a sweat 01:20.790 --> 01:24.780 when somebody writes down an equal sign, check out 120. 01:24.780 --> 01:29.110 Let's see, but that's not the biggest difference between this 01:29.114 --> 01:30.274 class and 120. 01:30.269 --> 01:34.399 I think the biggest difference is what the class is trying to 01:34.396 --> 01:34.736 do. 01:34.739 --> 01:38.549 Astronomy 120 and also 110 and other courses in our department, 01:38.548 --> 01:41.738 and elsewhere in the university, are basically survey 01:41.742 --> 01:42.482 courses. 01:42.480 --> 01:45.330 Most introductory science courses are survey courses. 01:45.330 --> 01:48.170 They cover a fairly wide subject matter. 01:48.170 --> 01:52.040 This is--isn't that, what this course is supposed to 01:52.037 --> 01:56.737 do is we're going to talk about three particular topics in very 01:56.739 --> 01:58.559 considerable detail. 01:58.560 --> 02:02.990 Enough detail so that by the end of our discussion you'll 02:02.987 --> 02:07.967 understand what's going on in current research in this topic. 02:07.968 --> 02:11.028 And by current, I don't mean this decade, 02:11.033 --> 02:12.493 I mean this week. 02:12.490 --> 02:15.970 Astronomy is currently in a stage of very rapid advancement, 02:15.965 --> 02:19.435 and one of the things that's happened every time I've taught 02:19.439 --> 02:22.639 this course in the past, is that at some point during 02:22.638 --> 02:25.678 the semester someone will publish some piece of research 02:25.680 --> 02:28.280 which changes some aspect of the curriculum. 02:28.280 --> 02:31.690 I'll come in waving some paper and everything will be changed, 02:31.694 --> 02:33.884 and I can't guarantee that of course, 02:33.878 --> 02:35.938 because I can't predict the future but it's happened every 02:35.935 --> 02:36.615 time in the past. 02:36.620 --> 02:40.660 So, we really are trying to get you all the way out to the 02:40.657 --> 02:42.567 frontiers of the subject. 02:42.568 --> 02:45.958 I think this is actually a better approach for non-science 02:45.960 --> 02:49.350 majors, because after all, we live in the Internet age. 02:49.348 --> 02:52.848 If you want to find out a bunch of facts about some scientific 02:52.854 --> 02:56.134 topic you could go online and go to Wikipedia or wherever, 02:56.129 --> 02:57.509 look these facts up. 02:57.509 --> 02:59.569 That's not a big problem. 02:59.568 --> 03:03.528 The problem comes when there are two sets of facts which 03:03.532 --> 03:05.912 directly contradict each other. 03:05.908 --> 03:10.468 This happens quite frequently in scientific topics these days, 03:10.469 --> 03:15.179 particularly those with kind of political or moral overtones, 03:15.180 --> 03:17.860 and you get facts that directly contradict each other. 03:17.860 --> 03:21.160 What are you supposed to do about that? 03:21.158 --> 03:24.678 What I'm hoping is that by talking about situations in 03:24.675 --> 03:28.385 which the facts at the moment really aren't known yet, 03:28.389 --> 03:32.879 you can develop some skill in interpreting these kinds of 03:32.882 --> 03:35.692 contradictory facts for yourself. 03:35.690 --> 03:38.960 If you don't do that, then the only alternative is to 03:38.961 --> 03:42.931 listen to the experts argue with each other and vote for whoever 03:42.925 --> 03:46.885 argues the loudest or looks the best when they're doing it, 03:46.889 --> 03:50.189 or has a degree from Harvard or whatever it is. 03:50.190 --> 03:53.250 You guys can do better than that. 03:53.250 --> 03:57.470 So, the hope is that by practicing this kind of skill of 03:57.467 --> 04:02.067 evaluating science when the answer isn't fully understood, 04:02.068 --> 04:05.618 that you can develop skills that will stand you in good 04:05.617 --> 04:09.027 stead when you run into scientific controversies in a 04:09.034 --> 04:11.734 political context or a legal context, 04:11.729 --> 04:16.659 or just as ordinary citizens in the course of your lives. 04:16.660 --> 04:22.070 It also happens that the three particular topics I think are of 04:22.067 --> 04:26.427 some real interest and importance in themselves. 04:26.430 --> 04:29.760 And I'll get to the three topics again in just a moment 04:29.757 --> 04:30.187 here. 04:30.189 --> 04:33.369 Let me point out that this kind of approach has a downside to it 04:33.374 --> 04:35.854 and this has been pointed out repeatedly on course 04:35.851 --> 04:36.661 evaluations. 04:36.660 --> 04:39.650 Because we're dealing with stuff which ultimately the 04:39.646 --> 04:42.686 answers are not yet understood there's no textbook. 04:42.690 --> 04:44.170 There can't be a textbook. 04:44.170 --> 04:47.000 We haven't figured out what to put in the textbooks yet. 04:47.000 --> 04:49.660 And the problem with that is that that makes the lectures 04:49.661 --> 04:52.321 very important because that's the only information you're 04:52.322 --> 04:53.132 going to get. 04:53.129 --> 04:55.559 There's a whole bunch of online readings and stuff but they tend 04:55.557 --> 04:58.677 to have a point of view, and so it's really the lectures 04:58.677 --> 05:00.997 that are the basis of the course. 05:01.000 --> 05:04.240 The problem with that is that I've chosen to give this course 05:04.237 --> 05:06.987 at the ungodly early hour of 9:30 in the morning, 05:06.990 --> 05:10.740 and you guys are going to have to show up and so here's the 05:10.737 --> 05:11.187 deal. 05:11.189 --> 05:14.919 I'll make a deal with you: Your job is to get to class by 05:14.923 --> 05:16.393 9:30 in the morning. 05:16.389 --> 05:20.259 My job is to keep you awake once you're here, 05:20.261 --> 05:25.451 and so if we both succeed in cooperating in this sense we'll 05:25.452 --> 05:27.302 probably be okay. 05:27.300 --> 05:30.200 But seriously, if you're anticipating regular 05:30.204 --> 05:34.174 difficulties in getting to class this is not actually a great 05:34.166 --> 05:37.796 class to take because there's no backup in the form of a 05:37.798 --> 05:38.788 textbook. 05:38.790 --> 05:42.440 All right, the particular topics that are under 05:42.444 --> 05:46.024 discussion, I've listed them here in green. 05:46.019 --> 05:48.459 The first of them are extra-solar planets, 05:48.459 --> 05:51.909 by which I mean planets around stars other than the Sun. 05:51.910 --> 05:55.250 It's well known that there are many, many of these planets. 05:55.250 --> 05:58.750 All you have to do is watch Star Trek or something like that 05:58.754 --> 06:02.254 and you'll find many, many examples and this has been 06:02.247 --> 06:05.747 a staple of science fiction for quite a long time. 06:05.750 --> 06:07.880 Oddly enough, until ten years ago, 06:07.884 --> 06:10.734 there was absolutely no evidence for this. 06:10.730 --> 06:12.990 We assumed that, because the stars are normal 06:12.990 --> 06:16.130 stars and there are many other stars--the Sun is a normal star 06:16.125 --> 06:19.255 and there are many other stars like the Sun that there must be 06:19.262 --> 06:22.352 many planets of the same kind as the planets in our own Solar 06:22.345 --> 06:25.065 System circling around all these other stars. 06:25.069 --> 06:29.349 But until 1995 there was not one bit of evidence to support 06:29.353 --> 06:30.243 that idea. 06:30.240 --> 06:33.840 Since 1995, this has become a huge growth industry and 06:33.843 --> 06:37.993 research, and we now know of literally hundreds of planets, 06:37.990 --> 06:40.690 all of them discovered in the last ten years. 