1 00:00:00,000 --> 00:00:05,217 We now have achieved our goal of understanding the motions of the sky, 2 00:00:05,217 --> 00:00:10,808 predicting which stars will be visible, which season, where on Earth, at what 3 00:00:10,808 --> 00:00:14,407 time of the night. there are some other things we'd like to 4 00:00:14,407 --> 00:00:17,490 understand. we talked about the orbital motion of the 5 00:00:17,490 --> 00:00:21,068 Eearth and how it affects which stars are visible in the sky when, 6 00:00:21,068 --> 00:00:25,705 of course, there's another phenomenon on Earth that repeats with the periodicity 7 00:00:25,705 --> 00:00:28,790 of once a year, namely the variation of the seasons. 8 00:00:28,790 --> 00:00:33,652 The climate on Earth changes once a year, and in fact, the original interest in 9 00:00:33,652 --> 00:00:38,140 astronomy, much of it, was derived from the fact that by understanding or 10 00:00:38,140 --> 00:00:43,127 watching which stars were visible in the sky, say early in the evening, you could 11 00:00:43,127 --> 00:00:48,052 predict the coming of harvest time, or the time to sew, or the inundation of the 12 00:00:48,052 --> 00:00:51,730 Nile, or whatever. All other phenomena that were periodic 13 00:00:51,730 --> 00:00:55,532 with annual periodicity, because they depended on the seasons. 14 00:00:55,532 --> 00:00:59,460 And the reason why the Earth's orbital motion is related to 15 00:00:59,460 --> 00:01:04,309 seasonal changes in temperature, of course, has to do with the fact that if 16 00:01:04,309 --> 00:01:09,159 you ever see one of these globes, it's always depicted in a tilted version. 17 00:01:09,159 --> 00:01:13,616 We all know that the globe is tilted by. Whoops, I had it upside down. 18 00:01:13,616 --> 00:01:16,696 Tilted by 23.5 degrees, but, this is interesting. 19 00:01:16,696 --> 00:01:20,170 We're out in space. 23.5 degrees, with respect to what? 20 00:01:20,170 --> 00:01:26,410 Well, it turns out that the globe is tilted by 23.5 degrees relative to the 21 00:01:26,410 --> 00:01:31,838 plane of the ecliptic, the plane in which the earth orbits the sun, in other words 22 00:01:31,838 --> 00:01:36,963 if I want to imagine that the earth orbits the sun in a horizontal plane then 23 00:01:36,963 --> 00:01:42,089 I must hold the globe titled by 23.5 degrees, rather than vertical with the 24 00:01:42,089 --> 00:01:47,280 north celestial pole, therefore, often that direction 23.5 degrees away from the 25 00:01:47,280 --> 00:01:50,171 vertical. Contrary-wise, if I want to present 26 00:01:50,171 --> 00:01:55,100 things with the north celestial's pole vertical, above me, then the plane in 27 00:01:55,100 --> 00:02:00,859 which the earth orbits the sun, and of course, the plain English the sun appears 28 00:02:00,859 --> 00:02:06,928 to orbit the Earth will be tilted by 23.5 degrees away from the horizontal because 29 00:02:06,928 --> 00:02:11,725 it was horizontal in this frame of reference and I have tilted everything 30 00:02:11,725 --> 00:02:16,780 23.5 degrees this way so that. The sun's orbit around the Earth, or the 31 00:02:16,780 --> 00:02:22,924 sun's motion along the celestial sphere, is not along the celestial equator, but 32 00:02:22,924 --> 00:02:28,601 along a circle tilted 23.5 degrees, with respect to the celestial equator. 33 00:02:28,601 --> 00:02:34,202 This trajectory of the sun moving to the east along the celestial sphere is called 34 00:02:34,202 --> 00:02:38,960 the ecliptic and it's a circle tilted with respect to the celestial equator by 35 00:02:38,960 --> 00:02:43,778 23.5 degrees, and if you take two circles and tilt one with respect to the other, 36 00:02:43,778 --> 00:02:47,994 they're hinged, so there are two points at which they continue to meet. 37 00:02:47,994 --> 00:02:52,951 Those are the points where the hinge meets and so those two points are the 38 00:02:52,951 --> 00:02:55,916 points where the ecliptic meets the equator. 