1 00:00:00,090 --> 00:00:02,490 The following content is provided under a Creative 2 00:00:02,490 --> 00:00:04,030 Commons license. 3 00:00:04,030 --> 00:00:06,330 Your support will help MIT OpenCourseWare 4 00:00:06,330 --> 00:00:10,720 continue to offer high quality educational resources for free. 5 00:00:10,720 --> 00:00:13,320 To make a donation or view additional materials 6 00:00:13,320 --> 00:00:17,280 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,280 --> 00:00:19,722 at ocw.mit.edu. 8 00:00:19,722 --> 00:00:21,930 PROFESSOR: And we've so far gotten to the point where 9 00:00:21,930 --> 00:00:23,880 we can calculate. 10 00:00:23,880 --> 00:00:31,980 So this is-- we can calculate the amount of energy. 11 00:00:34,610 --> 00:00:37,170 Remember now, we've moved beyond counts per second 12 00:00:37,170 --> 00:00:39,180 into energy per second. 13 00:00:39,180 --> 00:00:50,820 The amount of energy collected per second now is equal to-- 14 00:00:50,820 --> 00:00:52,890 we've still got the area of our collector. 15 00:00:55,560 --> 00:01:04,110 Divided by this 4 pi the distance 16 00:01:04,110 --> 00:01:16,470 from object to collector squared times-- 17 00:01:16,470 --> 00:01:21,880 and now we've got the we're going to call this 18 00:01:21,880 --> 00:01:33,330 the luminosity, and we said the luminosity is amount 19 00:01:33,330 --> 00:01:40,290 of energy emitted per second. 20 00:01:48,820 --> 00:01:50,930 Let's put this in parentheses. 21 00:01:50,930 --> 00:01:53,020 That's what this is. 22 00:01:55,700 --> 00:01:58,750 So what we can do now, if we wanted to-- we've 23 00:01:58,750 --> 00:02:02,079 got our measurement in energy per second. 24 00:02:02,079 --> 00:02:04,120 I could give you the area of the collector, which 25 00:02:04,120 --> 00:02:08,060 is just the area of the opening hole in the telescope. 26 00:02:08,060 --> 00:02:13,810 If I gave you the distance to this object, which I measured, 27 00:02:13,810 --> 00:02:17,200 I would be able to predict, from this measurement plugging 28 00:02:17,200 --> 00:02:19,480 in these values here, I would be able to predict what 29 00:02:19,480 --> 00:02:21,904 the luminosity of that bulb is. 30 00:02:21,904 --> 00:02:23,320 And that's what we're going to do. 31 00:02:23,320 --> 00:02:25,584 Luminosity is this measurement that we've 32 00:02:25,584 --> 00:02:26,500 been trying to get to. 33 00:02:26,500 --> 00:02:28,840 We wanted to turn a measurement of an image 34 00:02:28,840 --> 00:02:30,880 into a measurement of the total amount of light 35 00:02:30,880 --> 00:02:32,590 emitted by a source. 36 00:02:32,590 --> 00:02:34,330 So there it is luminosity is the amount 37 00:02:34,330 --> 00:02:38,290 of energy emitted per second from the source. 38 00:02:38,290 --> 00:02:40,180 Unfortunately, astronomers don't always 39 00:02:40,180 --> 00:02:44,470 do things in a nice, easy way that makes sense 40 00:02:44,470 --> 00:02:46,670 to the rest of us right away. 41 00:02:46,670 --> 00:02:49,960 So what they do, they don't measure the amount 42 00:02:49,960 --> 00:02:52,610 of energy collected per second. 43 00:02:52,610 --> 00:02:57,280 That is a measurement, but we want to, 44 00:02:57,280 --> 00:03:00,790 if we took the area of the collector, because look. 45 00:03:00,790 --> 00:03:06,149 This depends on our image and our collector and our detector. 46 00:03:06,149 --> 00:03:07,690 This, the area of the collector, also 47 00:03:07,690 --> 00:03:11,590 depends on the collector part of our system. 48 00:03:11,590 --> 00:03:14,740 The distance from the object to the collector, that kind of 49 00:03:14,740 --> 00:03:16,000 depends on the object. 50 00:03:16,000 --> 00:03:17,904 You know, if it's farther away, this number 51 00:03:17,904 --> 00:03:18,820 is going to be bigger. 52 00:03:18,820 --> 00:03:20,880 So the light will spread out further. 53 00:03:20,880 --> 00:03:25,090 And the luminocity is obviously a property of the object way 54 00:03:25,090 --> 00:03:26,119 out there in space. 