06:40.690 --> 06:43.800 So, this is a situation in which, what ten years ago was 06:43.795 --> 06:46.225 science fiction, has become science fact and 06:46.225 --> 06:49.605 we're very rapidly trying to figure out exactly what kinds of 06:49.613 --> 06:52.743 planets these are, whether there are Earth-like 06:52.735 --> 06:55.625 planets out there, and that has some bearing on 06:55.634 --> 06:59.484 what the science fiction people refer to when they say as, 06:59.480 --> 07:01.550 "life as we know it." 07:01.550 --> 07:07.650 And so, that's currently one of the hottest topics in astronomy. 07:07.649 --> 07:11.509 The next topic is going to be black holes, and this is a 07:11.507 --> 07:12.907 similar situation. 07:12.910 --> 07:16.000 Fifteen, twenty years ago black holes were sort of poised 07:16.000 --> 07:19.260 precariously on the boundary between theoretical physics and 07:19.255 --> 07:20.355 science fiction. 07:20.360 --> 07:24.000 A boundary that is more porous than you might believe. 07:24.000 --> 07:27.040 But again, in the past fifteen years or so this has been 07:27.043 --> 07:30.423 converted into a standard topic in observational astronomy. 07:30.420 --> 07:32.810 There are dozens, probably hundreds of objects we 07:32.807 --> 07:35.737 can point to in the sky and say, "yes those things are black 07:35.742 --> 07:36.292 holes." 07:36.290 --> 07:40.500 And so now, the current topic of research is do these things 07:40.497 --> 07:44.557 that we are pretty sure are black holes actually behave in 07:44.564 --> 07:47.944 the incredibly bizarre, science-fictiony manner that 07:47.935 --> 07:51.135 the theoretical physicists have been talking about for the past 07:51.137 --> 07:52.427 thirty or forty years. 07:52.430 --> 07:56.700 So, to what extent are these very exotic behaviors actually 07:56.697 --> 07:58.607 manifested in real life? 07:58.610 --> 08:01.070 Finally, I want to talk a little bit about cosmology. 08:01.069 --> 08:03.619 Cosmology is the study of the Universe as a whole. 08:03.620 --> 08:06.260 That's too big a topic to go into in depth, 08:06.262 --> 08:08.342 so I've picked one piece of it. 08:08.338 --> 08:12.638 The piece I've picked is the existence, which was discovered 08:12.639 --> 08:15.769 in the late 1990s, of something called "dark 08:15.774 --> 08:16.654 energy." 08:16.649 --> 08:21.079 Dark energy is an all-pervading anti-gravity; 08:21.079 --> 08:24.779 it's a repulsive force that turns out to occupy essentially 08:24.783 --> 08:28.263 all of the Universe, and 75% or more of the entire 08:28.257 --> 08:32.317 mass energy of the Universe turns out to be in the form of 08:32.320 --> 08:34.530 this mysterious dark energy. 08:34.529 --> 08:37.949 The evidence for this comes largely, but not entirely, 08:37.953 --> 08:41.253 from observations of a certain kind of supernova. 08:41.250 --> 08:44.810 And so what I'm going to focus on is the observations of the 08:44.807 --> 08:47.457 supernovae and how they demonstrated that, 08:47.460 --> 08:50.480 in fact, all ordinary matter and energy and so forth is a 08:50.476 --> 08:53.706 tiny fraction of what's actually going on in the Universe, 08:53.710 --> 08:56.930 and what's really happening out there is something we totally 08:56.933 --> 08:58.443 don't begin to understand. 08:58.440 --> 09:02.080 So, that will be the third topic of the course. 09:02.080 --> 09:04.540 These topics have something in common. 09:04.538 --> 09:08.258 All of them involve observing something that you can't 09:08.263 --> 09:09.953 actually see directly. 09:09.950 --> 09:12.840 We don't see these planets directly because they're too 09:12.841 --> 09:14.181 faint and too far away. 09:14.178 --> 09:16.448 We don't see black holes directly. 09:16.450 --> 09:19.870 By the definition of black hole you can't see these things 09:19.870 --> 09:20.530 directly. 09:20.528 --> 09:22.218 And of course, dark energy, 09:22.217 --> 09:24.877 by its very name, is also undetectable. 09:24.879 --> 09:27.469 So, how do we know that these things are there? 09:27.470 --> 09:30.890 The answer is we know that they're there because of their 09:30.889 --> 09:33.639 influence on other objects that we can see, 09:33.639 --> 09:36.369 and in particular, their gravitational influence 09:36.374 --> 09:38.414 on other objects that we can see. 09:38.408 --> 09:41.078 And so, what binds these three topics together, 09:41.083 --> 09:43.883 are first of all, the fact that the observational 09:43.875 --> 09:47.415 techniques to discover them are actually quite similar to each 09:47.422 --> 09:48.122 other. 09:48.120 --> 09:53.680 And second, that they all involve different manifestations 09:53.681 --> 09:54.951 of gravity. 09:54.950 --> 09:58.590 And so, we'll be talking in the first part of the course about 09:58.594 --> 09:59.794 Newtonian gravity. 09:59.788 --> 10:02.498 In the second part of the course when we get to black 10:02.495 --> 10:04.415 holes, that's relativistic gravity, 10:04.418 --> 10:07.168 general relativity, Newton's--Einstein's theory 10:07.173 --> 10:09.273 which supplanted Newton's theory. 10:09.269 --> 10:12.899 And then by the time we get to dark energy, it may not even be 10:12.899 --> 10:15.339 correctly described by Einstein's work, 10:15.340 --> 10:19.490 and we may be in the area of whole new kinds of physics that 10:19.485 --> 10:22.785 the theorists haven't even thought about yet. 10:22.788 --> 10:26.608 So, there will be a progression to more and more sophisticated 10:26.610 --> 10:29.870 theories of gravity underlying these observations. 10:29.870 --> 10:33.130 10:33.129 --> 10:38.209 There's another feature that these topics have in common, 10:38.207 --> 10:43.007 and that is that they can be understood in some detail 10:43.014 --> 10:47.644 without particularly sophisticated mathematics. 10:47.639 --> 10:51.179 Now, let me pause here and say some things about math. 10:51.178 --> 10:54.198 Astronomy is a mathematical topic. 10:54.200 --> 10:57.700 There will be math in this course, there ought to be math 10:57.702 --> 11:01.082 in any astronomy course or it isn't really an astronomy 11:01.080 --> 11:03.270 course, it's just a slide show. 11:03.269 --> 11:07.109 Now, the math in this course has been kept at a deliberately 11:07.109 --> 11:07.889 low level. 11:07.889 --> 11:10.129 That is to say, the kind of math we'll be doing 11:10.133 --> 11:12.283 is stuff you did in ninth and tenth grade. 11:12.278 --> 11:15.238 Introductory high school algebra, high school geometry, 11:15.241 --> 11:18.371 I think we take the sine of an angle a couple of times, 11:18.370 --> 11:22.930 but it's the one case it cancels out almost immediately, 11:22.931 --> 11:25.421 so don't let that scare you. 11:25.418 --> 11:29.168 It's the kind of thing that you all did on the math SATs and 11:29.174 --> 11:33.254 since you're all sitting in this room you must have done okay. 11:33.250 --> 11:36.810 Having said that, I have discovered that saying 11:36.806 --> 11:38.426 that is misleading. 11:38.428 --> 11:41.748 And the reason it's misleading is cast your mind back to ninth 11:41.745 --> 11:44.495 grade; ninth grade math is hard. 11:44.500 --> 11:46.240 Remember? 11:46.240 --> 11:49.270 In particular, word problems are hard. 11:49.269 --> 11:51.289 You remember word problems. 11:51.288 --> 11:53.608 This is where you drive from here to Cleveland and you fill 11:53.610 --> 11:56.300 your tank up with gas, and the gas costs so much per 11:56.303 --> 12:00.193 gallon, and the question is what is your shoe size or something. 