1 00:00:00,000 --> 00:00:03,329 . What did we see out there? 2 00:00:03,329 --> 00:00:09,746 Well, we saw that the universe around us is pretty fixed in it's shape as far as 3 00:00:09,746 --> 00:00:12,220 maintain their pattern. And then, 4 00:00:12,220 --> 00:00:15,889 we saw in addition that the entire pattern appears to rotate around us 5 00:00:15,889 --> 00:00:19,145 moving from east to west. Now, we have a modern understanding of 6 00:00:19,145 --> 00:00:22,400 all of this, of course. The modern understanding is that we live 7 00:00:22,400 --> 00:00:26,225 in a large three dimensional universe, the stars are very, very distant and 8 00:00:26,225 --> 00:00:30,049 that's why they appear not to move because they're so far away that their 9 00:00:30,049 --> 00:00:33,788 motion is irrelevant. And the reason the entire fixed universe 10 00:00:33,788 --> 00:00:38,973 appears to us to be rotating from east to west is simply that we, living on the 11 00:00:38,973 --> 00:00:44,094 earth, are rotating from west to east and so from our point of view things appear 12 00:00:44,094 --> 00:00:47,635 to be rotating. If you think everything is spinning, it's 13 00:00:47,635 --> 00:00:51,871 probably you that are. And so we live on this rotating spaceship 14 00:00:51,871 --> 00:00:57,119 earth and its daily rotation from west to east makes the universe appear to us to 15 00:00:57,119 --> 00:01:00,027 be rotating daily, from east to west. Very nice. 16 00:01:00,027 --> 00:01:04,700 We have an understanding what goes on. the picture that we see in the sky 17 00:01:04,700 --> 00:01:09,396 however, is a two dimensional picture. We do not have a good way of measuring or 18 00:01:09,396 --> 00:01:13,676 noticing the distance to stars. All stars appear to us to be essentially 19 00:01:13,676 --> 00:01:15,400 very far away. Though how far, 20 00:01:15,400 --> 00:01:18,393 will be a story that we'll have to develop later. 21 00:01:18,393 --> 00:01:23,218 Before we get there, at the level of just watching the planetarium show, that is 22 00:01:23,218 --> 00:01:26,273 the heavens, what we need to describe is direction. 23 00:01:26,273 --> 00:01:30,671 So we may as well assume that all the stars are at one very fixed large 24 00:01:30,671 --> 00:01:33,969 distance from us. In other words, they span a great big 25 00:01:33,969 --> 00:01:38,245 globe surrounding a terrestrial globe. We call it the celestial sphere. 26 00:01:38,245 --> 00:01:42,946 And the positions of the stars are fixed on the celestial sphere, because that is 27 00:01:42,946 --> 00:01:45,435 how they are. So here's Aristotle in 350 B.C. 28 00:01:45,435 --> 00:01:50,181 looking down his nose at the ancients who thought that it required gods in heaven 29 00:01:50,181 --> 00:01:54,464 to maintain the stars in their fixed positions and their regular periodic 30 00:01:54,464 --> 00:01:56,953 motion. Notice, Aristotle, there are laws of 31 00:01:56,953 --> 00:02:00,426 nature that compel the stars to do what do we see them doing. 32 00:02:00,426 --> 00:02:04,512 that is very much the spirit in which we will work, though we will try to take it 33 00:02:04,512 --> 00:02:08,231 a step further and actually understand those laws, [COUGH] comprehend them by 34 00:02:08,231 --> 00:02:11,708 making measurements down here on earth, because our laws are going to be 35 00:02:11,708 --> 00:02:13,930 universal. For Aristotle, there's a set of laws 36 00:02:13,930 --> 00:02:17,359 governing terrestrial phenomena and a completely different set of laws 37 00:02:17,359 --> 00:02:21,469 governing phenomena in the heavens. But, before we get to all of this, we 38 00:02:21,469 --> 00:02:26,642 need to describe the planetarium show. Where it is that we see which stars at 39 00:02:26,642 --> 00:02:29,061 what time? How the whole thing moves? 