1 00:00:00,000 --> 00:00:04,787 When looking at stars that are relatively close to Earth, there is another 2 00:00:04,787 --> 00:00:08,410 phenomenon that we are going to see. and that is that, 3 00:00:08,410 --> 00:00:13,044 the old statement that stars are fixed on the celestial sphere is not precisely 4 00:00:13,044 --> 00:00:16,983 true if you look close enough. Of course, stars in general in the sky 5 00:00:16,983 --> 00:00:19,532 are in orbit. They're moving in all kinds of 6 00:00:19,532 --> 00:00:22,371 directions. They're very far so their motions are 7 00:00:22,371 --> 00:00:25,500 typically minimal when you convert them to angular. 8 00:00:25,500 --> 00:00:31,349 measures but nearby stars are, if measured precisely enough, are observed 9 00:00:31,349 --> 00:00:35,401 to move relative to the distant stars. This is called proper motion. 10 00:00:35,401 --> 00:00:38,002 It is the term for the motion of the stars. 11 00:00:38,002 --> 00:00:42,715 And this is a motion over and above the annual oscillation that nearby stars 12 00:00:42,715 --> 00:00:46,660 perform due to parallax. But even if you subtract parallax, you 13 00:00:46,660 --> 00:00:51,623 observe that relative to the background stars there's an on going continual 14 00:00:51,623 --> 00:00:54,614 motion. This is due to the actual motion of the 15 00:00:54,614 --> 00:00:57,605 stars. So we can measure the motion of the star. 16 00:00:57,605 --> 00:01:02,950 it's characterized by the Greek letter mu, and mu is typically expressed in 17 00:01:02,950 --> 00:01:12,020 arc seconds per year, because those are the, useful units, for the 18 00:01:12,020 --> 00:01:16,630 the typical orders of magnitude of proper motion, and. 19 00:01:16,630 --> 00:01:21,995 When we're looking at an object, notice that an object can't be in motion and 20 00:01:21,995 --> 00:01:26,663 have zero proper motion if it's moving right at us or away from us. 21 00:01:26,663 --> 00:01:30,178 And so when. looking at an object, we define a plane 22 00:01:30,178 --> 00:01:34,387 called the transverse plane. The transverse plane in this image, is 23 00:01:34,387 --> 00:01:39,872 this direction and the direction perpendicular to it, coming out of the 24 00:01:39,872 --> 00:01:43,189 page towards us. And, a radial direction so there's a 25 00:01:43,189 --> 00:01:48,036 plane here, and then there's a radial direction, which is the direction along 26 00:01:48,036 --> 00:01:49,959 the line. From us, to the star. 27 00:01:49,959 --> 00:01:54,950 And, we think separately of radial motion, that's motion towards us or away 28 00:01:54,950 --> 00:02:00,683 from us which does not change the star's position angular in angular terms in the 29 00:02:00,683 --> 00:02:03,516 sky. And, transverse motion, which is motion 30 00:02:03,516 --> 00:02:06,350 along the sky, relative to the other stars. 31 00:02:06,350 --> 00:02:10,892 And, proper motion captures any motion in the transverse direction. 32 00:02:10,892 --> 00:02:15,986 And, we can convert, if we know the distance to the star, we can convert the 33 00:02:15,986 --> 00:02:21,273 angular motion, of course, to measure of its actual velocity, its actual 34 00:02:21,273 --> 00:02:24,492 transverse velocity which is label by VT. And 35 00:02:24,492 --> 00:02:27,646 basicaly the idea is imagine waiting a year, 36 00:02:27,646 --> 00:02:31,982 the star's positioned in the sky will have changed by an angle mu. 37 00:02:31,982 --> 00:02:36,909 If we know it's distance, which I call, capital D on like this diagram that the 38 00:02:36,909 --> 00:02:41,640 small angle formula, tells me that the little distance D that it travels. 39 00:02:41,640 --> 00:02:50,562 In the course of a year is D * mu and this is its motion in web units. 40 00:02:50,562 --> 00:02:57,600 Well if I write mu divided by 206, 265 arc seconds. 