1 00:00:00,000 --> 00:00:06,744 So first step, in trying to figure out more about how stars work, is going to be 2 00:00:06,744 --> 00:00:10,915 to figure out how far they are. Because, how we interpret what we see, 3 00:00:10,915 --> 00:00:15,255 which is a point of light, depends greatly on how far we think that 4 00:00:15,255 --> 00:00:18,737 point of light is. That will tell us how to read and 5 00:00:18,737 --> 00:00:23,558 interpret the information we see. So how do you measure the distances to 6 00:00:23,558 --> 00:00:26,504 stars. Well, you use a method that has an old 7 00:00:26,504 --> 00:00:31,124 and ancient and storied pedigree and was well known to the ancients. 8 00:00:31,124 --> 00:00:35,878 It was called Parallax and you probably used this to solve some high school 9 00:00:35,878 --> 00:00:39,621 algebra problems. So, the picture here is of someone stuck 10 00:00:39,621 --> 00:00:44,897 on a road here trying to estimate the distance to the boat out in the lake, and 11 00:00:44,897 --> 00:00:49,322 what this person notices is that as they move along the road, 12 00:00:49,322 --> 00:00:53,470 and you can see on the right what they see, 13 00:00:53,470 --> 00:00:58,203 The position of the boat, though the boat is not moving, it appears to move 14 00:00:58,203 --> 00:01:02,395 relative to the more distant shore, opposite shore of the lake. 15 00:01:02,395 --> 00:01:07,804 And so when I stand here for example, the boat line appears to me to be lined up 16 00:01:07,804 --> 00:01:13,484 with this tree at the top of the hill and when I move over here the boat appears to 17 00:01:13,484 --> 00:01:18,014 line up with that mountain. The boat didn't move but by drawing the 18 00:01:18,014 --> 00:01:20,899 lines. from me to the boat, whose angle changes? 19 00:01:20,899 --> 00:01:25,857 I see the boat obscuring different parts of the different scenes and by doing some 20 00:01:25,857 --> 00:01:30,240 calculations I can figure out the distance to the boat from trigonometry. 21 00:01:30,240 --> 00:01:37,086 So, we could try to do this, if we had a star that is playing the role of the 22 00:01:37,086 --> 00:01:39,768 boat. And who would play the role of the 23 00:01:39,768 --> 00:01:43,173 opposite shore? Well, the boat point is that, some very 24 00:01:43,173 --> 00:01:47,991 small number of stars are near to us. Why is that, or is the number of stars 25 00:01:47,991 --> 00:01:51,717 near to us small? Only because most of the universe is far 26 00:01:51,717 --> 00:01:54,865 from us. And so, most of the stars we see are very 27 00:01:54,865 --> 00:01:59,059 far, some of them are nearer. The ones that are nearer can play the 28 00:01:59,059 --> 00:02:02,279 role of the boat. The part, ones that are farther, much 29 00:02:02,279 --> 00:02:06,288 farther, will play the role of the opposite shore, and as I move my 30 00:02:06,288 --> 00:02:11,026 observation point the stars that are nearer will move relative to the more 31 00:02:11,026 --> 00:02:13,212 distant stars. Well that's very nice. 32 00:02:13,212 --> 00:02:17,950 That's in fact the way that I measure distances, you know, as I walk around and 33 00:02:17,950 --> 00:02:22,749 try not to hit walls I compare what my right eye sees to what my left eye sees 34 00:02:22,749 --> 00:02:27,183 and this difference in perspective, in, in the angle, this parallax, as it's 35 00:02:27,183 --> 00:02:31,590 called, tells me how far things are. The problem is that stars are very far 36 00:02:31,590 --> 00:02:34,045 away. the views seen by my two eyes are 37 00:02:34,045 --> 00:02:37,554 completely identical. The lines from my eyes to the star are 38 00:02:37,554 --> 00:02:40,535 