39 00:02:55,916 --> 00:03:01,171 Those are the positions along the Sun's motion when it is along the celestial 40 00:03:01,171 --> 00:03:06,630 equator and, the names of those points are the vernal and the autumnal equinox, 41 00:03:06,630 --> 00:03:09,554 for reasons we'll talking about in a minute. 42 00:03:09,554 --> 00:03:16,228 And these it turns out are the positions which by convention we chose to define 43 00:03:16,228 --> 00:03:21,962 the merid, prime celestial meridian of zero hours of right ascension. 44 00:03:21,962 --> 00:03:25,792 So when, the sun is at the vernal equinox, it is 45 00:03:25,792 --> 00:03:30,262 at 0 hours of our dissension, this means that the sun is overhead at 46 00:03:30,262 --> 00:03:33,977 Sidereal time 0. Sidereal time is off from Solar time by 47 00:03:33,977 --> 00:03:37,315 12 hours. And so, the sun is at the vernal equinox, 48 00:03:37,315 --> 00:03:40,967 if you look back at the last lesson on March 21st, 49 00:03:40,967 --> 00:03:46,256 and it is at the autumnal equinox, 180 degrees away 6 months later, at 12 hours 50 00:03:46,256 --> 00:03:52,610 of our dissension on September 21st. So March 21st and September 21st are the 51 00:03:52,610 --> 00:03:57,201 days of the year at which the sun is along the celestial equator and has 52 00:03:57,201 --> 00:04:02,287 celestial declination 0. And between those two after the sun 53 00:04:02,287 --> 00:04:08,716 passes the vernal equinox it moves into the northern hemisphere of the celestial 54 00:04:08,716 --> 00:04:14,006 sphere and its declination rises until at the full apex of its tilt. 55 00:04:14,006 --> 00:04:20,787 Its declination is 23.5 degrees north and then this happens on or around June 21st 56 00:04:20,787 --> 00:04:27,642 then it goes on September 21st it meets the equator and on or around December 57 00:04:27,642 --> 00:04:33,901 21st the sun is farthest south that it goes its declination is 23.5 degrees 58 00:04:33,901 --> 00:04:37,403 south. And, let's see how all of this relates to 59 00:04:37,403 --> 00:04:44,709 what we understand about the seasons. This demonstration will explain to us 60 00:04:44,709 --> 00:04:49,893 what the tilt of the Earth's axis, or equivalently in the Sun's motion around 61 00:04:49,893 --> 00:04:53,033 the celestial sphere, has to do with our seasons. 62 00:04:53,033 --> 00:04:56,186 So, what we have here is here's our celestial 63 00:04:56,186 --> 00:04:59,986 sphere of view, the green line is the celestial equator. 64 00:04:59,986 --> 00:05:05,265 The tilted line is the ecliptic, the motion, the line in which the Sun moves 65 00:05:05,265 --> 00:05:11,318 around the celestial sphere and, what we are seeing is that the Sun is located now 66 00:05:11,318 --> 00:05:16,035 at the line of 0 hours of right ascension, in other words, it is the 67 00:05:16,035 --> 00:05:19,801 vernal equinox. This is the position of the sun on March 68 00:05:19,801 --> 00:05:23,904 21st. Notice that at, on March 21st, the sun is 69 00:05:23,904 --> 00:05:28,880 at 0 hours at sidereal midnight. And so, it's sidereal midnight when the 70 00:05:28,880 --> 00:05:32,512 sun is overhead. In other words, when it is noon, indeed, 71 00:05:32,512 --> 00:05:37,967 sidereal time is off from local time by about 12 hours at the vernal equinox. 72 00:05:37,967 --> 00:05:42,835 So this is the position on March 1st. The sun is on the equator. 73 00:05:42,835 --> 00:05:48,505 What this tells us, if we switch to an orbit view is that the 74 00:05:48,505 --> 00:05:54,834 earth's tilt at this point is such that the sun is neither north nor south. 75 00:05:54,834 --> 00:06:00,605 In other words, the tilt is perpendicular to the direction to the sun, and if we 76 00:06:00,605 --> 00:06:05,954 look from above, we see that as the Earth rotates about its axis the line 77 00:06:05,954 --> 00:06:11,303 separating day from night, the sun side from the dark side of the earth, goes 78 00:06:11,303 --> 00:06:16,230 right though the North Pole and equivalently through the South Pole, so 79 00:06:16,230 --> 00:06:20,488 over the course of a day. Every point on earth, spends a half of 80 00:06:20,488 --> 00:06:25,616 it's time on the sun side, in daylight And a half of it's rotation on the dark 81 