12:00.190 --> 12:02.280 [laughter] The way one approaches that is 12:02.279 --> 12:05.519 through a kind of common sense approach which involves the fact 12:05.520 --> 12:07.560 that many of us have been in a car, 12:07.558 --> 12:10.338 driving from City A to City B, perhaps not Cleveland, 12:10.336 --> 12:12.686 but somewhere else, and so you have a kind of 12:12.687 --> 12:14.287 intuition to fall back on. 12:14.288 --> 12:17.498 When you do math problems that are logically the same, 12:17.504 --> 12:19.754 but apply to astrophysical systems, 12:19.750 --> 12:23.770 for which you have absolutely no common sense to back you up, 12:23.774 --> 12:27.804 then you have to reason purely from the internal logic of the 12:27.798 --> 12:30.078 problem and that's hard to do. 12:30.080 --> 12:32.070 It's a skill that can be learned; 12:32.070 --> 12:33.510 it's a skill that's worth learning; 12:33.509 --> 12:36.949 it's a skill that I'm sure many of you already have to a large 12:36.952 --> 12:39.042 extent, but it isn't an easy thing. 12:39.038 --> 12:44.238 So, the fact that the level of the math is low doesn't mean 12:44.240 --> 12:46.840 that the problems are easy. 12:46.840 --> 12:51.050 We do have a lot of help mechanisms, which I'll describe 12:51.049 --> 12:54.879 perhaps on Thursday, to keep you up to speed if you 12:54.878 --> 12:58.168 start having trouble with these things. 12:58.168 --> 13:00.578 So, I should say something about course requirements here. 13:00.580 --> 13:03.450 Let's see, we have sections in this class. 13:03.450 --> 13:06.230 The sections are not just problem solving sections, 13:06.225 --> 13:07.885 these are actually required. 13:07.889 --> 13:11.029 The fact that we're dealing in topics for which the answer 13:11.028 --> 13:14.328 isn't fully known means that one can actually have discussion 13:14.331 --> 13:16.591 sections unlike many science courses, 13:16.590 --> 13:18.200 so we're going to do that. 13:18.200 --> 13:20.490 And so, the structure of the course is like a history course. 13:20.490 --> 13:22.880 Two lectures a week plus required section, 13:22.884 --> 13:25.634 and so 10% of your grade comes from sections. 13:25.629 --> 13:28.489 A large fraction of that is just showing up, 13:28.486 --> 13:31.806 but there will also be something in terms of saying 13:31.808 --> 13:34.798 something intelligent once you get there. 13:34.799 --> 13:37.469 That's 10% of the course; 30% of the course is problem 13:37.470 --> 13:37.800 sets. 13:37.798 --> 13:39.848 We will hand these things out once a week. 13:39.850 --> 13:42.420 The first problem set will show up on Thursday, 13:42.423 --> 13:45.563 and if you have any question about whether this course is 13:45.557 --> 13:48.337 appropriate for you, the right thing to do is to 13:48.344 --> 13:51.664 look at that problem set and ask yourself is this reasonable. 13:51.658 --> 13:55.108 I will say that students on their evaluations have pointed 13:55.106 --> 13:57.946 out that it does--the course does get harder. 13:57.950 --> 14:00.230 It's not that the math gets more complicated, 14:00.225 --> 14:02.395 but the situations get more complicated. 14:02.399 --> 14:05.969 So, if you have serious trouble with the first problem set 14:05.971 --> 14:08.041 that's probably a warning sign. 14:08.038 --> 14:09.798 As I say, that will be handed out on Thursday. 14:09.798 --> 14:11.878 These things come about once a week; 14:11.879 --> 14:13.439 it's 30% of the grade. 14:13.440 --> 14:16.740 I'll say more about problem sets later on Thursday. 14:16.740 --> 14:18.890 Thirty percent comes from two midterm exams. 14:18.889 --> 14:21.989 The way we do this is the one where you get the better score 14:21.986 --> 14:22.666 counts 20%. 14:22.668 --> 14:25.108 The one that you get the worst score counts 10%. 14:25.110 --> 14:26.990 So, that gives you a little bit of a break. 14:26.990 --> 14:30.120 And then there will be the Final exam, that's the last 30% 14:30.116 --> 14:30.936 of the class. 14:30.940 --> 14:33.090 There's also an optional paper. 14:33.090 --> 14:36.490 If you choose to do that, that will count 15% of your 14:36.491 --> 14:40.421 grade, and what it will do is it will de-weight whichever the 14:40.418 --> 14:44.538 worst of your 30% parts of your grade are back down to 15%. 14:44.538 --> 14:49.148 So, if you're a word person rather than a number person, 14:49.149 --> 14:54.089 you get this opportunity to augment your score and de-weight 14:54.092 --> 14:59.042 some other part of the class in which you may have done less 14:59.038 --> 14:59.958 well. 14:59.960 --> 15:02.010 All of this stuff is on the classes server [Yale's online 15:02.009 --> 15:02.559 course tool]. 15:02.558 --> 15:06.918 I should say that the syllabus that I've put out here is just a 15:06.917 --> 15:10.217 direct copy off of what's on the classes server, 15:10.221 --> 15:12.331 so feel free to take that. 15:12.330 --> 15:18.590 But all the information, and actually more information 15:18.591 --> 15:20.011 is online. 15:20.009 --> 15:23.469 Let me pause now and ask whether there are questions 15:23.472 --> 15:26.532 about the course and the course procedures. 15:26.529 --> 15:28.009 Yes? 15:28.009 --> 15:31.139 Student: This may be a silly question, 15:31.138 --> 15:35.548 but I saw on the web that right below the times listed for this 15:35.547 --> 15:39.807 course was a "to be determined" or some sort of notation that 15:39.813 --> 15:43.653 could indicate that there is another of this class at a 15:43.654 --> 15:45.294 different time? 15:45.288 --> 15:47.368 Prof: No, no this class is going to meet 15:47.368 --> 15:47.638 now. 15:47.639 --> 15:49.869 I'll have to check and see what you were thinking of, 15:49.869 --> 15:52.269 but it may be that what that was referring to was section 15:52.270 --> 15:53.790 times, and actually this is something 15:53.792 --> 15:54.742 that I haven't mentioned. 15:54.740 --> 15:56.130 Sections are required. 15:56.129 --> 15:57.759 They're all going to be on Mondays. 15:57.759 --> 16:00.099 We're going to have a wide range of times, 16:00.101 --> 16:03.191 all of them on Mondays from 12:30 until I think 8:00 at 16:03.187 --> 16:03.757 night. 16:03.759 --> 16:06.059 But you do have to sign up for a section. 16:06.058 --> 16:08.008 Let me also say, I've mentioned here, 16:08.014 --> 16:09.754 I don't think this is--;actually, 16:09.753 --> 16:11.983 looking at the number of people here, 16:11.980 --> 16:14.720 I think we're going to be able to accommodate everyone, 16:14.716 --> 16:16.336 including juniors and seniors. 16:16.340 --> 16:20.080 But I did set it up in such a way that freshmen and sophomores 16:20.077 --> 16:21.177 get first crack. 16:21.178 --> 16:25.658 The way that's going to work is the online sectioning form opens 16:25.659 --> 16:29.569 up on Monday and juniors and seniors won't be allowed to 16:29.571 --> 16:33.271 officially register for the class until Tuesday. 16:33.269 --> 16:36.419 So, the freshmen and sophomores get to fill up the sections 16:36.416 --> 16:36.846 first. 16:36.850 --> 16:38.580 My guess is, again, looking at the number of 16:38.578 --> 16:40.628 people here today that we won't have any problem, 16:40.629 --> 16:46.979 and that if you're a junior or a senior you'll get in just 16:46.980 --> 16:47.760 fine. 16:47.759 --> 16:50.979 So, we'll be picking sections through what is now the standard 16:50.975 --> 16:53.605 online sectioning thing, which is going to open for 16:53.610 --> 16:54.930 business next Monday. 16:54.928 --> 16:58.388 I'll check the website and see if that's actually what you 16:58.394 --> 17:01.134 meant, but it may have been something else. 17:01.129 --> 17:01.569 Other questions? 