parallel. And I can't distinguish the distance to a 39 00:02:40,535 --> 00:02:44,352 star with my eyes, what I need are eyes spaced farther apart, 40 00:02:44,352 --> 00:02:49,509 or two observatories very far apart. Stars are so far apart that no matter 41 00:02:49,509 --> 00:02:55,285 where you put two observatories on Earth, measuring the difference in the way the, 42 00:02:55,285 --> 00:03:00,747 sky appears from two points on Earth. you will not obtain accurate parallax 43 00:03:00,747 --> 00:03:03,561 measurements. I need observatories that are even 44 00:03:03,561 --> 00:03:08,075 farther away than the size of the Earth. The easy way to do this, and the best, 45 00:03:08,075 --> 00:03:12,765 reliable way to do this is simply to stay in the same observatory, and allow the 46 00:03:12,765 --> 00:03:15,227 Earth's motion around the Sun to carry us. 47 00:03:15,227 --> 00:03:19,800 Because, remember, that over the course of a year, the Earth's motion carries us 48 00:03:19,800 --> 00:03:24,665 300,000 mile kilometers from where we are now to where we will be in six months, 49 00:03:24,665 --> 00:03:27,948 around the Earth's orbit. There's the way to get distant 50 00:03:27,948 --> 00:03:31,295 observatories. And so using this method, we apply this 51 00:03:31,295 --> 00:03:34,930 in, as follows. We have here, the Earth moving around the 52 00:03:34,930 --> 00:03:39,095 Sun, we have a star that is nearby playing the role of the boat. 53 00:03:39,095 --> 00:03:44,052 We have distant stars, way farther away, playing the role of the fixed stars. 54 00:03:44,052 --> 00:03:49,142 And we observe that relative to the distant stars, as the earth moves in a 55 00:03:49,142 --> 00:03:54,231 circle, this star move, appears to move in a circle in the sky relative to the 56 00:03:54,231 --> 00:03:57,933 fixed stars. And the geometry of the situation allows 57 00:03:57,933 --> 00:04:02,230 us, if we can measure this angle P. So, the angle P is this angle P. 58 00:04:02,230 --> 00:04:05,642 It's the radius of the, of apparent circle in the sky. 59 00:04:05,642 --> 00:04:10,148 Not the diameter the radius. Of the apparent angular circle in the sky 60 00:04:10,148 --> 00:04:14,397 that the star appears to move in relative to the distant stars. 61 00:04:14,397 --> 00:04:19,225 And if I measure this angle, and if I imagine that the distance to the star 62 00:04:19,225 --> 00:04:23,990 from the Earth or the Sun, stars are so far away that the difference is 63 00:04:23,990 --> 00:04:29,986 irrelevant, is d, then, since I know that this side of this triangle is just one 64 00:04:29,986 --> 00:04:34,058 astronomical unit. It's the radius of the Earth's orbit. 65 00:04:34,058 --> 00:04:39,685 I could use my small angle formula. My small angle formula tells me that one 66 00:04:39,685 --> 00:04:44,149 AU divided by D. Is the angle P, divided by 206, 265 67 00:04:44,149 --> 00:04:48,670 arcseconds. I'm interested in finding these, so I'll 68 00:04:48,670 --> 00:04:55,584 invert both sides and write this as D, divided by one astronomical unit, is 206, 69 00:04:55,584 --> 00:05:01,612 265 arcseconds, divided by P. most stars will be many astronomical 70 00:05:01,612 --> 00:05:05,778 units away, so their paralex angle will be much 71 00:05:05,778 --> 00:05:12,869 smaller than an arcsecond, and you need precise measurement to obtain parallax 72 00:05:12,869 --> 00:05:15,676 angles. But in principle it's doable. 