00:06:25,616 --> 00:06:29,298 side, at night time. Hence the word equinox, night and day, 82 00:06:29,298 --> 00:06:34,558 are equal length, everywhere on Earth and this happens, whenever the sun hits the 83 00:06:34,558 --> 00:06:38,305 ecliptic. In another words, on March 21st, when the 84 00:06:38,305 --> 00:06:45,340 sun is at the vernal equinox and again 12 months 6 months later on September 21st 85 00:06:45,340 --> 00:06:51,125 when the sun is at the autumnal equinox. Now what happens as we moving back to the 86 00:06:51,125 --> 00:06:55,232 celestial sphere, as time goes by, the sun moves around, 87 00:06:55,232 --> 00:07:00,557 not the equator, but the ecliptic. So a few months later, the sun is now 88 00:07:00,557 --> 00:07:06,262 north of the celestial equator. It's declination at this point its right 89 00:07:06,262 --> 00:07:10,826 ascension is 3 hours. So let's move it a little bit more. 90 00:07:10,826 --> 00:07:17,292 its right ascension is 4 hours, that means, that about 2 months have passed. 91 00:07:17,292 --> 00:07:25,079 It is now, if it was March 21st it is now May 21st and the Sun's declination is 20 92 00:07:25,079 --> 00:07:30,671 degrees north, which means the Sun is well north of the celestial equator. 93 00:07:30,671 --> 00:07:36,733 That means that the Sun is directly overhead at a point of it's a terrestrial 94 00:07:36,733 --> 00:07:40,952 latitude 20 degrees. You see the direction from which the 95 00:07:40,952 --> 00:07:46,069 sun's rays are reaching Earth. And you see that the lines separating 96 00:07:46,069 --> 00:07:51,533 dark from light on Earth no longer goes through the poles, but that in fact the 97 00:07:51,533 --> 00:07:55,060 whole region around the north pole is encircled 98 00:07:55,060 --> 00:08:00,644 such that it is always in the sunlight. If we look from the Sun, we will see that 99 00:08:00,644 --> 00:08:05,809 this whole region around the North Pole is always visible from the Sun, 100 00:08:05,809 --> 00:08:10,346 and therefore, as the Earth rotates, the Sun never sets at the pole, or points 101 00:08:10,346 --> 00:08:16,736 sufficiently close to the pole. And the Sun impinges overhead at latitude 102 00:08:16,736 --> 00:08:21,995 20 degrees. And, as we move the sun farther along the 103 00:08:21,995 --> 00:08:29,603 ecliptic, it reaches its northernmost point in June, on June 21st, when the 104 00:08:29,603 --> 00:08:36,740 sun's declination is 23.5 degrees. The sun is now at the point where it's 105 00:08:36,740 --> 00:08:42,825 maximally north on the celestial sphere. What that means from the point of view of 106 00:08:42,825 --> 00:08:48,399 the orbit is that the Earth's North Pole is tilted, the direction in which the 107 00:08:48,399 --> 00:08:53,973 Earth's North Pole is tilted which is always towards, in the same direction is 108 00:08:53,973 --> 00:08:58,903 now the direction of the sun. So now, points all the way to within a, a 109 00:08:58,903 --> 00:09:04,549 circle of 23.5 degrees latitude around the north pole are visible from the sun 110 00:09:04,549 --> 00:09:09,280 and therefore have a continuous sunlight throughout 24 hours, 111 00:09:09,280 --> 00:09:14,464 whereas, a full circle of radius 23.5 degrees around the South Pole is 112 00:09:14,464 --> 00:09:19,950 invisible to the sun, and the sun never rises there, and the sun is overhead at 113 00:09:19,950 --> 00:09:25,576 the tropic of, of Capricorn, the north of Cancer, the northern tropic, where the 114 00:09:25,576 --> 00:09:28,812 sun is overhead at a latitude of 23.5 degrees. 115 00:09:28,812 --> 00:09:34,579 And this means that this is the point at which sunlight impinges most directly. 116 00:09:34,579 --> 00:09:39,994 This will be the point at which solar heating is, is most intense on Earth. 117 00:09:39,994 --> 00:09:45,342 And as the Earth continues it's orbit around the sun or equivalently, as the 118 00:09:45,342 --> 00:09:50,410 sun continues its path around the celestial sphere, it again reaches an 119 00:09:50,410 --> 00:09:56,745 equinox on September 21st at which point the separate lines separating light from 120 00:09:56,745 --> 00:10:01,671 dark passes through both poles. The sun is overhead at the equator and 121 00:10:01,671 --> 00:10:05,823 night and day are of equal length everywhere on the planet. 