40 00:02:29,061 --> 00:02:33,362 And for this, we can follow the mathematical model, which is what 41 00:02:33,362 --> 00:02:37,730 Aristotle is describing, which is this picture of the stars fixed 42 00:02:37,730 --> 00:02:42,299 on this large celestial sphere. Inside this sphere, the earth rotates 43 00:02:42,299 --> 00:02:45,415 daily, from west to east or if you want, the entire 44 00:02:45,415 --> 00:02:49,877 celestial sphere rotates daily from east to west with the earth fixed inside it. 45 00:02:49,877 --> 00:02:52,220 From the point of view of lines of vision, 46 00:02:52,220 --> 00:02:56,540 well the, the celestial sphere rotates or the earth rotates inside the stationary 47 00:02:56,540 --> 00:03:01,075 celestial sphere is a matter of complete indifference that the two are completely 48 00:03:01,075 --> 00:03:03,849 equivalent. So we have the celestial sphere on which 49 00:03:03,849 --> 00:03:06,996 the stars are fixed. And what we need to get a more precise 50 00:03:06,996 --> 00:03:11,370 mathematical description of where stars are is we need to be able to label points 51 00:03:11,370 --> 00:03:15,104 on the celestial sphere, because somewhere on the celestial sphere, say 52 00:03:15,104 --> 00:03:18,945 over here is the constellation Orion, somewhere on the other side of the 53 00:03:18,945 --> 00:03:22,092 celestial sphere, say over here is the constellation Cygnus. 54 00:03:22,092 --> 00:03:25,990 You can say a star is in Orion, but if you want to be more precise than that, we 55 00:03:25,990 --> 00:03:30,633 need to say where exactly in Orion it is. We need the way of specifying positions 56 00:03:30,633 --> 00:03:35,185 on this sphere or directions in the sky. Luckily, we know very well how to 57 00:03:35,185 --> 00:03:39,613 describe positions on a sphere, because remember again, we live on a sphere. 58 00:03:39,613 --> 00:03:42,306 We use precisions on the sphere all the time. 59 00:03:42,306 --> 00:03:46,256 We specify points on earth by giving their latitude and longitude, 60 00:03:46,256 --> 00:03:50,206 those are the coordinates on the earth, reminds us what that means. 61 00:03:50,206 --> 00:03:54,935 Well, the earth, because it spins as an axis with poles where the axis meets the 62 00:03:54,935 --> 00:03:59,190 surface, a north and a south pole. Splitting the distance between them is 63 00:03:59,190 --> 00:04:03,926 this great circle of the equator and we measure latitude as the angular distance 64 00:04:03,926 --> 00:04:08,493 north or south of the equator. So that the north pole is at latitude +90 65 00:04:08,493 --> 00:04:13,203 and the south pole is latitude -90 and picking the latitude gives you a 66 00:04:13,203 --> 00:04:16,323 particular circle, a parallel, say the 38th parallel. 67 00:04:16,323 --> 00:04:21,033 If you live at the latitude at 38 north, you live somewhere along this circle. 68 00:04:21,033 --> 00:04:25,804 To specify where along the circle, we split the earth into these orange slices 69 00:04:25,804 --> 00:04:30,759 with great circles passing through the poles, those are lines of longitude or 70 00:04:30,759 --> 00:04:33,451 meridians. And if you know what parallel and 71 00:04:33,451 --> 00:04:38,100 meridian you are on, that's a street address and then you know where you are. 72 00:04:38,100 --> 00:04:43,197 Now picking those 0 of latitude is very natural, it was the equator that split 73 00:04:43,197 --> 00:04:46,846 the distance to the poles. Picking the 0 of longitude is a more 74 00:04:46,846 --> 00:04:49,886 tricky business. We know that we measure longitude from 75 00:04:49,886 --> 00:04:52,319 this particular meridian, the prime meridian. 76 00:04:52,319 --> 00:04:56,244 What makes it prime is that it passes through the Royal Observatory in 77 00:04:56,244 --> 00:04:59,683 Greenwich, England. Of course, that's a political decision 78 00:04:59,683 --> 00:05:03,991 which tells us that there is no natural way to set a 0 meridian. 