17:01.570 --> 17:07.460 17:07.460 --> 17:10.240 Let me, in general, encourage you to ask questions. 17:10.240 --> 17:13.230 I know that that's hard to do in a big lecture setting, 17:13.230 --> 17:15.610 but we have an advantage over other courses, 17:15.612 --> 17:17.442 particularly science courses. 17:17.440 --> 17:21.630 We're not trying to prepare you for the astronomy part of the 17:21.628 --> 17:25.468 MCATs, so we don't have to cover a specific syllabus. 17:25.470 --> 17:28.750 We're not even trying to follow a textbook. 17:28.750 --> 17:32.360 And so we have a little more leeway than is ordinarily true 17:32.356 --> 17:36.276 to ask questions and go in weird directions, so please feel free 17:36.276 --> 17:37.206 to do that. 17:37.210 --> 17:41.060 I reserve the right to put a question off into the future or 17:41.056 --> 17:44.706 into discussion section or something, but do by all means 17:44.708 --> 17:45.228 ask. 17:45.230 --> 17:46.840 We have some freedom of action. 17:46.839 --> 17:48.079 Yes? 17:48.078 --> 17:50.018 Student: Is it possible to take an early 17:50.021 --> 17:50.361 final? 17:50.359 --> 17:52.919 Prof: An early final? 17:52.920 --> 17:53.880 Let me think about that. 17:53.880 --> 17:56.890 I prefer to avoid it because then I have to invent another 17:56.886 --> 17:57.306 final. 17:57.308 --> 18:01.168 The problem with that is trying to make them come out even. 18:01.170 --> 18:03.650 I will say this, that if I do an early final, 18:03.653 --> 18:06.933 I'm probably going to err on the side of making it hard. 18:06.930 --> 18:10.590 But it's very hard to make them come out even, 18:10.588 --> 18:13.028 but let me think about that. 18:13.029 --> 18:16.289 Other questions? 18:16.289 --> 18:17.259 Yes. 18:17.259 --> 18:18.599 Student: In discussion sections, 18:18.596 --> 18:20.666 is it just going to be like discussing things or is it going 18:20.672 --> 18:22.012 to be working on the problem sets? 18:22.009 --> 18:23.839 Prof: It's going to be some--So, the question is, 18:23.835 --> 18:25.655 "What are the discussions sections going to be like?" 18:25.660 --> 18:28.230 Are there going to be discussion of the problem sets 18:28.234 --> 18:31.114 or is it going to sort of general discussion of the course 18:31.113 --> 18:31.773 material? 18:31.769 --> 18:33.749 The answer is both. 18:33.750 --> 18:36.450 I think there will be both, in any given discussion 18:36.452 --> 18:39.592 section, there will probably both be an opportunity to talk 18:39.587 --> 18:42.887 about the previous problem set and to clarify things about the 18:42.885 --> 18:45.985 next problem set, and also some kind of activity 18:45.987 --> 18:49.447 that sort of extends and advances what we've been talking 18:49.454 --> 18:50.574 about in class. 18:50.568 --> 18:52.158 So, I'm hoping to do some of both. 18:52.160 --> 18:55.940 If we veer too much in either one direction that's probably 18:55.941 --> 18:57.181 not a good thing. 18:57.180 --> 18:59.690 There will be other ways of getting help as well, 18:59.690 --> 19:02.670 if you start to have trouble on the problem sets or in the 19:02.671 --> 19:03.771 course generally. 19:03.769 --> 19:05.529 I'll talk about those a little bit on Thursday. 19:05.529 --> 19:06.759 Yes sir? 19:06.759 --> 19:08.379 Student: How are problem sets graded? 19:08.380 --> 19:10.600 Prof: How are problem sets graded? 19:10.599 --> 19:12.249 Very carefully. 19:12.250 --> 19:17.520 Let's see, I think we'll probably--it'll probably be on a 19:17.517 --> 19:21.277 kind of zero to twenty-point schedule. 19:21.278 --> 19:23.608 But let me say this about the problem sets. 19:23.608 --> 19:25.838 There are going to be two kinds of things on the problem sets. 19:25.838 --> 19:29.218 One are kind of quantitative problems which have a right 19:29.217 --> 19:29.767 answer. 19:29.769 --> 19:33.029 Those are relatively easy to grade on some kind of a point 19:33.031 --> 19:36.131 scale; you give partial credit and so 19:36.133 --> 19:36.753 forth. 19:36.750 --> 19:39.660 But we will also--because this is a course that's not only 19:39.657 --> 19:42.567 about the specific of this topic but also about science in 19:42.567 --> 19:44.707 general, we're also going to have things 19:44.705 --> 19:47.655 that look kind of like essay questions on the problem sets. 19:47.660 --> 19:50.040 Those are a little harder to grade in this way, 19:50.037 --> 19:53.187 but we've got to grade them in the same way so that we can add 19:53.189 --> 19:54.119 the points up. 19:54.118 --> 19:57.178 And I'll talk a little bit more about how those are graded. 19:57.180 --> 20:01.030 I will say one thing; one thing that we do is we make 20:01.032 --> 20:05.832 sure that each problem or essay is graded by one T.A. 20:05.828 --> 20:08.108 or by myself, so that we don't have different 20:08.105 --> 20:11.255 people--so that if you're in a section it's not like your--all 20:11.261 --> 20:14.111 the problem sets for that section are all graded by your 20:14.107 --> 20:17.107 section leader and some other section leader grades all the 20:17.108 --> 20:19.578 other problems, because that leads to 20:19.576 --> 20:21.336 imbalances of various kinds. 20:21.338 --> 20:25.718 So, we assign each problem to a specific person for the whole 20:25.715 --> 20:26.295 class. 20:26.298 --> 20:28.948 It's basically a zero through twenty scale, 20:28.951 --> 20:32.611 although what that means varies depending on what kind of a 20:32.613 --> 20:33.753 problem it is. 20:33.750 --> 20:35.360 I'll say a little bit more about that. 20:35.358 --> 20:38.798 I will also say there is a rather detailed lateness policy 20:38.799 --> 20:42.179 that's linked to the classes server, please read that. 20:42.180 --> 20:44.310 We're going to stick to it. 20:44.308 --> 20:47.258 And one of the features of that is that there will be answer 20:47.259 --> 20:47.709 sheets. 20:47.710 --> 20:49.980 Problem sets are typically due Thursday, there will be an 20:49.979 --> 20:51.599 answer sheet up the following Tuesday, 20:51.598 --> 20:55.808 so if you don't get it done by five days after it's due, 20:55.814 --> 20:59.344 you're toast because the answers are posted. 20:59.339 --> 21:00.009 Other questions? 21:00.009 --> 21:03.809 21:03.809 --> 21:06.499 Great, let's start. 21:06.500 --> 21:09.080 This is very cool. 21:09.078 --> 21:15.218 All right, this is going to be all kinds of fun. 21:15.220 --> 21:18.290 21:18.288 --> 21:22.138 Planets, planets around other stars, but planets in general. 21:22.140 --> 21:25.320 So, let's start by talking a little bit about orbits, 21:25.317 --> 21:26.477 planetary orbits. 21:26.480 --> 21:35.140 21:35.140 --> 21:38.950 You probably know some of this story, originally in the old 21:38.951 --> 21:43.031 days, people used to think that the Earth was the center of the 21:43.025 --> 21:43.875 Universe. 21:43.880 --> 21:48.140 So, the Earth was at the middle and planets went around them in 21:48.142 --> 21:48.832 circles. 21:48.828 --> 21:50.698 That's not much of a circle [drawing on overhead], 21:50.699 --> 21:51.729 but you know what I mean. 21:51.730 --> 21:55.520 And so, everything was circles around the Earth. 21:55.519 --> 22:00.309 And that's what planets did, where planets also included to 22:00.307 --> 22:04.257 their way of thinking, the Sun and the Moon as well, 22:04.261 --> 22:07.461 and so you had these circles around the Earth. 22:07.460 --> 22:10.720 This is what's called the geocentric model; 22:10.720 --> 22:12.170 Earth at the middle. 