122 00:10:05,823 --> 00:10:11,520 And as the sun continues its path to its December solstice. 123 00:10:11,520 --> 00:10:18,304 In December, the Sun is, as far south of the celestial equator as 124 00:10:18,304 --> 00:10:22,390 it gets. It's at a declination of negative 23.5. 125 00:10:22,390 --> 00:10:28,041 At this point, the sun is overhead at a latitude of negative 23.5. 126 00:10:28,041 --> 00:10:35,285 The entire Antarctic Circle latitudes within 23.5 of the south terrestrial pull 127 00:10:35,285 --> 00:10:41,305 have 24 hours of sunlight and latitudes to within 23.5 of the north terrestrial 128 00:10:41,305 --> 00:10:46,347 pole have 24 hours of dark. The sun never rises in the North and 129 00:10:46,347 --> 00:10:51,540 never sets in the South and maximal heating is at southern temperate 130 00:10:51,540 --> 00:10:55,604 latitudes. And I hope that this picture, if you play 131 00:10:55,604 --> 00:11:00,270 with it a little bit, will clarify the relation between the 132 00:11:00,270 --> 00:11:05,355 orbit of the Sun around the celestial sphere, the tilt of the Earth's axis 133 00:11:05,355 --> 00:11:11,434 relative to the Sun, note that the, where its axis points in the same direction 134 00:11:11,434 --> 00:11:17,640 towards the celestial North Pole as the Earth rotates around the sun and 135 00:11:17,640 --> 00:11:23,486 the changing, changes in length of day and night and in terrestrial heating. 136 00:11:23,486 --> 00:11:28,086 So, let's summarize this. Let's summarize what we've learned. 137 00:11:28,086 --> 00:11:33,881 between, [COUGH], March 21st and September 21st, the sun is north of the 138 00:11:33,881 --> 00:11:39,054 celestial equator, increasingly so until June, and then decreasingly so from June 139 00:11:39,054 --> 00:11:42,676 through September. And then from September through March, 140 00:11:42,676 --> 00:11:47,332 the sun is south of the equator, increasingly so until December, and then 141 00:11:47,332 --> 00:11:52,401 decreasing from December through March. When the sun is, either, say to the north 142 00:11:52,401 --> 00:11:57,210 of the equator, then days are longer in the northern hemisphere and the sun is 143 00:11:57,210 --> 00:12:01,711 higher in the sky in the northern hemisphere, because it's declination is 144 00:12:01,711 --> 00:12:06,520 closer to the declination of your Zenith, if you're in the northern hemisphere. 145 00:12:06,520 --> 00:12:11,205 We saw that your, Zenith is located in declination equal to your latitude. 146 00:12:11,205 --> 00:12:15,506 The sun will closer to that, Zenith, at its highest point if you're in 147 00:12:15,506 --> 00:12:19,803 the Northern hemisphere, when the Sun is north of the celestial equator. 148 00:12:19,803 --> 00:12:22,345 And, we saw that the Sun's rays impact the 149 00:12:22,345 --> 00:12:27,127 earth more directly in the northern hemisphere, so climate is warming in the 150 00:12:27,127 --> 00:12:29,850 North and cooling in the southern hemisphere. 151 00:12:29,850 --> 00:12:34,632 And of course, the reverse is true from September to June when the Sun is south 152 00:12:34,632 --> 00:12:38,299 of the equator. Inside the Arctic circle, at least for 153 00:12:38,299 --> 00:12:43,817 some part of that time, the Sun becomes circumpolar and the Sun comes so far 154 00:12:43,817 --> 00:12:49,216 north that it's close enough to the celestial north pole never to set four 155 00:12:49,216 --> 00:12:54,540 regions North of the Arctic Circle, for at least one day, of course, at the 156 00:12:54,540 --> 00:12:59,294 precise North Pole, the sun is circumpolar for 6 months. For precisely 6 157 00:12:59,294 --> 00:13:04,301 months, so long as the Sun is North of the celestial Equator, the Sun never sets 158 00:13:04,301 --> 00:13:09,624 at the North Pole and the Sun never rises at the South Pole and then the inverse is 159 00:13:09,624 --> 00:13:13,644 true as when the Sun is South of the celestial equator. 