79 00:05:03,991 --> 00:05:08,685 You just pick one and then you measure longitude east or west of that in 80 00:05:08,685 --> 00:05:11,900 degrees. So that say Aristotle in Athens, Greece 81 00:05:11,900 --> 00:05:16,658 is 37 point something degrees north of the equator and about 24 degrees east of 82 00:05:16,658 --> 00:05:20,001 the prime meridian that specifies where Athens lies. 83 00:05:20,001 --> 00:05:23,473 Let's review in a minute what we exactly mean by this. 84 00:05:23,473 --> 00:05:28,580 So here's a model of earth and on this model, I can add the poles, because the 85 00:05:28,580 --> 00:05:32,287 earth rotates. So I will orient the earth as we usually 86 00:05:32,287 --> 00:05:37,612 do with the north pole on top and here are two diameters through the center of 87 00:05:37,612 --> 00:05:41,252 the earth, the axis, and another perpendicular diameter. 88 00:05:41,252 --> 00:05:45,161 Here is the earth's equator, as best I can draw it. 89 00:05:45,161 --> 00:05:50,553 And we are going to place some observer at some particular point on the surface 90 00:05:50,553 --> 00:05:54,189 of the earth. And, the position of that observer is 91 00:05:54,189 --> 00:05:58,440 determined by measuring this angle, which is his latitude. 92 00:05:58,440 --> 00:06:03,353 And that determines a line of latitude, a parallel, on which the observer lives, 93 00:06:03,353 --> 00:06:07,951 but we need to specify which of the points on this parallel is the point 94 00:06:07,951 --> 00:06:12,549 occupied by our particular observer. Notice that this parallel is, in fact, 95 00:06:12,549 --> 00:06:17,462 the trajectory of the observer's motion as the earth makes its daily rotation, 96 00:06:17,462 --> 00:06:22,123 the observer who is now here, will, 12 hours later be on the other side. 97 00:06:22,123 --> 00:06:27,100 And in general, this is your trajectory as you move around the world once a day. 98 00:06:27,100 --> 00:06:32,993 And so, to specify that, of course we drew our lines of longitude, our 99 00:06:32,993 --> 00:06:41,650 meridians. We draw some meridians and pick which one 100 00:06:41,650 --> 00:06:46,585 of these you live on and that tells you where you, where along this line of 101 00:06:46,585 --> 00:06:50,269 longitude you live. Now, where you are on earth, of course, 102 00:06:50,269 --> 00:06:54,810 also determines among other things. What it is of the sky you can see? 103 00:06:54,810 --> 00:07:00,021 So, if you live at this particular point, then this roughly measures your horizon, 104 00:07:00,021 --> 00:07:05,080 you can see the part half of the sky that lies above your horizon and not the half 105 00:07:05,080 --> 00:07:08,474 that lies below it. Your horizon changes as the earth 106 00:07:08,474 --> 00:07:11,868 rotates. 12 hours later, you will see this half of 107 00:07:11,868 --> 00:07:14,750 the sky and fail to see that half of the sky. 108 00:07:14,750 --> 00:07:19,578 We have coordinates on earth. We know how to specify coordinates on a sphere. 109 00:07:19,578 --> 00:07:24,662 Let's take this to the next level and apply the same idea to design coordinates 110 00:07:24,662 --> 00:07:28,250 on a celestial sphere. So, here we have the model that I was 111 00:07:28,250 --> 00:07:31,270 describing. We have the earth sitting in the middle 112 00:07:31,270 --> 00:07:35,296 of a large celestial sphere. You could imagine that the earth is very 113 00:07:35,296 --> 00:07:38,730 small, the celestial sphere very large. Celestial sphere 114 00:07:38,730 --> 00:07:43,082 inside the celestial sphere, the earth rotates from west to east or equivalently 115 00:07:43,082 --> 00:07:45,638 the celestial sphere rotates from east to west. 116 00:07:45,638 --> 00:07:49,718 Either way extending the earth's north, south axis we find an axis for the 117 00:07:49,718 --> 00:07:52,928 relative rotation. So this is the celestial sphere like the 118 00:07:52,928 --> 00:07:55,702 earth comes equipped with a north and a south pole, 119 00:07:55,702 --> 00:07:59,674 that the north celestial pole is the point that you would see in the sky. 120 00:07:59,674 --> 00:08:02,720 If you stood at the earth's north pole and looked up straight up, 121 00:08:02,720 --> 00:08:07,126 and similarly, the celestial south pole is what you would see