1 00:00:00,000 --> 00:00:03,928 So, that's what went down in the inner solar system. 2 00:00:03,928 --> 00:00:09,855 with 90% of the non-solar mass being in Venus and Saturn, 3 00:00:09,855 --> 00:00:14,073 you wouldn't be surprised to learn that the real action Went wn in the outer 4 00:00:14,073 --> 00:00:17,124 solar system beyond what we call the snow line. 5 00:00:17,124 --> 00:00:22,411 The snow line is that line that separates the inner solar system where water was a 6 00:00:22,411 --> 00:00:26,148 vapor from the outer solar system where water was a solid. 7 00:00:26,148 --> 00:00:30,238 Why is this so important? Because those initial dust, solid dust 8 00:00:30,238 --> 00:00:34,717 fragments that coalesced chemically to form planetesimals slowly and 9 00:00:34,717 --> 00:00:38,287 painstakingly in the inner solar system were very rare. 10 00:00:38,287 --> 00:00:43,351 They were made of these trace elements, iron, nickel, alumina, they are very rare 11 00:00:43,351 --> 00:00:47,165 in the solar system. In the outer solar system, water was a 12 00:00:47,165 --> 00:00:50,277 solid. Little grains of ice could stick to each 13 00:00:50,277 --> 00:00:54,182 other chemically. Water is much more prevalent in the solar 14 00:00:54,182 --> 00:00:59,611 nebula and in the solar system today, than iron or nickel or aluminum or all of 15 00:00:59,611 --> 00:01:03,384 them put together. Despite the smaller overall density at 16 00:01:03,384 --> 00:01:08,614 larger radius, the fact that water was available to coalesce as solid particles 17 00:01:08,614 --> 00:01:13,314 meant that the whole process of planetesimal and protoplanet formation 18 00:01:13,314 --> 00:01:17,646 goes much, much faster. This is especially true right at the snow 19 00:01:17,646 --> 00:01:21,078 line, about five astronomical units from the sun. 20 00:01:21,078 --> 00:01:24,510 And so, Jupiter, which lives, right at that radius, 21 00:01:24,510 --> 00:01:30,170 grows very, very fast. it goes through the initial accretion of 22 00:01:30,170 --> 00:01:36,563 planetesimals to protoplanets much, much faster than the inner planet and reaches 23 00:01:36,563 --> 00:01:40,399 very rapidly a massive ten to fifteen earth masses. 24 00:01:40,399 --> 00:01:43,097 And, this is a crucial borderline 25 00:01:43,097 --> 00:01:46,660 what is this object made of? Well, by this time, it's certainly 26 00:01:46,660 --> 00:01:49,990 spherical, it has melted. It has chemically differentiated. 27 00:01:49,990 --> 00:01:52,563 Iron will have dropped into the central core. 28 00:01:52,563 --> 00:01:57,139 There will be an outer core of silicates and rocky materials and then the outer 29 00:01:57,139 --> 00:02:00,399 mantle will be water. It was made, much, much of the planet 30 00:02:00,399 --> 00:02:04,116 would have been made of ice. The ice would have melted, so we now have 31 00:02:04,116 --> 00:02:08,578 this sort of layered structure with an inner iron core, an outer silicate core, 32 00:02:08,578 --> 00:02:11,952 and a watery mantle. And this object, when it reaches ten to 33 00:02:11,952 --> 00:02:16,127 fifteen Earth masses, achieves an important milestone besides melting and 34 00:02:16,127 --> 00:02:20,417 chemical differentiation, one that the Earth, which never got this big, never 35 00:02:20,417 --> 00:02:23,340 had a chance to achieve. At this point, 36 00:02:23,340 --> 00:02:28,174 the gravitational attraction of this large object, which is become quite 37 00:02:28,174 --> 00:02:33,747 compact under the force of its gravity, because it's held up by pressure is large 38 00:02:33,747 --> 00:02:37,238 enough to bind an atmosphere of hydrogen and helium. 