22:12.170 --> 22:16.950 It's associated with the name of a Greek astronomer named 22:16.945 --> 22:17.795 Ptolemy. 22:17.798 --> 22:20.878 The problem with this model is very simple. 22:20.880 --> 22:23.700 Namely, that if you actually go out and observe where the 22:23.701 --> 22:26.701 planets, and the Sun, and the Moon are night after 22:26.701 --> 22:29.661 night after night it doesn't work very well. 22:29.660 --> 22:33.150 So, this doesn't fit the observations. 22:33.150 --> 22:35.860 Doesn't fit observations. 22:35.858 --> 22:38.048 So, they said, all right well maybe that 22:38.045 --> 22:41.235 doesn't work all that well, so what we'll do is instead of 22:41.239 --> 22:44.769 imagining that the planets are on circles around the Earth, 22:44.769 --> 22:48.139 we'll imagine that there are circles on circles around the 22:48.141 --> 22:50.331 Earth, and the planets go on those. 22:50.328 --> 22:54.378 So, you add a kind of extra circle here, so the circle goes 22:54.380 --> 22:58.640 around the Earth and the planet goes around on that circle. 22:58.640 --> 23:01.520 These circles were called epicycles. 23:01.519 --> 23:07.369 So, add epicycles. 23:07.368 --> 23:11.008 And what happened is they would add an epicycle and then they'd 23:11.009 --> 23:13.659 go out and observe some more, and in particular, 23:13.655 --> 23:15.625 the Arab astronomers a thousand years ago. 23:15.630 --> 23:21.760 A thousand years ago the center of all science was in the Arab 23:21.762 --> 23:25.172 countries; they gave us all their--all our 23:25.172 --> 23:29.082 star names by the way are in Arabic, so are mathematical 23:29.077 --> 23:32.897 techniques such as algebra; it all comes from the Arabs. 23:32.900 --> 23:36.460 They knew what they were doing back then when the Europeans 23:36.461 --> 23:38.061 were kind of in squalor. 23:38.058 --> 23:40.398 And they made these great observations, 23:40.404 --> 23:43.984 and every time they made more observations it turned out it 23:43.983 --> 23:44.913 didn't fit. 23:44.910 --> 23:46.770 So, they had to add more epicycles. 23:46.769 --> 23:49.209 So then, they added one here, and one here, 23:49.211 --> 23:51.191 and so on until you had circles, 23:51.190 --> 23:52.820 and circles, and circles, 23:52.820 --> 23:56.290 and circles in order to explain the observations. 23:56.289 --> 24:00.199 So, add epicycles repeatedly. 24:00.200 --> 24:03.360 And this is kind of unsatisfying because it's not a 24:03.361 --> 24:07.281 good thing where every time you get more or better observations 24:07.280 --> 24:10.190 you have to revise and extend your theory. 24:10.190 --> 24:12.030 That's not such a great theory. 24:12.028 --> 24:14.898 In fact, the word epicycles has now become a kind of a swear 24:14.903 --> 24:16.613 word in the scientific community, 24:16.608 --> 24:20.058 meaning a sort of theory that has become so complex it's just 24:20.061 --> 24:23.171 ridiculous and you don't want to believe it anymore. 24:23.170 --> 24:26.080 So, someone will come up with some really seemingly 24:26.078 --> 24:29.048 sophisticated but very complicated theory and if you 24:29.047 --> 24:32.187 don't like that you just go that's just epicycles, 24:32.190 --> 24:36.030 forget about it. 24:36.029 --> 24:41.099 So, this has become a little bit of a swear word, 24:41.102 --> 24:45.332 and it was unsatisfactory at the time. 24:45.328 --> 24:48.738 Now, let me pause for a moment and confess that the story I've 24:48.736 --> 24:52.096 just told you, which is the standard story 24:52.098 --> 24:57.038 about Ptolemaic epicycles is, well, it has what I think 24:57.038 --> 25:00.878 Colbert would refer to as "truthiness." 25:00.880 --> 25:04.150 It's a commonly told story that people like to believe, 25:04.146 --> 25:07.406 but if you talk to the historians of science this isn't 25:07.414 --> 25:09.174 actually how it happened. 25:09.170 --> 25:11.280 And, in fact, this idea of circles on 25:11.284 --> 25:14.694 circles, on circles that isn't the way epicycles worked, 25:14.690 --> 25:18.610 they had circles and they did get more complicated every time 25:18.609 --> 25:22.269 they fit the observations, but not by adding more and more 25:22.269 --> 25:22.799 circles. 25:22.798 --> 25:24.878 They would move the circles side to side, 25:24.876 --> 25:27.836 they would have things going at variable speeds around the 25:27.837 --> 25:30.297 circle, all sorts of things but this 25:30.298 --> 25:33.878 little picture that I've just drawn here has a kind of 25:33.875 --> 25:35.355 "truthiness" to it. 25:35.358 --> 25:38.968 I would say that this is a general issue with the way 25:38.965 --> 25:41.735 scientists describe how science works. 25:41.740 --> 25:45.500 We tell these nice anecdotes and we put them in the textbooks 25:45.502 --> 25:47.612 too; in the little bars that go down 25:47.606 --> 25:50.446 the side of the textbook, where you get the head and 25:50.449 --> 25:53.739 shoulder shot of the famous dead white male scientist and so 25:53.737 --> 25:54.347 forth. 25:54.349 --> 25:57.169 And then we tell these stories. 25:57.170 --> 26:00.880 And the historians of science hate this because it isn't 26:00.875 --> 26:02.555 actually what happened. 26:02.558 --> 26:04.258 Nevertheless, we persist in telling these 26:04.259 --> 26:06.469 stories, and I've been thinking about why that is. 26:06.470 --> 26:11.430 I think the way to think about this is what these stories are, 26:11.432 --> 26:12.492 are fables. 26:12.490 --> 26:16.550 And like any fable, the point is not that the story 26:16.548 --> 26:17.358 is true. 26:17.358 --> 26:20.758 The point is that it vividly illustrates a moral, 26:20.758 --> 26:25.078 which tells you how to behave or how not to behave and they're 26:25.077 --> 26:26.987 useful for that reason. 26:26.990 --> 26:30.110 You'll recall the famous fable of the ant and the grasshopper. 26:30.108 --> 26:33.008 Grasshopper sings and plays and dances all summer long. 26:33.009 --> 26:35.009 The ant is very industrious, piles up food, 26:35.012 --> 26:36.112 doesn't have any fun. 26:36.108 --> 26:39.838 But then in the winter, the grasshopper starves and the 26:39.843 --> 26:40.953 ant does fine. 26:40.950 --> 26:44.570 If an entomologist were to come along and say but that's not how 26:44.568 --> 26:48.038 ants and grasshoppers behave, you would correctly say that 26:48.038 --> 26:49.788 he's missed the whole point. 26:49.788 --> 26:53.138 And the point is that it's just a nice story which illustrates 26:53.144 --> 26:56.504 certain kinds of behaviors and whether they're good or bad. 26:56.500 --> 26:59.320 So, here's what I'm going to do; I'm going to tell these 26:59.317 --> 27:02.847 stories, but I'm going to label them fables and I'm going to 27:02.852 --> 27:04.952 point out the morals explicitly. 27:04.950 --> 27:08.730 And the optional paper is going to be: go and take any one of 27:08.730 --> 27:12.320 these things and find out what really happened and comment 27:12.319 --> 27:16.289 somewhat on the implications of the real story for science. 27:16.288 --> 27:21.088 I should say that the biggest of these fables is probably the 27:21.088 --> 27:24.608 one about Galileo and the Catholic Church, 27:24.608 --> 27:28.148 where the Catholic Church oppresses the pioneering 27:28.151 --> 27:32.201 scientist and the scientist stands firm against this huge 27:32.198 --> 27:35.398 impersonal bureaucracy, and the establishment trying to 27:35.400 --> 27:36.490 squelch them and so forth. 