if you stood at the 122 00:08:07,126 --> 00:08:09,411 earth's south pole and looked straight up. 123 00:08:09,411 --> 00:08:12,730 And so, we naturally have, splitting the distance between them, 124 00:08:12,730 --> 00:08:17,065 a celestial equator which is either the set of all points that are 90 degrees 125 00:08:17,065 --> 00:08:21,287 away from either of the poles. Or, if you wish, take the earth's equator 126 00:08:21,287 --> 00:08:26,022 imagine lighting a light bulb inside that earth there and projecting the shadow of 127 00:08:26,022 --> 00:08:30,414 the equator all the way to the celestial sphere, that gives you the celestial 128 00:08:30,414 --> 00:08:33,153 equator. And once we have a celestial equator, we 129 00:08:33,153 --> 00:08:37,437 can measure the latitude of a star. Again, just as we do on earth by 130 00:08:37,437 --> 00:08:42,440 measuring the angular distance from the celestial horizon to the star, 131 00:08:42,440 --> 00:08:46,831 so that this star here is at a latitude of north 44.7 degrees. 132 00:08:46,831 --> 00:08:53,036 We call celestial latitude declination. As I move the star around the sky, its 133 00:08:53,036 --> 00:08:57,798 declination will change. Declinations south of the celestial 134 00:08:57,798 --> 00:09:03,926 equator are negative, declinations north of the celestial equator are positive. 135 00:09:03,926 --> 00:09:10,331 And, now as the Earth rotates we observe if you want as the celestial sphere 136 00:09:10,331 --> 00:09:15,991 rotates from east to west, the star will move along this line of latitude. 137 00:09:15,991 --> 00:09:21,961 And just as on earth, we need to add to the specification of declamation some 138 00:09:21,961 --> 00:09:27,156 specification of longitude. And just as on earth, we pick randomly a 139 00:09:27,156 --> 00:09:31,523 line a meridian, a projection of some meridian on earth at 140 00:09:31,523 --> 00:09:34,486 some time a circle that crosses both poles. 141 00:09:34,486 --> 00:09:39,171 We call that the 0 longitude. Celestial longitude is called right 142 00:09:39,171 --> 00:09:42,823 ascension. So this is the 0 right ascension circle. 143 00:09:42,823 --> 00:09:47,922 it is chosen so that it intersects the celestial equator and then some 144 00:09:47,922 --> 00:09:52,745 particular star, in this case, this star is in the constellation Pisces. 145 00:09:52,745 --> 00:09:58,808 And so choosing the longitude of that particular star in Pisces, we call that 0 146 00:09:58,808 --> 00:10:04,212 longitude and we measure longitude east along the celestial sphere away from 147 00:10:04,212 --> 00:10:07,346 that. So that, for example, a star might be 90 148 00:10:07,346 --> 00:10:11,051 degrees away, you'd call that celestial longitude 90 149 00:10:11,051 --> 00:10:14,257 degrees. Or if it were 90 degrees to the west, 150 00:10:14,257 --> 00:10:17,677 you'd call that celestial longitude 270 degrees. 151 00:10:17,677 --> 00:10:22,735 In a twist, celestial longitude is measured not in degrees but in hours. 152 00:10:22,735 --> 00:10:28,078 So instead of a full circle being 360 degrees, the full circle describes 24 153 00:10:28,078 --> 00:10:32,227 hours of right ascension. That means a conversion rate of 15 154 00:10:32,227 --> 00:10:35,542 degrees per hour. So that a star that is 90 degrees away 155 00:10:35,542 --> 00:10:40,455 from the prime meridian, instead of being a celestial longitude 90, will be said to 156 00:10:40,455 --> 00:10:44,276 be at right ascension 6 hours. Remember, this is quite reasonable, 157 00:10:44,276 --> 00:10:48,640 because the celestial sphere rotates from east to west, which means if you're 158 00:10:48,640 --> 00:10:51,474 looking overhead and you see the seventh meridian, 159 00:10:51,474 --> 00:10:54,478 wait an hour. In an hour, the celestial sphere rotates 160 00:10:54,478 --> 00:10:57,708 15 degrees and the eighth meridian will be overhead. 161 00:10:57,708 --> 00:11:01,845 Wait 24 hours, the celestial sphere will have completed a full 360 degree 162 00:11:01,845 --> 00:11:04,509 rotation, you'll see the seventh meridian again. 