39 00:02:37,238 --> 00:02:39,790 Now, this is a breakthrough because, of course, 40 00:02:39,790 --> 00:02:45,332 while water is more prevalent than the solar nebula then, nickel water and 41 00:02:45,332 --> 00:02:51,091 nickel together are both trace elements. What the solar nebula is really full of 42 00:02:51,091 --> 00:02:54,618 is hydrogen and helium gas, that's 98% of the mass. 43 00:02:54,618 --> 00:02:59,729 Once you have an object massive enough and to bind hydrogen and helium, 44 00:02:59,729 --> 00:03:05,977 remember, we saw that hydrogen and helium are not bound to earth, but at the lower 45 00:03:05,977 --> 00:03:10,172 temperatures in the outer nebula, they will bind to Jupiter. 46 00:03:10,172 --> 00:03:14,864 Jupiter is rapidly able to gravitationally attract all of the gas 47 00:03:14,864 --> 00:03:20,197 essentially in its vicinity. in fact, one can imagine the formation of 48 00:03:20,197 --> 00:03:25,813 Jupiter as a gas giant essentially as a gravitational collapse, a gravitational 49 00:03:25,813 --> 00:03:31,643 instability, similar in smaller scale to what happened at the center that produced 50 00:03:31,643 --> 00:03:35,691 the protosun. In other words, the dense core that is 51 00:03:35,691 --> 00:03:42,031 the core of Jupiter forms an instability, causes a chunk of the gaseous disk to 52 00:03:42,031 --> 00:03:45,975 collapse onto that core. What does this produce? 53 00:03:45,975 --> 00:03:52,083 Well, it produces the usual phenomena, it produces increased angular velocity as 54 00:03:52,083 --> 00:03:56,491 the gas collapses, we find that the rotation speeds up. 55 00:03:56,491 --> 00:04:01,130 Indeed, Jupiter rotates about its axis once every nine hours. 56 00:04:01,130 --> 00:04:06,930 And a giant object like Jupiter, indeed, spins much faster than Earth does. 57 00:04:06,930 --> 00:04:12,145 In addition this causes the flattening into a disk, just as the solar system 58 00:04:12,145 --> 00:04:16,239 flattened into a disk. So, we get the phenomenon around Jupiter 59 00:04:16,239 --> 00:04:21,730 of an accretion disk which is the place from which gas is falling onto the 60 00:04:21,730 --> 00:04:24,460 nascent planet. And in that disk, 61 00:04:24,460 --> 00:04:29,205 some of the material, because of the centrifugal barrier, will not fall on to 62 00:04:29,205 --> 00:04:31,140 Jupiter. Some of it will be icy. 63 00:04:31,140 --> 00:04:36,073 And we have as with the inner solar system, we have the formation of planets. 64 00:04:36,073 --> 00:04:40,887 Here, the leftovers will form moons, and as we'll see closer to the planet rings, 65 00:04:40,887 --> 00:04:45,878 and so these structures in the equatorial plane of Jupiter are just mimicking on a 66 00:04:45,878 --> 00:04:50,347 smaller scale, the entire planetary system that lives on the equatorial plane 67 00:04:50,347 --> 00:04:52,785 of the sun, it's the same issue of a cloud 68 00:04:52,785 --> 00:04:56,964 collapsing, spinning up, and flattening. In addition, of course, the core is 69 00:04:56,964 --> 00:05:01,658 heated by Kelvin-Helmholtz heating, but we have a, a rapid runaway growth, 70 00:05:01,658 --> 00:05:05,589 especially towards the end. I takes about ten million years, 71 00:05:05,589 --> 00:05:10,719 not a, coincidentally, a very good time scale because that's when the gas gets 72 00:05:10,719 --> 00:05:16,898 blown away by the sun for Jupiter to accrete roughly its current mass and over 73 00:05:16,898 --> 00:05:21,117 the same time it essentially exhaust all the 74 00:05:21,117 --> 00:05:26,139 available gas near its orbit. For whereas, Earth was able to trap all 75 00:05:26,139 --> 00:05:30,755 the planetisimal matter, but the gas was essentially unbound and the the inner 76 00:05:30,755 --> 00:05:36,184 nebula was still full of hydrogen and helium gas until the T Tauri wind blew it 77 00:05:36,184 --> 00:05:39,239 away. And the outer nebula before the T Tauri 78 00:05:39,239 --> 00:05:44,397 went, cleans up Jupiter and Saturn have essentially sucked up all the gas in 79 00:05:44,397 --> 00:05:47,742 their orbits. Now, Saturn is not as massive as Jupiter. 