73 00:05:15,676 --> 00:05:20,803 Let's rewrite that cleanly. The distance of in astronomical units to 74 00:05:20,803 --> 00:05:27,062 a store is 206265 arc seconds divided by it's parallax angle which remember is the 75 00:05:27,062 --> 00:05:31,360 radius of the circle that appears to inscribe in the sky. 76 00:05:31,360 --> 00:05:37,166 this definition is very useful, it inspires in fact the invention of a new 77 00:05:37,166 --> 00:05:41,313 distance unit, a parsec. And one parsec is defined to be 78 00:05:41,313 --> 00:05:47,270 approximately, I'll define it exactly in a minute, 206,265 astronomical units. 79 00:05:47,270 --> 00:05:53,258 The reason that we use this definition is that then, if I divide both sides by this 80 00:05:53,258 --> 00:05:58,886 crazy number, I find that the distance to a star in parsecs is exactly one arc 81 00:05:58,886 --> 00:06:03,865 second divided by its parallax angle. And this is, in fact, the precise 82 00:06:03,865 --> 00:06:08,538 definition of a parsec. A parsec is that distance at which a star 83 00:06:08,538 --> 00:06:11,680 sub, has a parallax angle of one arc second. 84 00:06:11,680 --> 00:06:16,600 A star at a distance of ten parsecs has a parallax angle of one tenth of an arc 85 00:06:16,600 --> 00:06:19,217 second. The farther the star, the smaller the 86 00:06:19,217 --> 00:06:23,024 parallax angle, as we expected. So here's that expression written 87 00:06:23,024 --> 00:06:25,403 cleanly. And this is what a parsec means. 88 00:06:25,403 --> 00:06:27,901 And it, we'll often use parsecs to measure 89 00:06:27,901 --> 00:06:29,566 distances. And this is great. 90 00:06:29,566 --> 00:06:32,659 I can define the geometry. Can I actually measure it? 91 00:06:32,659 --> 00:06:36,347 the definitions in the geometry were known to the ancients. 92 00:06:36,347 --> 00:06:41,164 The first successful measurement of a parallax angle to star was by Bessel in 93 00:06:41,164 --> 00:06:43,781 1838. And this is an important thing because 94 00:06:43,781 --> 00:06:48,539 once you the measure a distance to a star and you realize there are other stars 95 00:06:48,539 --> 00:06:51,988 that are farther, this is the end of the celestial sphere. 96 00:06:51,988 --> 00:06:55,735 We now are beginning to build an actual 3-dimentional universe. 97 00:06:55,735 --> 00:07:00,195 Building a 3-dimentional universe, understanding the distances to things, is 98 00:07:00,195 --> 00:07:04,060 going to be a light motif. Something we'll come back to again and 99 00:07:04,060 --> 00:07:09,293 again in this class because interpreting what we see depends on critically on how 100 00:07:09,293 --> 00:07:12,445 far we think it is. In particular, as an example to 101 00:07:12,445 --> 00:07:17,202 understand what a parsec really is, well I told you what a parsec is it's the 102 00:07:17,202 --> 00:07:22,105 distance at which the parallax angle is one arcsecond. Well how many meters is a 103 00:07:22,105 --> 00:07:25,329 parsec? Well to know that I have to know the 104 00:07:25,329 --> 00:07:30,093 parsec is 206,265 astronomical units, what's an astronomical unit? 105 00:07:30,093 --> 00:07:33,008 Well. Astronomical unit is the radius of 106 00:07:33,008 --> 00:07:35,959 Earth's orbit, or now it's defined some other way. 107 00:07:35,959 --> 00:07:40,657 More importantly, how do I measure the radius of Earth's orbit, which is what I 108 00:07:40,657 --> 00:07:43,668 really need. Well, to measure the radius of Earth's 109 00:07:43,668 --> 00:07:46,767 orbit, initially you make whatever measurements 110 00:07:46,767 --> 00:07:51,842 you can that, that, the way Kepler did. Our best measurement today involves 111 00:07:51,842 --> 00:07:56,850 measuring the distance from Earth to Mercury in a given moment by bouncing 112 00:07:56,850 --> 00:08:00,710 radar waves from a, an antenna on Earth off of Mercury, and 113 00:08:00,710 --> 00:08:03,898 measuring the time of flight. Multiply by the speed of light. 