163 00:11:04,509 --> 00:11:09,099 This is why measuring right ascension in hours increasing to the east totally 164 00:11:09,099 --> 00:11:11,856 makes sense. Now, before we proceed, there's a 165 00:11:11,856 --> 00:11:17,048 technical question we would need to ask, which is, I said the celestial sphere is 166 00:11:17,048 --> 00:11:19,450 large. What do you mean by large? Well, 167 00:11:19,450 --> 00:11:24,269 the statement I want to make, is that we need the celestial sphere to be large 168 00:11:24,269 --> 00:11:27,482 enough for this model to be mathematically accurate. 169 00:11:27,482 --> 00:11:32,179 That the lines of sight from any two points on earth to a given star can be 170 00:11:32,179 --> 00:11:35,577 taken to be parallel. In other words, we can assume that 171 00:11:35,577 --> 00:11:40,150 everywhere on earth is effectively in the center of the celestial sphere. 172 00:11:40,150 --> 00:11:43,857 And so in particular if in this picture, these two points, 173 00:11:43,857 --> 00:11:49,054 say A and B, are two different points on earth and this point O is the position of 174 00:11:49,054 --> 00:11:52,062 the star. I need to imagine the two within the 175 00:11:52,062 --> 00:11:56,894 accuracy of our measurements, the line from A or from B to O are in fact 176 00:11:56,894 --> 00:12:02,107 parallel or this angle, which I shall call alpha, is smaller then anything we 177 00:12:02,107 --> 00:12:04,990 can measure. The size of the celestial sphere here, 178 00:12:04,990 --> 00:12:09,383 representing the distance from points on earth to the stars, would be represented 179 00:12:09,383 --> 00:12:13,392 in this picture by this radius R. So what I need is a relation between 180 00:12:13,392 --> 00:12:19,263 distances and angles and the relation is going to be something we are going to use 181 00:12:19,263 --> 00:12:23,650 repeatedly in the class. So let's develop it and understand it. 182 00:12:23,650 --> 00:12:27,682 So, I have here this circle of radius R about the point O, 183 00:12:27,682 --> 00:12:33,059 and where I start with is the formula for the circumference S of the circle, 184 00:12:33,059 --> 00:12:37,843 and we all remember that the circumference of a circle is 2 pi R. 185 00:12:37,843 --> 00:12:43,876 Suppose I want to know the length of the segment of this circle, this arc between 186 00:12:43,876 --> 00:12:49,090 A and B mathematically, we denote this as AB with a little squiggle on top 187 00:12:49,090 --> 00:12:53,037 reminding me that this is the arc. So, this is not too hard. 188 00:12:53,037 --> 00:12:57,953 Imagine slicing a pie. To figure out how much crust you get, you 189 00:12:57,953 --> 00:13:03,390 take the amount of crust in the entire pie and then figure out how much your 190 00:13:03,390 --> 00:13:07,041 slice is. Your slice is a fraction of the entire 191 00:13:07,041 --> 00:13:11,287 pie that is a ratio of alpha, your angle, to 360 degrees. 192 00:13:11,287 --> 00:13:17,552 This tells you how much of the pie you have and I multiply that by 2 pi R and 193 00:13:17,552 --> 00:13:21,617 that gives me the arc length between A and B. 194 00:13:21,617 --> 00:13:28,940 And if I perform the full division here, this is alpha divided by 360. 195 00:13:28,940 --> 00:13:38,357 Excuse me. This is alpha / by 57.3 degrees * R. 196 00:13:38,357 --> 00:13:46,152 Now the point that I want to make is that if the angle alpha is in fact small, then 197 00:13:46,152 --> 00:13:50,425 the difference between measuring the arc length from A to B and the actual 198 00:13:50,425 --> 00:13:54,683 distance between A and B, which is the straight line distance along the green 199 00:13:54,683 --> 00:14:00,096 line is very small. And so, for small alpha, the distance 200 00:14:00,096 --> 00:14:06,670 from A to B is similar or approximately given by the arc length. 201 00:14:06,670 --> 00:14:13,963 And this expression, called the small angle formula, is the one that we will 202 00:14:13,963 --> 00:14:20,024 use very often in the class. It relates distances to angles. 