160 00:13:13,644 --> 00:13:19,369 And, twice a year, at the equinoxes, March and September 21st, day and night 161 00:13:19,369 --> 00:13:24,362 are of equal length everywhere. And then, there are these two tropics, 23 162 00:13:24,362 --> 00:13:29,315 latitude, plus or minus 23.5 degrees. If you live somewhere between those two 163 00:13:29,315 --> 00:13:34,204 tropics, there will be some day a year when the sun is directly overhead at 164 00:13:34,204 --> 00:13:39,027 noon, and passes through your Zenith. The sun, interestingly, is over only at 165 00:13:39,027 --> 00:13:41,960 your Zenith, directly overhead on the Equator, 166 00:13:41,960 --> 00:13:47,418 precisely on the equinox. Let's apply what we've learned to answer the 167 00:13:47,418 --> 00:13:51,242 question, how high the sun is at noon? And since 168 00:13:51,242 --> 00:13:55,734 we've started with Aristotle, let's continue with Aristotle. 169 00:13:55,734 --> 00:14:01,446 We'll be working at Athens latitude of 37.7 approximately, degrees north. 170 00:14:01,446 --> 00:14:06,471 Remember, that noon is the time when the sun is highest in the sky, 171 00:14:06,471 --> 00:14:12,106 that's its meridian crossing, and so it's altitude or its Zenith angle, 172 00:14:12,106 --> 00:14:17,817 will be determined precisely by the sun's declination, and at the equinoxes. 173 00:14:17,817 --> 00:14:23,274 March or September 21st, the sun's declination is 0 degrees, Those are the 174 00:14:23,274 --> 00:14:28,102 days when the Sun crosses the celestial equator and for the course of a day we 175 00:14:28,102 --> 00:14:32,624 can imagine the sun fixed along the celestial sphere because it only moves by 176 00:14:32,624 --> 00:14:35,435 about four minutes along the celestial sphere. 177 00:14:35,435 --> 00:14:41,560 And if the sun is at declination 0, then at noon, it's Zenith angle. 178 00:14:41,560 --> 00:14:47,193 Is just the difference between its declination and the declination of our 179 00:14:47,193 --> 00:14:53,436 Zenith, which is given by our latitude. Its Zenith Zenith angle is 37.7 degrees, 180 00:14:53,436 --> 00:15:00,027 which means its altitude is 90 degrees minus 37.7, which is I believe, 52.3 181 00:15:00,027 --> 00:15:04,428 degrees. At the summer solstice and the summer 182 00:15:04,428 --> 00:15:12,559 solstice is June 21st, so this is the northern summer solstice, the sun has 183 00:15:12,559 --> 00:15:17,630 reached a northern declination of 23.5 degrees north. 184 00:15:17,630 --> 00:15:24,268 The Zenith angle, therefore, at noon, is the difference between our latitude and 185 00:15:24,268 --> 00:15:30,821 the sun's declination, which at this point is only 14.2 degrees. 186 00:15:30,821 --> 00:15:37,460 So, at noon in midsummer, the sun in Athens will reach an altitude of 75 point 187 00:15:37,460 --> 00:15:43,588 eight degrees in the sky. On the other hand, on December 21st, the 188 00:15:43,588 --> 00:15:49,660 sun's declination is now negative 23.5 degrees, 189 00:15:49,660 --> 00:15:55,477 so its Zenith angle. When it's as high in the sky as it gets 190 00:15:55,477 --> 00:16:01,873 at its meridian crossing is the difference between plus 37.7 and negative 191 00:16:01,873 --> 00:16:09,010 23.5, which is if I got it right. 61.2 degrees, which means the sun's 192 00:16:09,010 --> 00:16:16,561 maximum altitude in the winter is only 28.8 degrees. 193 00:16:16,561 --> 00:16:21,797 You know that, the sun solar heating in Athens is 194 00:16:21,797 --> 00:16:26,189 minimal in December 21st/. December twenty-first is not by far the 195 00:16:26,189 --> 00:16:28,968 coldest day of the year in the northern hemisphere. 196 00:16:28,968 --> 00:16:32,020 the coldest day is usually somewhere around February. 197 00:16:32,020 --> 00:16:35,551 There's something like a thermal inertia. There's a time, 198 00:16:35,551 --> 00:16:40,408 it takes time for the Earth to respond to the, the change in solar heating. 