1 00:00:01,280 --> 00:00:06,382 So, using closely looking at the stars and making some measurements and thinking 2 00:00:06,382 --> 00:00:09,517 about it, we can actually measure the mass of stars. 3 00:00:09,517 --> 00:00:12,774 And we can ask, we're almost ready to start modelling. 4 00:00:12,774 --> 00:00:17,504 We need to know where do the masses of stars along the main sequence line up 5 00:00:17,504 --> 00:00:21,006 with their masses. And so, we can add masses into our plot 6 00:00:21,006 --> 00:00:24,692 for the main sequence. And here's what we learn, masses don't 7 00:00:24,692 --> 00:00:28,316 vary very much. way down here, down where the red dwarves 8 00:00:28,316 --> 00:00:33,169 reside, masses of stars, we discover, are as small as a tenth of a solar mass, but 9 00:00:33,169 --> 00:00:37,531 not much smaller than that. And the biggest, most luminous, hottest, 10 00:00:37,531 --> 00:00:40,996 main sequence stars top out at 50 solar masses. 11 00:00:40,996 --> 00:00:46,600 We rarely find anything even up there. And so, by measuring a few stars along 12 00:00:46,600 --> 00:00:52,498 the main sequence, we can figure out the mass of a point along the main sequence. 13 00:00:52,498 --> 00:00:57,264 The main story is that the heaviest amounts stars are the hottest 14 00:00:57,264 --> 00:01:00,853 and the most luminous. And now, we can fit it into the model. 15 00:01:00,853 --> 00:01:05,781 Because when you're going model of star, basically, if you say a star is a ball of 16 00:01:05,781 --> 00:01:10,465 hydrogen, I don't need to tell a good model or the luminosity of the radius. I 17 00:01:10,465 --> 00:01:13,020 would tell them take a bottle of hydrogen, 18 00:01:13,020 --> 00:01:19,751 held up on in hydrostatic equilibrium against its gravitational attraction by 19 00:01:19,751 --> 00:01:23,845 hydrogen fusion, and then run your equation. Now, in practice, that's a 20 00:01:23,845 --> 00:01:27,518 little bit difficult. But in principle, nature knows how to do 21 00:01:27,518 --> 00:01:30,288 that. So, if you give nature a ball of hydrogen 22 00:01:30,288 --> 00:01:34,864 of a given mass, it'll produce a star, and that star will lie somewhere along 23 00:01:34,864 --> 00:01:39,006 the main sequence. And we can now attempt to study modeling. 24 00:01:39,006 --> 00:01:42,564 We'll discuss the results of that in our next clip. 25 00:01:42,564 --> 00:01:47,837 But first, let's note that there's a very reasonable approximation you can do 26 00:01:47,837 --> 00:01:52,450 better but the luminosity along the main sequence scales with mass. 27 00:01:52,450 --> 00:01:57,392 As I said, the heavier stars are more luminous and it scales like the three, 28 00:01:57,392 --> 00:02:00,358 third, three and a half, or fourth power of mass. 29 00:02:00,358 --> 00:02:05,828 It's not exactly fixed relation you can improve this, and go into the details, 30 00:02:05,828 --> 00:02:10,544 but this is good enough. What this means is that a ma, a star that 31 00:02:10,544 --> 00:02:15,815 is twice as massive as the sun has a luminosity between eight and sixteen 32 00:02:15,815 --> 00:02:21,799 times the luminosity of the sun. It's way more luminous, this is how change from a 33 00:02:21,799 --> 00:02:27,284 tenth of a solar mass, to ten solar masses, gives us this five orders of 34 00:02:27,284 --> 00:02:31,345 magnitude or seven orders magnitude change in luminosity. 35 00:02:31,345 --> 00:02:36,758 Now, this sort of makes and are models bear this out. A heavier star has more 36 00:02:36,758 --> 00:02:41,260 pressure from the outer layers crushing down on its core, the pressure in the 37 00:02:41,260 --> 00:02:44,098 center is higher, densities in the center are higher. 38 00:02:44,098 --> 00:02:48,526 We said that fusion proceeds best at high temperatures and densities, and that 39 00:02:48,526 --> 00:02:51,592 means the rate of fusion in a big star will be higher. 40 00:02:51,592 --> 00:02:55,339 That's the way that mass is going to determine the rate of fusion. 41 00:02:55,339 --> 00:02:58,859 And so, it makes sense that bigger stars will be more luminous. 42 00:02:58,859 --> 00:03:01,788 But note, that if say, the core of a star like the 43 00:03:01,788 --> 00:03:06,505 sun, we estimated how long the sun would last by saying, if it converted all of 44 00:03:06,505 --> 00:03:09,891 it's hydrogen to helium, it would last 100 billion years. 45 00:03:09,891 --> 00:03:14,305 But, the sun will actually stop converting hydrogen to helium when it has 46 00:03:14,305 --> 00:03:18,780 converted a tenth of it's hydrogen because that's the amount that will be 47 00:03:18,780 --> 00:03:22,590 available in the core. If all stars had a bout a tenth of their 48 00:03:22,590 --> 00:03:27,488 hydrogen available in the core, what this would tell us is that big stars run out 49 00:03:27,488 --> 00:03:33,525 of hydrogen much faster than slow stars, and indeed, appended to this table of the 50 00:03:33,525 --> 00:03:39,634 main sequence is a list of main sequence lifetimes adjusted. Remember, right over 51 00:03:39,634 --> 00:03:44,890 here, the sun has a main sequence lifetime of about ten billion years and 52 00:03:44,890 --> 00:03:50,350 stars with te, luminosity ten times that of the sun, it turns out only last a 53 00:03:50,350 --> 00:03:55,742 billion years. And up here, the really bright type O and B stars might last only 54 00:03:55,742 --> 00:04:00,861 ten or a few million years, and the lightest red dwarfs last hundreds of 55 00:04:00,861 --> 00:04:04,810 billions of years. What that tells us is that if we see a 56 00:04:04,810 --> 00:04:09,971 type O main sequence star, since they only live, two, three, five, ten million 57 00:04:09,971 --> 00:04:11,910 years, that star is brand new. 58 00:04:11,910 --> 00:04:16,750 When the sun was formed five billion years ago, that star was nowhere near to 59 00:04:16,750 --> 00:04:19,768 existing. So, when we see, say in Orions belt type 60 00:04:19,768 --> 00:04:23,854 O stars, we know that very recently stars have been forming there. 61 00:04:23,854 --> 00:04:28,884 And we'll see what modeling tells us and conclude the week and the last clip of 62 00:04:28,884 --> 00:04:29,818 the week now.