203 00:14:20,024 --> 00:14:27,420 I can rewrite it as alpha / 57.3 degrees is AB / r. 204 00:14:27,420 --> 00:14:32,976 So what this tells us is for example, if we can measure angles with some 205 00:14:32,976 --> 00:14:38,385 precision, we need the ratio of all terrestrial distance to the celestial 206 00:14:38,385 --> 00:14:44,387 sphere to be small enough that the angle you get from this expression is smaller 207 00:14:44,387 --> 00:14:48,240 than the precision of any of the measurements we do. 208 00:14:49,360 --> 00:14:54,430 Now you may see the same formula written with very different numbers. 209 00:14:54,430 --> 00:14:59,147 So compare what I wrote to this expression and it's, they look very 210 00:14:59,147 --> 00:15:02,809 different. this brings up another important point 211 00:15:02,809 --> 00:15:07,668 that I do not want to miss. neither of these expressions, of course, 212 00:15:07,668 --> 00:15:11,470 is wrong. they're just expressing the same angle in 213 00:15:11,470 --> 00:15:15,169 different units. In measuring small angles, we often 214 00:15:15,169 --> 00:15:20,745 measure units in fractions of a degree. And for the same Babylonian reasons that 215 00:15:20,745 --> 00:15:25,851 give us minutes and seconds, we measure fractions of a degree in arcminutes, 216 00:15:25,851 --> 00:15:30,890 sixty of which make up a degree and in arc seconds, sixty of which make up an 217 00:15:30,890 --> 00:15:33,980 arcminute. And if you perform the computation, you 218 00:15:33,980 --> 00:15:39,565 find that 57.3 degrees corresponds to this great number 206,265 arcseconds. 219 00:15:39,565 --> 00:15:43,551 So that these two expressions are in fact the same expression. 220 00:15:43,551 --> 00:15:48,244 the same angle is written as the different numbers of different units, 221 00:15:48,244 --> 00:15:53,580 which reminds us, that, when we're doing physical science numbers are in fact the 222 00:15:53,580 --> 00:15:57,502 ratios of one physical quantity to another physical quantity. 223 00:15:57,502 --> 00:16:00,266 If I say that my height is 178 centimeters. 224 00:16:00,266 --> 00:16:04,510 That means its 178 times some fiducial unit, which is a centimeter. 225 00:16:04,510 --> 00:16:10,577 And so when we specify a relay, a physical property by a number it's very 226 00:16:10,577 --> 00:16:15,011 essential to remember the units in which it is expressed. 227 00:16:15,011 --> 00:16:20,457 And often, if you misunderstand the units, you get incorrect answers. 228 00:16:20,457 --> 00:16:26,291 And at this point you may be saying, wait Ronin, what about your consistency. 229 00:16:26,291 --> 00:16:31,270 You never specified in this expression, units for the length A, B, 230 00:16:31,270 --> 00:16:34,627 and for the length R. Those are two physical properties and 231 00:16:34,627 --> 00:16:38,725 what units are you measuring them, is that in light years? In millimeters? 232 00:16:38,725 --> 00:16:41,570 In angstrom? And the answer, of course, is that this 233 00:16:41,570 --> 00:16:46,180 expression will be correct no matter what units I use for A, B, and R as long as I 234 00:16:46,180 --> 00:16:49,481 use the same units. Because, remember, one way we wrote this 235 00:16:49,481 --> 00:16:57,280 formula was that alpha / 57.3 degrees is AB / R. 236 00:16:57,280 --> 00:17:01,083 Now we see that on the left-hand side, I have the ratio of two angles, 237 00:17:01,083 --> 00:17:04,224 an actual number. And on the right-hand side, the ratio of 238 00:17:04,224 --> 00:17:07,146 two lengths, and the ratio of the number representing 239 00:17:07,146 --> 00:17:11,610 AB, and the number representing R will be the actual ratio of the lengths so long 240 00:17:11,610 --> 00:17:15,138 as they're expressed in the same units, whatever those units are. 241 00:17:15,138 --> 00:17:18,445 But, this reminds us, A, that we have to be careful when doing 242 00:17:18,445 --> 00:17:21,201 physics. The correspondence between quantities and 243 00:17:21,201 --> 00:17:24,563 numbers involves units. And B, that the best way to avoid unit 244 00:17:24,563 --> 00:17:29,555 errors is to always write our expressions in terms of ratios of objects of the same 245 00:17:29,555 --> 00:17:32,780 unit, then those numbers are actually meaningful. 