80 00:05:47,742 --> 00:05:51,743 Well, Saturn is a little farther out. The density is smaller there. 81 00:05:51,743 --> 00:05:57,098 There is less water Saturn accretes to critical helium and hydrogen binding mass 82 00:05:57,098 --> 00:06:00,853 a little bit later. The density is also smaller but mostly it 83 00:06:00,853 --> 00:06:04,054 starts later. It has less time, has less gas left, and 84 00:06:04,054 --> 00:06:08,855 so Saturn never quite attains the dimensions of Jupiter, but it repeats the 85 00:06:08,855 --> 00:06:13,657 same process, gravitational instability, collapse of a cloud, speeding up of the 86 00:06:13,657 --> 00:06:17,473 rotation, flattening out of an of accretion disk and moves in the 87 00:06:17,473 --> 00:06:21,612 equatorial plane. So, Jupiter and Saturn lives the rich 88 00:06:21,612 --> 00:06:25,710 life outside the snow line and so become fat and big. 89 00:06:25,710 --> 00:06:29,897 What about Uranus and Neptune? Well, those are qualitatively different 90 00:06:29,897 --> 00:06:32,506 object. They're giants on terrestrial scale. 91 00:06:32,506 --> 00:06:37,361 They're not as big as Jupiter and Saturn and they're not predominantly hydrogen, 92 00:06:37,361 --> 00:06:41,003 despite what we might have heard. They're predominantly ices. 93 00:06:41,003 --> 00:06:45,615 each of them has only about a sole Earth mass, of hydrogen bound to it. 94 00:06:45,615 --> 00:06:49,560 presumably, they started, yet later there was not much gas left. 95 00:06:49,560 --> 00:06:54,570 But even so, we have a problem. In their current orbits, there is no way 96 00:06:54,570 --> 00:07:00,440 that the modeling tells us that these planets would have grown in time to bind 97 00:07:00,440 --> 00:07:05,666 any hydrogen at all in the time before the sun blew the hydrogen away. 98 00:07:05,666 --> 00:07:11,536 What must have happened is that they must have formed closer to the sun where the 99 00:07:11,536 --> 00:07:16,980 nebula was denser and then migrated out, migrated out. 100 00:07:16,980 --> 00:07:21,124 I thought that we solved Newton's equations and they told us that an object 101 00:07:21,124 --> 00:07:24,670 orbiting the sun will move in a closed orbit, which is an ellipse. 102 00:07:24,670 --> 00:07:29,246 Newton solved these equations, he solved the correctly, what is this, migrating, 103 00:07:29,246 --> 00:07:32,811 why would something move in an orbit that is not an ellipse? 104 00:07:32,811 --> 00:07:36,140 This is an important topic so let's pay attention to it. 105 00:07:36,140 --> 00:07:40,910 So indeed, the motion of an object around the sun or, in fact, the slightly more 106 00:07:40,910 --> 00:07:45,374 complicated problem of two objects orbiting each other is a problem that 107 00:07:45,374 --> 00:07:49,655 physics students solve in their first or second year of doing physics. 108 00:07:49,655 --> 00:07:54,608 And it's completely solved when the solutions are ellipses or hyperbolas if 109 00:07:54,608 --> 00:07:58,400 the motion is not bound, but we know how to solve that problem. 110 00:07:58,400 --> 00:08:02,400 Things become complicated when we have not one planet orbiting the sun but, say, 111 00:08:02,400 --> 00:08:06,249 two planets orbiting the sun and you want to take into account not only the 112 00:08:06,249 --> 00:08:09,997 gravitational attraction of the sun on each of these objects but also the 113 00:08:09,997 --> 00:08:12,377 gravitational attraction of one upon the other. 