199 00:16:40,408 --> 00:16:45,642 there are many other complicated factors that govern climate heat exchange between 200 00:16:45,642 --> 00:16:50,436 the equator and the poles and so on. But to good approximation, solar heating 201 00:16:50,436 --> 00:16:54,850 is maximal at the summer solstice, and therefore, in June, and about 2 202 00:16:54,850 --> 00:16:58,571 months later in August, the temperature has reached maximum. 203 00:16:58,571 --> 00:17:03,420 By that time, solar heating is in decline and with the, the same 20 month lag, the 204 00:17:03,420 --> 00:17:06,881 Earth starts cooling off. Solar heating is minimal in December, 205 00:17:06,881 --> 00:17:11,013 always in the northern hemisphere, of course everything is reversed in the 206 00:17:11,013 --> 00:17:13,693 south. And 2 months later the Earth is as cold 207 00:17:13,693 --> 00:17:18,047 as it's going to be. And while we're discussing solar days and 208 00:17:18,047 --> 00:17:23,873 the Earth's orbital motion, there are two other small imprecisions in what I said 209 00:17:23,873 --> 00:17:28,477 that I need to correct. One is, I said that 24 hours are adjusted 210 00:17:28,477 --> 00:17:33,800 to be a mean a solar day and you can ask, what's so mean about a solar day? 211 00:17:33,800 --> 00:17:39,442 this was mean in the sense of average. It turns out solar days are not all th, 212 00:17:39,442 --> 00:17:41,905 same length. why is this? 213 00:17:41,905 --> 00:17:45,910 Well, the Earth's rotation about its axis is extremely uniform. 214 00:17:45,910 --> 00:17:51,401 We'll talk later about how it fails to be uniform, but it's almost exactly uniform 215 00:17:51,401 --> 00:17:55,028 certainly on the levels of precision that we're talking here. 216 00:17:55,028 --> 00:17:58,820 So the Earth's, well, the length of a sidereal day is very constant. 217 00:17:58,820 --> 00:18:02,900 But the length of a solar day is not, remember, the difference between a 218 00:18:02,900 --> 00:18:07,095 sidereal day and a solar day is associated to the sun's motion along the 219 00:18:07,095 --> 00:18:10,658 celestial sphere. The sun moves to the east by 4 minutes, 220 00:18:10,658 --> 00:18:13,359 every day, and therefore, there is a 4-minute 221 00:18:13,359 --> 00:18:15,830 difference between solar and sidereal days. 222 00:18:15,830 --> 00:18:21,133 But, the sun's motion to the east along the celestial sphere is not uniform. 223 00:18:21,133 --> 00:18:26,789 So, the first cause of this is that, the sun moves uniformly if the Earth orbits 224 00:18:26,789 --> 00:18:30,466 the sun uniformly. Even the the sun would move uniformly 225 00:18:30,466 --> 00:18:35,910 around the Earth, but it would move along this tilted path of the ecliptic. 226 00:18:35,910 --> 00:18:40,344 What this means is that, at, near the equinoxes, the sun's motion 227 00:18:40,344 --> 00:18:45,586 is not parallel to the celestial equator. It's not purely in right ascension, it's 228 00:18:45,586 --> 00:18:50,763 also changing declination, since, where as near the solstices the sun's motion is 229 00:18:50,763 --> 00:18:55,682 parallel at the maximum, and minimum. The sun's motion is now parallel to the 230 00:18:55,682 --> 00:19:00,536 celestial equator, and so, its motion and right ascension is slower near the 231 00:19:00,536 --> 00:19:05,390 equinoxes and faster near the solstices and the four minutes is an average. 232 00:19:05,390 --> 00:19:10,280 And that is one reason why the length of solar days is not uniform. 233 00:19:10,280 --> 00:19:15,222 There's another correction to this. In fact the rate at which the Earth 234 00:19:15,222 --> 00:19:20,098 orbits the sun or equivalently, the sun orbits the earth, is not precisely 235 00:19:20,098 --> 00:19:24,974 uniform even along the ecliptic. This is because the Earth's orbit is not 236 00:19:24,974 --> 00:19:29,916 precisely circular, and the Earth is, in fact, very slightly near the sun in 237 00:19:29,916 --> 00:19:33,189 January than it is at any other time of the year. 238 00:19:33,189 --> 00:19:37,263 At that time, the sun's apparent motion in the sky was fastest. 