27:36.490 --> 27:39.840 The truth of that is actually very subtle and very interesting 27:39.837 --> 27:42.557 and I can't go into it now, among other things because I'm 27:42.564 --> 27:44.764 not a historian of science, I'm not the best person to talk 27:44.756 --> 27:47.146 about it, but check that out sometime. 27:47.150 --> 27:54.810 Anyway, for this particular--this is the fable of 27:54.814 --> 28:04.394 the Ptolemaic epicycles and the moral is that simple theories 28:04.394 --> 28:06.794 are better. 28:06.789 --> 28:10.099 28:10.098 --> 28:13.868 And you particularly don't like theories which get more and more 28:13.874 --> 28:17.114 complicated, the better and better your data become. 28:17.108 --> 28:20.018 I should say that the word simple in there turns out to 28:20.015 --> 28:23.185 have a technical meaning if you take a statistics course. 28:23.190 --> 28:26.850 What I mean by simple is something that has relatively 28:26.849 --> 28:28.369 few free parameters. 28:28.369 --> 28:30.239 I'll just leave that at that. 28:30.240 --> 28:33.590 You can go talk to the statisticians about it. 28:33.588 --> 28:37.368 So, if your theory is getting overwhelmed by epicycles, 28:37.365 --> 28:41.415 then you'd better go out and come up with some other better 28:41.420 --> 28:42.190 theory. 28:42.190 --> 28:46.010 And so, people tried to do that, and the first step along 28:46.007 --> 28:48.527 the way was, of course, Copernicus. 28:48.529 --> 28:52.259 Copernicus, as you probably recall, decides that the 28:52.259 --> 28:55.479 geocentric model is wrong, things ought to be 28:55.476 --> 28:58.426 heliocentric; the Sun in the middle. 28:58.430 --> 29:01.310 So, you put the Sun in the middle and everything, 29:01.314 --> 29:04.564 including the Earth, goes in circles around the Sun. 29:04.559 --> 29:07.679 29:07.680 --> 29:10.070 This was revolutionary, and in fact, 29:10.067 --> 29:12.997 the title of the book he published was De 29:13.001 --> 29:15.801 Revolutionibus Orbium Coelestium, 29:15.798 --> 29:18.948 which means "of the revolutions" in the sense of 29:18.952 --> 29:21.572 "revolving of the celestial spheres." 29:21.568 --> 29:25.818 The use of that word revolution is one of the things that pushed 29:25.821 --> 29:28.861 the word revolution to its current meaning, 29:28.858 --> 29:31.818 meaning overthrowing authority in some ways. 29:31.818 --> 29:35.788 Originally, it just meant to revolve but this was so 29:35.785 --> 29:40.055 revolutionary that people started to use the word in the 29:40.060 --> 29:41.150 other way. 29:41.150 --> 29:44.390 This wasn't actually as great a theory as you might think, 29:44.392 --> 29:46.442 because it still needed epicycles. 29:46.440 --> 29:53.270 Not as big, not as many, but it didn't get rid of the 29:53.273 --> 29:56.563 problem with epicycles. 29:56.558 --> 30:00.898 And that didn't work itself out until a generation or two later 30:00.900 --> 30:02.650 when Kepler came along. 30:02.650 --> 30:06.330 Kepler was a famous astronomer and he had in his possession, 30:06.325 --> 30:11.825 because he stole them, the best naked-eye results that 30:11.827 --> 30:18.807 had ever been obtained of the motions of the planets, 30:18.809 --> 30:20.279 in particular, Mars. 30:20.278 --> 30:29.218 He described these motions in Three Laws of Planetary Motion. 30:29.220 --> 30:31.160 You can look them all up in a textbook. 30:31.160 --> 30:33.960 In other kinds of courses we would have you memorize these 30:33.958 --> 30:35.548 things; I'm not going to do that. 30:35.548 --> 30:38.788 The key point here is that these are not circles; 30:38.789 --> 30:42.329 they're ellipses around the Sun. 30:42.328 --> 30:45.848 That, it turns out, gives you a model for planetary 30:45.851 --> 30:48.951 orbits which, when you take better and better 30:48.949 --> 30:50.709 data, doesn't change. 30:50.710 --> 30:53.280 They're still ellipses; you don't need little ellipses 30:53.281 --> 30:56.381 on top of these ellipses to explain everything that's going 30:56.378 --> 30:56.698 on. 30:56.700 --> 30:59.110 So, this now has excellent descriptive power. 30:59.109 --> 31:03.799 31:03.798 --> 31:06.308 It really describes what's going on, and when you make 31:06.311 --> 31:08.781 further observations, it still describes what's going 31:08.778 --> 31:09.108 on. 31:09.108 --> 31:12.488 It does not have any explanatory power in the sense 31:12.490 --> 31:14.790 that if you say, "why ellipses?" 31:14.789 --> 31:16.469 Kepler had no idea. 31:16.470 --> 31:18.630 That's just the way God made it. 31:18.630 --> 31:24.840 So, it's not in any particular way an explanation. 31:24.838 --> 31:27.788 For the explanation you have to wait another generation or two 31:27.794 --> 31:28.864 until we get Newton. 31:28.859 --> 31:32.889 31:32.890 --> 31:36.940 Newton writes down three laws of his own, but these are now 31:36.944 --> 31:40.024 three laws of motion, not planetary motion in 31:40.020 --> 31:41.070 particular. 31:41.068 --> 31:43.378 And again, one could write these down and memorize them and 31:43.377 --> 31:45.167 learn them, and that would be a good thing. 31:45.170 --> 31:48.340 Let me write down one of them, the Second Law, 31:48.337 --> 31:50.937 looks like this: F = ma, 31:50.942 --> 31:53.832 force equals mass times acceleration. 31:53.828 --> 31:58.218 And I write this one down simply to point out that that 31:58.217 --> 32:01.867 equation is the entire intellectual content of 32:01.874 --> 32:05.454 Introductory Physics for physics majors. 32:05.450 --> 32:09.470 If you go take Physics 180 this is all that they do and they 32:09.471 --> 32:11.041 spend the whole time. 32:11.038 --> 32:12.878 It turns out you don't actually want acceleration, 32:12.875 --> 32:14.595 that doesn't tell you what you want to know. 32:14.598 --> 32:17.038 What you want to know is the trajectory, where the object is 32:17.038 --> 32:18.028 as a function of time. 32:18.028 --> 32:20.768 Those of you who have taken some calculus may recall that if 32:20.769 --> 32:24.069 you take the acceleration, and you take an integral twice, 32:24.069 --> 32:27.619 you'd come up with the position as a function of time. 32:27.618 --> 32:30.198 So here's what--so in the next thirty seconds I'm going to 32:30.198 --> 32:31.508 explain Physics 180 to you. 32:31.509 --> 32:35.089 You substitute in some kind of a force, you divide by mass, 32:35.090 --> 32:37.870 you take two integrals, and that gives you the 32:37.869 --> 32:39.599 trajectory of the thing. 32:39.599 --> 32:40.779 That's all you need to know. 32:40.779 --> 32:43.389 Technically, of course, it's quite hard, 32:43.394 --> 32:46.284 but conceptually pretty straight-forward. 32:46.279 --> 32:49.459 One of the things that Newton did with this equation was he 32:49.455 --> 32:53.225 took a particular force, namely the force of gravity, 32:53.226 --> 32:56.826 which he also wrote down a Law of Gravity. 32:56.828 --> 33:00.418 That tells you for any given situation what the force due to 33:00.419 --> 33:02.669 gravity is, substituted it in here, 33:02.670 --> 33:05.870 and figured out what the motions of the planets ought to 33:05.868 --> 33:06.158 be. 33:06.160 --> 33:12.430 And it turns out that he could derive Kepler's Laws. 33:12.430 --> 33:17.500 He derives Kepler's Laws. 33:17.500 --> 33:19.150 Very nice. 33:19.150 --> 33:21.810 Now, of course, in order to do this he has to 33:21.808 --> 33:24.588 invent calculus, so it takes a little while. 33:24.588 --> 33:27.308 He was a great genius but even so, inventing calculus from 33:27.309 --> 33:29.839 scratch, not something you want to attempt at home. 33:29.839 --> 33:33.089 33:33.088 --> 33:37.928 And that was basically the start of both modern science and 33:37.928 --> 33:39.678 modern mathematics. 