41 00:02:57,600 --> 00:03:03,489 Then, this is a number D will be in whatever units you measure capital D 42 00:03:03,489 --> 00:03:06,741 distance to the star. If you write it this way. 43 00:03:06,741 --> 00:03:12,185 but since this is in arc seconds per year, I will get an answer for the 44 00:03:12,185 --> 00:03:16,568 velocity when I this, this number, is the distance the 45 00:03:16,568 --> 00:03:21,234 star travels in a year. that'll give me say, parsecs per year, as 46 00:03:21,234 --> 00:03:24,416 the units in which I measure the velocity. 47 00:03:24,416 --> 00:03:29,930 Typically, we measure velocity in a more convenient units of kilometers per 48 00:03:29,930 --> 00:03:32,970 second. And so, in kilometers per second, one 49 00:03:32,970 --> 00:03:41,303 finds that V In kilometer per second, is basically given by mu divided by one 50 00:03:41,303 --> 00:03:48,380 arc second times D in parsec times a collection of 51 00:03:48,380 --> 00:03:53,584 convertion factors converting parsecs to kilometers and years to seconds. 52 00:03:53,584 --> 00:03:59,288 And the net result is that the conversion factor you can do the algebra is 4.74. 53 00:03:59,288 --> 00:04:05,206 So that's the meaning of this rather dimensionally confusing expression that 54 00:04:05,206 --> 00:04:08,700 we have here. this is only a measure of stars' 55 00:04:08,700 --> 00:04:12,692 transverse velocity. A star can also have an a radial 56 00:04:12,692 --> 00:04:16,717 velocity. We can measure its radial velocity up by 57 00:04:16,717 --> 00:04:20,842 measuring the Dopler shift. If you find some spectral line, we find 58 00:04:20,842 --> 00:04:24,217 its shift. if you're careful you will notice that I 59 00:04:24,217 --> 00:04:29,276 have changed the sign here of the radial velocity relative to our convention, the 60 00:04:29,276 --> 00:04:33,503 previous convention that I used when I explained the Doppler shift, is the one 61 00:04:33,503 --> 00:04:37,560 common among when studying sound. This convention is the astronomical 62 00:04:37,560 --> 00:04:40,322 convention. A positive radial velocity here means 63 00:04:40,322 --> 00:04:43,534 that lambda is bigger than lambda zero. That's a redshift. 64 00:04:43,534 --> 00:04:48,211 A positive radial velocity represents a star moving away from us and that's the 65 00:04:48,211 --> 00:04:52,438 convention we will follow from now on. So that if I'm looking at a star, and 66 00:04:52,438 --> 00:04:57,171 it's over here then the radial velocity is a measure that I get from the Doppler 67 00:04:57,171 --> 00:05:01,696 shift measures this component of its motion, the tangential velocity measures 68 00:05:01,696 --> 00:05:06,119 this component of its motion, and this represents a star that is doing both 69 00:05:06,119 --> 00:05:10,483 motions at the same time in other words, moving in some diagonal direction. 70 00:05:10,483 --> 00:05:14,492 And that way, I can get a complete picture of the motion of the star. 71 00:05:14,492 --> 00:05:19,210 And just to give you an illustration of the dramatic effects over the long term 72 00:05:19,210 --> 00:05:23,456 of proper motion, most stars move relatively slowly, but if you give them 73 00:05:23,456 --> 00:05:28,230 enough time, things get interesting. This is an animation of the constellation 74 00:05:28,230 --> 00:05:33,135 that we now call the Big Dipper. this is not the way the Big Dipper looks. 75 00:05:33,135 --> 00:05:38,298 This is as it would have looked from earth in 100,000 BC were you to look at, 76 00:05:38,298 --> 00:05:42,945 at it and time runs rather quickly here, but you see the stars moving. 77 00:05:42,945 --> 00:05:46,947 we are approaching the present. Here we have the Big Dipper. 78 00:05:46,947 --> 00:05:50,045 The stars of the Big Dipper are a constellation. 79 00:05:50,045 --> 00:05:54,111 They are not a cluster. They are not near each other in the sky, 80 00:05:54,111 --> 00:05:57,532 in any sense. And over time their peculiar motions as 81 00:05:57,532 --> 00:06:01,544 it's called will completely change the appearance of a constellation. 82 00:06:01,544 --> 00:06:05,440 It will not stay the way it is. Stars do move, if you give them time.