246 00:17:34,920 --> 00:17:42,093 Here again is our favorite view of the sky from Athens at nine pm on November 27 247 00:17:42,093 --> 00:17:48,668 and what I've had the software add here in green is the celestial coordinate 248 00:17:48,668 --> 00:17:52,682 grid. So here we have the celestial equator and 249 00:17:52,682 --> 00:17:59,685 if we raise our gaze a bit, then we can take a look at the celestial north pole 250 00:17:59,685 --> 00:18:00,710 here. And 251 00:18:00,710 --> 00:18:07,545 we see the lines of right fixed declination are concentric circles around 252 00:18:07,545 --> 00:18:11,390 the pole. And we see the lines of fixed right 253 00:18:11,390 --> 00:18:17,628 ascension are the lines of longitude spanning out of the pole. And, we see 254 00:18:17,628 --> 00:18:24,297 right here the prime celestial meridian, which as promised, meets the celestial 255 00:18:24,297 --> 00:18:28,230 equator in the constellation Pisces over here. 256 00:18:28,230 --> 00:18:35,839 And so we have the appearance of the celestial coordinate grid in the sky over 257 00:18:35,839 --> 00:18:39,515 Athens. And what we can see is that, as time 258 00:18:39,515 --> 00:18:43,106 progresses. notice, that here, we have, 259 00:18:43,106 --> 00:18:47,980 I will mark for us the position of the prime meridian. 260 00:18:47,980 --> 00:18:51,520 This is where 0 hours of right ascension is, 261 00:18:51,520 --> 00:18:58,300 and then, to east of it to by 30 degrees. We have the 2 hour right ascension line 262 00:18:58,300 --> 00:19:01,691 and 4 hour right ascension line and so on. 263 00:19:01,691 --> 00:19:07,190 And the reason that this makes sense is that, if I let 2 hours go by, by 264 00:19:07,190 --> 00:19:12,313 magically moving the clock. Notice that the 2 hour right ascension 265 00:19:12,313 --> 00:19:17,155 line, the sphere having rotated 30 degrees is now exactly in the position 266 00:19:17,155 --> 00:19:20,504 where the 9 hour right ascension previously was. 267 00:19:20,504 --> 00:19:23,590 0 hours of right ascension has rotated over. 268 00:19:23,590 --> 00:19:28,712 And so hopefully this clarifies the way in which right ascension measures the 269 00:19:28,712 --> 00:19:34,924 rotation of the celestial sphere. To summarized what we've learned in this 270 00:19:34,924 --> 00:19:40,763 quick first video, we've learned that we can imagine the stars as fixed on a large 271 00:19:40,763 --> 00:19:44,810 celestial sphere, concentric with earth and surrounding it. 272 00:19:44,810 --> 00:19:50,322 the size of this sphere is governed by our favorite formula, the small angle 273 00:19:50,322 --> 00:19:53,709 formula. So the, angle, angle between the lines of 274 00:19:53,709 --> 00:19:56,463 sight to a star, for example, is AB / by R, 275 00:19:56,463 --> 00:20:01,030 where R is the radius of the celestial sphere, distance to the stars. 276 00:20:01,030 --> 00:20:06,336 AB is some distance between two points on earth and we pick R so big, that this 277 00:20:06,336 --> 00:20:11,642 angle is too small to be measured. the motion of the stars is carried by the 278 00:20:11,642 --> 00:20:15,202 fact that the sphere rotates daily from east to west. 279 00:20:15,202 --> 00:20:20,374 We measure positions on the celestial sphere by giving declination celestial 280 00:20:20,374 --> 00:20:24,063 latitude in degrees north and south of the celestial equator. 281 00:20:24,063 --> 00:20:28,654 And right ascension, measuring from some particular meridian in hours of right 282 00:20:28,654 --> 00:20:33,362 ascension moving to the east and this corresponds to the rate of rotation of 283 00:20:33,362 --> 00:20:34,598 the celestial sphere.