33:39.680 --> 33:43.070 So, this marks the start of science in the following 33:43.074 --> 33:47.074 sense--that Newton has to make a couple assumptions along the 33:47.067 --> 33:49.277 way, sort of deep assumptions about 33:49.281 --> 33:50.461 how the world works. 33:50.460 --> 33:55.090 One is that the Universe is governed by laws, 33:55.094 --> 33:58.574 and in fact, by universal laws. 33:58.568 --> 34:01.788 What I mean by universal, in this sense, 34:01.788 --> 34:06.118 is that they apply everywhere; that the same law of gravity 34:06.116 --> 34:09.666 that resulted in the top of my pen falling to the floor over 34:09.673 --> 34:13.173 there also is responsible for the orbits of the planets and 34:13.170 --> 34:14.980 the motions of the stars. 34:14.980 --> 34:17.130 This was a new idea. 34:17.130 --> 34:20.370 It's very familiar to us by now, but the idea that the 34:20.369 --> 34:23.609 planets ought to behave according to the same rules as 34:23.610 --> 34:26.850 stuff down here on Earth was a whole new concept. 34:26.849 --> 34:29.539 The other piece of the new concept is that these laws are 34:29.539 --> 34:30.739 mathematical in nature. 34:30.739 --> 34:34.269 34:34.268 --> 34:38.048 This is why science is hard, because it's hard for human 34:38.050 --> 34:38.670 beings. 34:38.670 --> 34:41.170 I think it's something to do with the way our brains are 34:41.168 --> 34:42.848 wired, to accept that this is true. 34:42.849 --> 34:45.629 It's very easy to imagine a world in which that's not true. 34:45.630 --> 34:47.950 Go read any fantasy novel. 34:47.949 --> 34:51.589 Any fantasy novel has a situation where the hero or the 34:51.590 --> 34:55.570 villain, by virtue of their strength of character influences 34:55.568 --> 34:57.388 the events around them. 34:57.389 --> 34:59.899 So that is a rule governed by laws, perhaps, 34:59.904 --> 35:03.354 that are not mathematical in nature, but depend on the moral 35:03.353 --> 35:05.813 character of the individuals involved. 35:05.809 --> 35:09.299 Every human culture has such stories including our own. 35:09.300 --> 35:12.670 It's very hard to get away from it, and the idea that there's 35:12.672 --> 35:15.992 just this sort of mathematical structure and that your moral 35:15.989 --> 35:19.529 stature has no bearing on what's going to happen is kind of hard 35:19.530 --> 35:20.430 to accept. 35:20.429 --> 35:22.629 Fortunately, people turn out to be pretty 35:22.630 --> 35:25.000 good at math, so we can actually solve these 35:24.998 --> 35:26.648 problems and move forward. 35:26.650 --> 35:31.050 These two ideas were revolutionary and they are the 35:31.054 --> 35:34.144 basis pretty much of all science. 35:34.139 --> 35:38.209 So then Newton's laws get elaborated on for several 35:38.211 --> 35:39.191 centuries. 35:39.190 --> 35:43.480 By the end of the nineteenth century things are starting to 35:43.483 --> 35:45.413 come apart a little bit. 35:45.409 --> 35:51.639 There are now problems that show up with Newtonian physics. 35:51.639 --> 35:54.699 It's been a big success on the whole but there are now 35:54.695 --> 35:55.325 problems. 35:55.329 --> 36:03.669 And in the early twentieth century what happens is two new 36:03.672 --> 36:08.212 laws of physics are invented. 36:08.210 --> 36:15.590 These are the given the names quantum mechanics and general 36:15.594 --> 36:17.254 relativity. 36:17.250 --> 36:22.340 And the situation with these is they don't overturn Newton's 36:22.335 --> 36:24.485 laws, they extend them. 36:24.489 --> 36:27.859 It turns out that in the kinds of situations that Newton was 36:27.862 --> 36:30.442 looking at, both quantum mechanics and general 36:30.436 --> 36:33.006 relativity, reduced down to Newton's law. 36:33.010 --> 36:36.490 So, you have a situation where here are Newton's laws, 36:36.487 --> 36:39.897 Ns Laws, of which Kepler's laws are a tiny subset. 36:39.900 --> 36:45.450 And then general relativity; I'm drawing a kind of Venn 36:45.447 --> 36:48.727 diagram here, is here, relativity, 36:48.733 --> 36:54.213 occupying Newton's laws but that's some other stuff. 36:54.210 --> 36:57.240 Quantum mechanics looks kind of like this; 36:57.239 --> 37:00.319 37:00.320 --> 37:02.550 extends in a different direction. 37:02.550 --> 37:04.940 Let me make these axes-specific. 37:04.940 --> 37:07.750 I don't like Venn diagrams when they don't tell you what you're 37:07.751 --> 37:08.661 actually plotting. 37:08.659 --> 37:11.479 This is mass, so heavy things are when 37:11.481 --> 37:13.161 relativity kicks in. 37:13.159 --> 37:16.359 This is size, and so small things are when 37:16.358 --> 37:18.618 quantum mechanics kicks in. 37:18.619 --> 37:20.109 But you can see the problem. 37:20.110 --> 37:22.130 We've got two big theories. 37:22.130 --> 37:26.350 You really want those theories to be encompassed by one yet 37:26.353 --> 37:27.523 bigger theory. 37:27.518 --> 37:30.248 And that is the current goal of theoretical physics, 37:30.253 --> 37:33.313 to try and find the one great theory that encompasses both 37:33.307 --> 37:35.717 quantum mechanics and general relativity, 37:35.719 --> 37:38.249 which contradict each other in various awkward ways, 37:38.251 --> 37:40.141 particularly in this region up here. 37:40.139 --> 37:46.789 This is called the Theory of Everything, or TOE. 37:46.789 --> 37:49.809 And the best current guess as to what kind of a theory that 37:49.811 --> 37:52.731 will be is that it will be some kind of string theory. 37:52.730 --> 37:56.070 I won't go into string theories now, you can go read many 37:56.068 --> 37:58.858 popular books on this; it's very exciting. 37:58.860 --> 38:02.250 There is currently no string theory that really works out all 38:02.250 --> 38:05.870 that well but the people who are studying this kind of thing like 38:05.867 --> 38:09.707 to believe that that's going to work out sometime in the future. 38:09.710 --> 38:11.220 This is good. 38:11.219 --> 38:16.729 We've gone about forty minutes from the start of science to the 38:16.731 --> 38:20.111 Theory of Everything, so we're done. 38:20.110 --> 38:25.740 Everything else is a detail and so the whole rest of the course 38:25.739 --> 38:27.919 is filling in details. 38:27.920 --> 38:33.440 The first of which--so let's start on the details. 38:33.440 --> 38:36.790 The first of which, I want to go back and catch one 38:36.786 --> 38:38.056 of Kepler's Laws. 38:38.059 --> 38:49.139 And I want to write down the Newtonian Modification of 38:49.139 --> 38:53.529 Kepler's Third Law. 38:53.530 --> 38:58.960 That is an equation that looks like this: a^(3) = 38:58.963 --> 39:04.993 GMP^(2)/4 π^(2 ) We're going to circle this in red. 39:04.989 --> 39:08.239 This is something you're going to want to memorize. 39:08.239 --> 39:11.169 This, it turns out to be, a basis of a large fraction of 39:11.168 --> 39:13.298 what we're going to do in this course. 39:13.300 --> 39:21.580 So, let me explain the symbols; a is the semi-major axis 39:21.577 --> 39:26.937 of an elliptical orbit. 39:26.940 --> 39:31.510 39:31.510 --> 39:33.570 Remember these orbits are going to be ellipses; 39:33.570 --> 39:34.360 here's an ellipse. 39:34.360 --> 39:38.430 The long side is the major axis; the short side is the minor 39:38.425 --> 39:38.805 axis. 39:38.809 --> 39:43.779 Half the major axis is the semi-major axis, 39:43.777 --> 39:47.677 so this is a right here. 39:47.679 --> 39:53.849 P is the orbital period, how long it takes the planet or 39:53.849 --> 39:59.919 whatever orbiting object you've got to go around one orbit. 