239 00:19:37,263 --> 00:19:43,422 And 12 months later it is slowest, and so even along the ecliptic, the Sun's motion 240 00:19:43,422 --> 00:19:45,870 is not precisely uniform. Moreover, 241 00:19:45,870 --> 00:19:50,525 I kept talking about the fact that the Earth's north pole maintains its 242 00:19:50,525 --> 00:19:55,504 orientation in space as the Earth orbits. So that, it always points it in this 243 00:19:55,504 --> 00:20:00,742 direction of the celestial north pole where sits some particular star, say the 244 00:20:00,742 --> 00:20:03,328 pole star. And this, it turns out is also 245 00:20:03,328 --> 00:20:06,554 inaccurate. we are building up more and more 246 00:20:06,554 --> 00:20:11,652 precision into our model, and in fact, the Earth is spinning about its axis. 247 00:20:11,652 --> 00:20:17,030 It's acted upon, as we will see, by the sun and the moon applying tidal forces. 248 00:20:17,030 --> 00:20:22,408 And like a spinning top spinning on a table and acted upon by gravity the 249 00:20:22,408 --> 00:20:27,926 Earth's axis wobbles in the same way that a spinning top wobbles except it's a 250 00:20:27,926 --> 00:20:31,907 little bit tricky. A spinning top will wobble, in the same 251 00:20:31,907 --> 00:20:35,050 sense in which it is spinning. The Earth's 252 00:20:35,050 --> 00:20:40,650 polar axis actually wobbles, in the opposite sense to the sense it rotates. 253 00:20:40,650 --> 00:20:45,488 In the other words, the celestial north pole moves to the west along the 254 00:20:45,488 --> 00:20:48,982 celestial sphere. So, the Earth's North Pole does not 255 00:20:48,982 --> 00:20:53,685 always point in the same direction as I've been saying so far, 256 00:20:53,685 --> 00:20:59,385 instead it's tilted by 23.5 degrees to the orbit, but as the Earth rotates to 257 00:20:59,385 --> 00:21:08,707 the east, the celestial pole very slowly wobbles in a big circle in the sky of 258 00:21:08,707 --> 00:21:14,005 radius 23.5 degrees, about the perpendicular to the orbit. 259 00:21:14,005 --> 00:21:18,690 And this wobble called the precession takes about 26,000 years. 260 00:21:18,690 --> 00:21:24,863 What that means is that the point that we define as the celestial north pole moves 261 00:21:24,863 --> 00:21:28,082 in with time. And what this means, is that, what we now 262 00:21:28,082 --> 00:21:32,023 call the Pole Star, will in a few thousand years no longer be the Pole 263 00:21:32,023 --> 00:21:34,443 Star. The Earth's North Pole will face in a 264 00:21:34,443 --> 00:21:37,590 different direction. More intriguingly, 265 00:21:37,590 --> 00:21:42,570 the celestial equator changes as the earth wobbles, 266 00:21:42,570 --> 00:21:47,397 the tilt of the celestial equator relative to the orbit or of the ecliptic 267 00:21:47,397 --> 00:21:52,160 relative to the celestial equator, is always 23.5 degrees but in different 268 00:21:52,160 --> 00:21:55,443 orientations. What this means is that the equinoxes, 269 00:21:55,443 --> 00:22:00,593 the hinges at which the point at which these two circles are hinged move around 270 00:22:00,593 --> 00:22:04,648 the celestial equator. Hence, this whole wobble leads to what is 271 00:22:04,648 --> 00:22:09,411 called the precession of the equinoxes. The vernal equinox shifts, then the 272 00:22:09,411 --> 00:22:12,630 coordinates of all stars shifts because the origin, 273 00:22:12,630 --> 00:22:18,073 the intersection of the equator, with the meridian, including the vernal equinox 274 00:22:18,073 --> 00:22:21,363 moves, and so, the coordinates of a given star change. 275 00:22:21,363 --> 00:22:26,296 This is most clear if you think about it. The star which now has the celestial 276 00:22:26,296 --> 00:22:31,167 coordinates declination 90 north, which is the north star, will not have those 277 00:22:31,167 --> 00:22:34,962 same coordinates very long as the Earth continues to wobble. 278 00:22:34,962 --> 00:22:40,085 And, so when you look at right ascension and declination for a given star it will 279 00:22:40,085 --> 00:22:43,860 be given in terms of some epoch, most typically epoch J2000. 