114 00:08:03,898 --> 00:08:06,608 Divide by two. You have a distance to Mercury, or to 115 00:08:06,608 --> 00:08:10,380 Venus at a particular instant. And since we know the relative distances 116 00:08:10,380 --> 00:08:13,037 in the solar system very well from Keppler's laws. 117 00:08:13,037 --> 00:08:16,065 This tells us how much an astronomical unit is in meters. 118 00:08:16,065 --> 00:08:20,262 Use that to defi-, determine parsecs. We'll later use parsecs to define other, 119 00:08:20,262 --> 00:08:23,663 distance measurements. We're building the first steps in what it 120 00:08:23,663 --> 00:08:27,382 called the cosmic distance ladder. The point I want to emphasize is that 121 00:08:27,382 --> 00:08:31,154 every time somebody improves the precision of a measurement low on the 122 00:08:31,154 --> 00:08:34,029 rung, that improves the precision of everything 123 00:08:34,029 --> 00:08:38,440 above, that depends on it. So for example, parallax angle, as a measure of 124 00:08:38,440 --> 00:08:42,105 distance, depends on how well you know an astronomical unit. 125 00:08:42,105 --> 00:08:47,013 Obviously measuring distances to stars is important, it is so important, that in 126 00:08:47,013 --> 00:08:51,114 1989, the Hipparcos mission was launched, with the express purpose. 127 00:08:51,114 --> 00:08:56,643 It actually spent about a decade in space with the express mission, of measuring 128 00:08:56,643 --> 00:09:01,427 the parallax angles to as many stars as it could, of course, to the stars near 129 00:09:01,427 --> 00:09:03,780 us. And if a host produced initially a 130 00:09:03,780 --> 00:09:07,004 catalog of 120,000 stars, that catalog's been expanded. 131 00:09:07,004 --> 00:09:11,134 We now got 2,500,000 stars to which we have reasonably reliable distance 132 00:09:11,134 --> 00:09:13,434 measurements. So this is great. 133 00:09:13,434 --> 00:09:19,076 We now have a whole ball around Earth. More distant things perhaps not but a 134 00:09:19,076 --> 00:09:22,974 whole ball around Earth where we can build a three dimensional atlas, that's 135 00:09:22,974 --> 00:09:26,646 what Hipparcos catalog is. It's a three dimensional atlas of at 136 00:09:26,646 --> 00:09:31,456 least our local neighborhood, the, data is so important that a Gaia mission 137 00:09:31,456 --> 00:09:37,022 is planned to launch in 2013 with the express purpose of vastly extending the 138 00:09:37,022 --> 00:09:41,447 Hipparcos catalog. Hipparcos produced many useful scientific 139 00:09:41,447 --> 00:09:44,873 observations, also the following beautiful image. 140 00:09:44,873 --> 00:09:49,775 these are two images of Sirius, and it's stellar neighbors taken in two 141 00:09:49,775 --> 00:09:52,423 seasons. And if you look at them carefully, you 142 00:09:52,423 --> 00:09:56,682 will see that Sirius is farther to the left in the image on the right and 143 00:09:56,682 --> 00:10:01,172 farther to the right relative to the nearby stars in the image on the left. 144 00:10:01,172 --> 00:10:03,877 In fact, this is one of those serial box images. 145 00:10:03,877 --> 00:10:08,252 If you relax your eyes, it's best to print this and look at it from just the 146 00:10:08,252 --> 00:10:11,706 right distance. the images of the stars will merge and 147 00:10:11,706 --> 00:10:15,850 you will see, be seeing a three dimensional picture of the region of the 148 00:10:15,850 --> 00:10:19,650 sky near Sirius using the your brain's interpretation of 149 00:10:19,650 --> 00:10:24,730 the images in your two eyes, and this is just simply produced by the images that 150 00:10:24,730 --> 00:10:27,669 Hipparcos took at two different times of year.