39:59.920 --> 40:06.110 M is the total mass of the two things in orbit around 40:06.114 --> 40:10.004 each other, of the orbiting bodies. 40:10.000 --> 40:12.590 And the existence of that M is why this is Newton's 40:12.588 --> 40:13.268 modification. 40:13.268 --> 40:15.968 In Kepler's law, it was always planets going 40:15.969 --> 40:18.539 around the Sun, so the mass was always the 40:18.543 --> 40:21.003 same; the mass was that of the Sun 40:21.001 --> 40:22.691 and so it cancelled out. 40:22.690 --> 40:25.830 In general, you can use the same equation to deal with 40:25.831 --> 40:29.391 things orbiting the Earth or things orbiting the Moon as long 40:29.387 --> 40:31.697 as you put in the right mass there. 40:31.699 --> 40:35.829 G is a constant of nature, the gravitational 40:35.829 --> 40:40.539 constant, and it equals some value depending on what units 40:40.538 --> 40:41.528 you use. 40:41.530 --> 40:43.590 And we'll come back to that later. 40:43.590 --> 40:49.080 Four is 4, π is this obscure number from elementary 40:49.079 --> 40:54.029 mathematics 3.14159 whatever the heck it is. 40:54.030 --> 40:58.380 And you can punch it in on your calculator or whatever. 40:58.380 --> 41:02.990 So, you can use this equation to find things out. 41:02.989 --> 41:06.139 Now, these numbers tend to be awkward to work with. 41:06.139 --> 41:10.619 The mass of the Sun is some huge number of kilograms, 41:10.623 --> 41:15.543 G is a very awkward number, π is always a mess. 41:15.539 --> 41:17.819 But let me show you a trick. 41:17.820 --> 41:19.370 Consider the Earth's orbit around the Sun. 41:19.369 --> 41:24.209 41:24.210 --> 41:30.880 The semi-major axis of the Earth's orbit is a very common 41:30.880 --> 41:36.720 unit in astronomy, and it's called an Astronomical 41:36.717 --> 41:37.787 Unit. 41:37.789 --> 41:44.739 It's a unit of length, or AU. 41:44.739 --> 41:48.089 The mass of the Sun, mass of the Earth plus the Sun 41:48.086 --> 41:52.026 is mostly the mass of the Sun; of Sun, is called the solar 41:52.030 --> 41:54.770 mass obviously, and it's given this symbol 41:54.766 --> 41:57.896 M with a little circle with a dot inside, 41:57.904 --> 42:00.244 that's the symbol for the Sun. 42:00.239 --> 42:04.099 What's the orbital period of the Earth? 42:04.099 --> 42:05.899 A year, thank you very much. 42:05.900 --> 42:09.710 Period of Earth--one year. 42:09.710 --> 42:13.140 That's what a year means; it takes a year for the Earth 42:13.135 --> 42:14.805 to go around the Sun. 42:14.809 --> 42:19.449 So, it must be the case that one Astronomical Unit cubed, 42:19.454 --> 42:23.524 is equal to G times the mass of the Sun, 42:23.518 --> 42:28.308 times one year squared, that's P^(2) over 42:28.309 --> 42:29.939 π^(2). 42:29.940 --> 42:32.770 Now, let me show you a trick. 42:32.768 --> 42:38.708 Take the general equation, it's a useful trick, 42:38.706 --> 42:43.606 and divide by the specific equation. 42:43.610 --> 42:48.960 So a^(3) = P^(2)GM/ π^(2) 42:48.960 --> 42:55.590 and we're going to divide that by 1 AU^(3) equals one year 42:55.592 --> 42:59.362 squared, G mass of the Sun over 42:59.362 --> 43:00.182 4π ^(2). 43:00.179 --> 43:02.709 We can do this because these two things are equal so we're 43:02.710 --> 43:05.240 dividing both sides of the equation by the same amount. 43:05.239 --> 43:07.699 G cancels, 4π ^(2) cancels; 43:07.699 --> 43:09.029 that's very nice. 43:09.030 --> 43:14.600 We end up with a over 1 AU^(3) equals P over one 43:14.599 --> 43:18.709 year squared, M over the solar mass. 43:18.710 --> 43:23.360 This is just saying that quantity is a in units of 43:23.360 --> 43:25.270 an Astronomical Unit. 43:25.268 --> 43:28.718 This quantity is P in units of a year. 43:28.719 --> 43:31.729 If this is two years then this number will come out to 2, 43:31.731 --> 43:34.691 and this is M in units of the mass of the Sun. 43:34.690 --> 43:38.590 So, you can say a^(3) = P^(2)M, 43:38.585 --> 43:43.805 providing you're dealing in units of the mass of the Sun, 43:43.809 --> 43:51.479 units of one year, and units of an AU. 43:51.480 --> 43:53.320 So, this is now much easier to work with. 43:53.320 --> 43:56.020 You've got rid of all kinds of terrible things, 43:56.016 --> 43:59.706 so let me give you the first numerical example of the course. 43:59.710 --> 44:02.030 This will be the last thing we do today, namely, 44:02.025 --> 44:03.155 the orbit of Jupiter. 44:03.159 --> 44:06.539 44:06.539 --> 44:09.679 Turns out the distance from Jupiter to the Sun is about five 44:09.677 --> 44:12.067 times the distance of the Earth to the Sun. 44:12.070 --> 44:16.670 So, a of Jupiter is approximately five times 44:16.670 --> 44:21.770 a, a of Earth; a of Earth you'll recall 44:21.766 --> 44:24.476 is this 1 AU so this is about 5 AU. 44:24.480 --> 44:26.330 So, how does this equation work out? 44:26.329 --> 44:29.929 You get 5^(3) equals P^(2)M, 44:29.929 --> 44:35.009 M is the mass of the Sun, 1 solar mass. 44:35.010 --> 44:40.870 And since Jupiter is going around the Sun that's equal to 44:40.871 --> 44:41.291 1. 44:41.289 --> 44:46.249 So, you have 5^(3), 5 times 5 is 25,25 times 5 is 44:46.246 --> 44:51.406 125, so you end up with 125 equals P^(2), 44:51.409 --> 44:53.699 so you can answer the question now. 44:53.699 --> 44:57.319 What is the orbital period of Jupiter in years? 44:57.320 --> 45:02.590 Obviously, that's going to equal the square root of 125. 45:02.590 --> 45:04.140 Here's another trick. 45:04.139 --> 45:05.899 What's the square root of 125? 45:05.900 --> 45:08.210 Quickly? 45:08.210 --> 45:11.370 Good, more decimals? 45:11.369 --> 45:14.369 You could type it into your calculator though and find out, 45:14.367 --> 45:15.967 but let me make a suggestion. 45:15.969 --> 45:19.069 Don't take the square root of 125; 45:19.070 --> 45:21.830 take the square root of 121 instead. 45:21.829 --> 45:24.529 What's the square root of 121? 45:24.530 --> 45:25.190 11. 45:25.190 --> 45:26.820 Much easier, right? 45:26.820 --> 45:31.030 And notice this, a of Jupiter is 45:31.032 --> 45:36.802 approximately five, so 5^(3) is approximately 125, 45:36.800 --> 45:42.110 and it's just as good to say 121 is equal to the square 45:42.106 --> 45:48.936 root--the square of the period, and P equals 11 years. 45:48.940 --> 45:50.880 That's the orbital period of Jupiter. 45:50.880 --> 45:53.510 All right, so now, I'm aware that many of you are 45:53.510 --> 45:56.530 shopping the course today and may not be back for future 45:56.527 --> 45:57.237 lectures. 45:57.239 --> 46:00.189 And so, I want for those people who have decided against this 46:00.186 --> 46:03.326 that they'll do something far more worthwhile with their time, 46:03.329 --> 46:07.039 I want to leave you with something you can carry through 46:07.038 --> 46:10.948 your life from your brief experience with Astronomy 160. 46:10.949 --> 46:16.459 And that is the following piece of advice: Don't take the square 46:16.458 --> 46:20.218 root of 125, take the square root of 121. 46:20.219 --> 46:22.139 It's much easier. 46:22.139 --> 46:25.769 This is what the business people call thinking outside the 46:25.768 --> 46:26.148 box. 46:26.150 --> 46:28.850 Don't do the stupid hard thing. 46:28.849 --> 46:33.019 Do the thing that is just as good but requires some thought 46:33.018 --> 46:35.388 first in order to make it easy. 46:35.389 --> 46:41.979 So, I will leave you with that, the rest of you I'll see you on 46:41.980 --> 46:44.000 Thursday morning.