114 00:08:12,377 --> 00:08:16,580 This brings you into the three or four or whatever body problem and the three body 115 00:08:16,580 --> 00:08:19,416 problem in Newtonian physics is not a freshman exercise. 116 00:08:19,416 --> 00:08:23,289 In fact, it's not solved and in some technical sense, not analytically 117 00:08:23,289 --> 00:08:26,829 solvable because the problem has a property called chaos. 118 00:08:26,829 --> 00:08:31,921 it is the fact that small, infinitesimal changes in these initial conditions, 119 00:08:31,921 --> 00:08:36,082 where and with what velocity you start the objects out, can lead to 120 00:08:36,082 --> 00:08:40,430 qualitatively different results. And so, a direct solution is difficult. 121 00:08:40,430 --> 00:08:45,274 How do we actually understand what's going to happen in something complicated 122 00:08:45,274 --> 00:08:49,559 like the solar system, which is at the very least a nine body problem? 123 00:08:49,559 --> 00:08:51,926 Well, one possibility is we numerically 124 00:08:51,926 --> 00:08:55,254 simulate the problem. In other words, we run through the 125 00:08:55,254 --> 00:08:59,609 exercise that I described at the end of our Newton's Laws discussion. 126 00:08:59,609 --> 00:09:04,328 We start with the initial positions and velocities, we compute an acceleration. 127 00:09:04,328 --> 00:09:08,140 Figure out from that, where things will be a few years hence. 128 00:09:08,140 --> 00:09:11,706 Repeat the, recalculate the forces, recalculate the accelerations, and 129 00:09:11,706 --> 00:09:14,224 basically go through that process on a computer. 130 00:09:14,224 --> 00:09:18,001 It's difficult but it's doable. That's how we know what the solar system 131 00:09:18,001 --> 00:09:21,830 will do billions of years hence and what it did, billions of years ago. 132 00:09:21,830 --> 00:09:26,288 but under some circumstances, it's useful to think the, under most circumstances, 133 00:09:26,288 --> 00:09:30,117 the gravitational force of the sun dominates gravity in the solar system 134 00:09:30,117 --> 00:09:33,370 simply because the sun is so much massive than everybody else. 135 00:09:33,370 --> 00:09:36,940 This might not be true when two objects come very near to each other. 136 00:09:36,940 --> 00:09:41,081 So certainly, the dominant gravitational force acting on me right now is that of 137 00:09:41,081 --> 00:09:44,393 the Earth, not of the sun. Despite the sun being more massive, the 138 00:09:44,393 --> 00:09:47,581 Earth is much closer. So, if two objects are moving in solar 139 00:09:47,581 --> 00:09:51,949 orbits but then, approach each other very close, what I can do is sort of stitch 140 00:09:51,949 --> 00:09:55,820 together approximations as long as they're far enough apart, I'm going to 141 00:09:55,820 --> 00:09:58,695 ignore their gravitational attraction on each other. 142 00:09:58,695 --> 00:10:03,064 When they get close, then for an instant, I'm going to forget about the sun and let 143 00:10:03,064 --> 00:10:07,101 them collide with each other and only treat the gravitational attraction 144 00:10:07,101 --> 00:10:09,939 between them. And then, once they've moved far apart 145 00:10:09,939 --> 00:10:12,393 again, they will have new, changed velocities. 146 00:10:12,393 --> 00:10:16,967 I will plug those in to the equations for solar orbit And essentially, the objects 147 00:10:16,967 --> 00:10:21,150 will have transitioned through the collision from one solar orbit to a new 148 00:10:21,150 --> 00:10:24,834 solar orbit. And this process goes under many names, 149 00:10:24,834 --> 00:10:30,361 gravitational slingshot, gravity assist. It's often used by NASA to propel its 150 00:10:30,361 --> 00:10:35,027 spacecraft to higher orbits. This is how Voyager got to leave the 151 00:10:35,027 --> 00:10:39,477 solar system, it's how Galileo got to travel as far as Jupiter. 