55 00:03:26,119 --> 00:03:28,660 So what we want to do is we want to say, let's put everything 56 00:03:28,660 --> 00:03:31,060 on this side that has to do with the object, 57 00:03:31,060 --> 00:03:33,010 and put everything on this side that 58 00:03:33,010 --> 00:03:37,580 has to do with our collector and our detector. 59 00:03:37,580 --> 00:03:42,610 So what astronomers do is they divide both sides 60 00:03:42,610 --> 00:03:44,160 by the area of the collector. 61 00:03:53,580 --> 00:03:57,840 Now in this case, we can cancel out the area of the collector. 62 00:03:57,840 --> 00:04:02,860 We've just divided both sides of an equation by a number. 63 00:04:02,860 --> 00:04:07,990 And what we have over here, this is a new measurement. 64 00:04:07,990 --> 00:04:14,160 And astronomers call this flux equals, 65 00:04:14,160 --> 00:04:22,140 now we've got 1 over 4 pi times the distance 66 00:04:22,140 --> 00:04:36,920 from object squared times the luminosity. 67 00:04:41,680 --> 00:04:44,950 And the flux is just the amount of energy 68 00:04:44,950 --> 00:04:50,416 collected per second divided by the area of the collector. 69 00:04:50,416 --> 00:04:51,790 So in the same way that before we 70 00:04:51,790 --> 00:04:55,210 were talking about normalizing to the amount of time 71 00:04:55,210 --> 00:04:57,370 that you have your camera open, which 72 00:04:57,370 --> 00:04:59,590 meant that we divided by the amount of time 73 00:04:59,590 --> 00:05:01,790 that was in our exposure. 74 00:05:01,790 --> 00:05:05,860 Now, we're normalizing to the area of our collector. 75 00:05:05,860 --> 00:05:08,870 So we just divide by how many square meters, 76 00:05:08,870 --> 00:05:14,150 or how many square centimeters are there in our detector. 77 00:05:14,150 --> 00:05:18,700 So this relationship, again, whenever we have-- so 78 00:05:18,700 --> 00:05:22,390 this is important. 79 00:05:22,390 --> 00:05:25,000 This is going to be our relationship between what 80 00:05:25,000 --> 00:05:27,370 do we measure here on earth. 81 00:05:27,370 --> 00:05:34,480 So flux is what we measure or what we observe. 82 00:05:38,980 --> 00:05:41,260 Flux is what we observe. 83 00:05:41,260 --> 00:05:45,520 Luminosity and distance are properties of the object. 84 00:05:56,674 --> 00:05:57,660 OK? 85 00:05:57,660 --> 00:06:02,370 So over here on this side, we've got properties of the object. 86 00:06:02,370 --> 00:06:07,230 On this side, we've got this is what we observe. 87 00:06:17,310 --> 00:06:23,696 So let's just do a little bit of algebra together. 88 00:06:23,696 --> 00:06:24,950 Let me erase this. 89 00:06:29,150 --> 00:06:32,110 So right now, we have a relationship between something 90 00:06:32,110 --> 00:06:34,639 that we can observe, and something 91 00:06:34,639 --> 00:06:35,680 that we want to find out. 92 00:06:35,680 --> 00:06:38,560 We want to find out the luminosity of this object. 93 00:06:38,560 --> 00:06:39,640 OK? 94 00:06:39,640 --> 00:06:46,600 So if I wanted to solve this equation for this number right 95 00:06:46,600 --> 00:06:48,460 here-- 96 00:06:48,460 --> 00:06:51,560 to do a little bit of changeeroo here, 97 00:06:51,560 --> 00:06:55,450 I'm going to replace each of these words with a letter 98 00:06:55,450 --> 00:06:58,120 just so that we can see it a little bit easier. 99 00:06:58,120 --> 00:07:00,490 And I'm just going to rewrite up here, 100 00:07:00,490 --> 00:07:08,080 we're going to say flux, f, is equal to 1 divided by 4 pi 101 00:07:08,080 --> 00:07:11,640 d squared times l. 102 00:07:14,869 --> 00:07:15,368 OK? 103 00:07:18,170 --> 00:07:26,490 I can rewrite that as just f equals 1 times l is l over 4 pi 104 00:07:26,490 --> 00:07:26,990 d squared. 105 00:07:29,840 --> 00:07:37,680 If I'm measuring flux and I want to find luminosity, 106 00:07:37,680 --> 00:07:42,850 I want you, as a group, to solve this equation. 107 00:07:42,850 --> 00:07:51,930 Solve the equation for l, which means 108 00:07:51,930 --> 00:07:55,600 I want l to be alone on one side of the equation, 109 00:07:55,600 --> 00:07:57,990 and I want everything else to be on the other side. 110 00:07:57,990 --> 00:07:59,540 OK?