280 00:22:43,860 --> 00:22:49,110 That means these coordinates are given relative to the position of the celestial 281 00:22:49,110 --> 00:22:54,423 equator and the vernal equinox, as of the orbital parameters on January 282 00:22:54,423 --> 00:22:59,296 1, 2000. Back in Athens, it's still November 27th. 283 00:22:59,296 --> 00:23:05,985 What I've done is I've, attempted to have the software keep us centered on the 284 00:23:05,985 --> 00:23:12,849 north celestial pull, so that we will be following the north celestial pull as 285 00:23:12,849 --> 00:23:18,650 time goes on and I will make time move by centuries. 286 00:23:18,650 --> 00:23:24,060 And what you will notice is that over time the celestial pull moves. 287 00:23:24,060 --> 00:23:30,824 the celestial pull started out very near this pull star of Polaris and the, the 288 00:23:30,824 --> 00:23:36,394 celestial pull moves and it moves in this great big circle in the sky. 289 00:23:36,394 --> 00:23:40,564 So that by the time you get to 10,000 or 11,000 290 00:23:40,564 --> 00:23:46,235 AD Vega is closer to being a pole star, and of course, in 26,000 years, the pole 291 00:23:46,235 --> 00:23:52,595 star will of the, the celestial pull will have completed its wobble and we will 292 00:23:52,595 --> 00:23:58,872 again have Polaris as a good North Star. Let's try to see that again, and in this 293 00:23:58,872 --> 00:24:04,997 at this point we should pay attention to the position of the vernal equinox. 294 00:24:04,997 --> 00:24:09,778 Of course, as the pole star moves, so too does the vernal equinox. 295 00:24:09,778 --> 00:24:15,335 Remember that it is currently in the constellation of Pisces, you can see that 296 00:24:15,335 --> 00:24:18,442 its moved quite a distance along the equator. 297 00:24:18,442 --> 00:24:24,382 remember, it completes a full circuit of the equator and over this time and I'm 298 00:24:24,382 --> 00:24:30,045 now dialing time back to the present, and the vernal equinox is moving to the east 299 00:24:30,045 --> 00:24:34,120 along the celestial equator. And as we approach the present, 300 00:24:34,120 --> 00:24:39,670 we find that around the present 1000 years ago, the vernal equinox is indeed 301 00:24:39,670 --> 00:24:44,307 in the constellation Pisces, and as you move time forward, you will 302 00:24:44,307 --> 00:24:49,576 see that on or about 2600 A.D., the vernal equinox leaves the constellation 303 00:24:49,576 --> 00:24:53,160 of Pisces and enters the constellation of Aquarius. 304 00:24:53,160 --> 00:24:59,355 That means we are currently living in what is called the Age of Pisces and as 305 00:24:59,355 --> 00:25:03,406 of 2600 and some, we will be in the Age of Aquarius. 306 00:25:03,406 --> 00:25:08,331 If you look at 20, 2000 B.C. or so the time that pyramids in Egypt 307 00:25:08,331 --> 00:25:14,229 were being constructed, the North Star that we use today was nowhere near the 308 00:25:14,229 --> 00:25:19,850 north celestial pole. And in fact dating of pyramids, is based to some extent, on 309 00:25:19,850 --> 00:25:25,471 astronomical conjectures of what it was the Egyptians used as a north pole and 310 00:25:25,471 --> 00:25:30,887 there's real information to be gleaned from this wobble of the Earth's pole. 311 00:25:30,887 --> 00:25:36,234 We started out trying to understand which stars were going to be visible when. 312 00:25:36,234 --> 00:25:41,581 This was, in itself, enriching, along the way, we figured out the reasons for the 313 00:25:41,581 --> 00:25:45,032 seasons. and, we started investigating this sort of 314 00:25:45,032 --> 00:25:50,004 arcane phenomenon of the wobble of the Earth's axis and the precession of the 315 00:25:50,004 --> 00:25:54,275 equinoxes and came up with an understanding of ways to date the 316 00:25:54,275 --> 00:25:58,100 Egyptian pyramids based on which North Star they aligned to. 317 00:25:58,100 --> 00:26:02,562 So, we're making progress in understanding the moving parts of this 318 00:26:02,562 --> 00:26:06,833 model of the universe that we're constructing. The most conspicuous 319 00:26:06,833 --> 00:26:10,403 absence is the moon and it is to that that we turn next.