152 00:10:39,477 --> 00:10:45,630 And the way it works is that if you take into account that the, the scattering 153 00:10:45,630 --> 00:10:50,475 process, the collision is with the gravitational collision, is with a moving 154 00:10:50,475 --> 00:10:53,439 planet and you adjust the initial conditions right, 155 00:10:53,439 --> 00:10:56,810 you can set it up. So, that in the process of collision, the 156 00:10:56,810 --> 00:11:01,879 light or object, in this case, say, the spacecraft picks up some extra orbital 157 00:11:01,879 --> 00:11:07,395 velocity from the moving planet and here is, for example, a demonstration. 158 00:11:07,395 --> 00:11:13,205 This is the trajectory of the Dawn Craft, whose images of Vesta, the asteroid, we 159 00:11:13,205 --> 00:11:17,765 were looking at before. This was launched from Earth on one of 160 00:11:17,765 --> 00:11:23,648 those Hohmann Transfer, those elliptical orbits we talked about, such that almost 161 00:11:23,648 --> 00:11:27,620 at the antipodal point it was meeting up with Mars. 162 00:11:27,620 --> 00:11:31,601 And then it wasn't quite antipodal, it didn't go into Mars orbit. 163 00:11:31,601 --> 00:11:35,894 But as it zoomed past Mars, Mars accelerated it, and then, of course, as 164 00:11:35,894 --> 00:11:40,435 it passed Mars, Mars slowed it down. Then in effect though, because Mars is 165 00:11:40,435 --> 00:11:45,788 moving, is that it acquired some extra energy from the collision with Mars went 166 00:11:45,788 --> 00:11:51,357 from one solar orbit into a new solar orbit and the design of the orbit was 167 00:11:51,357 --> 00:11:56,926 such, this was precisely a minimum energy trajectory to the orbit with which we 168 00:11:56,926 --> 00:12:01,747 wanted, in, to which we wanted it to arrive, which is Vesta's orbit out here, 169 00:12:01,747 --> 00:12:07,316 at a larger distance from the sun, and it arrived and then slowed down and orbited 170 00:12:07,316 --> 00:12:10,440 along with Vesta, fell into orbit around Vesta. 171 00:12:10,440 --> 00:12:15,456 This is object of careful design and there, it took those beautiful images. 172 00:12:15,456 --> 00:12:20,646 And when it leaves, Vesta will hop up to an, the orbit of Ceres, another asteroid 173 00:12:20,646 --> 00:12:25,311 and will take images of Ceres. And so this gravity assist is nothing 174 00:12:25,311 --> 00:12:27,808 new. This is a, this perturbative 175 00:12:27,808 --> 00:12:32,276 approximation works well when the objects encounter each other once. 176 00:12:32,276 --> 00:12:37,992 And then, are not, not any very close in the future because Dawn is now in Vesta 177 00:12:37,992 --> 00:12:41,277 orbit and will not get close to Mars the future. 178 00:12:41,277 --> 00:12:46,086 It looks different when this situation is that two objects are in 179 00:12:46,086 --> 00:12:52,376 closed orbits around the sun and so will be at a nearest approach every time their 180 00:12:52,376 --> 00:12:57,130 orbital periods coincide. We'll see that in a moment in this nice 181 00:12:57,130 --> 00:13:01,400 demonstration and maybe that will clarify the situation. 182 00:13:01,400 --> 00:13:07,118 So this is our old planetary configurations simulator which I'm going 183 00:13:07,118 --> 00:13:11,554 to re-purpose to a different goal. So, imagine that we have two planets, 184 00:13:11,554 --> 00:13:14,471 both orbiting the sun, initially circular orbits. 185 00:13:14,471 --> 00:13:18,785 I'm going to start, as always, when the two planets are in opposition or 186 00:13:18,785 --> 00:13:23,525 conjunction, or whatever you want to call it, but they're lined up with the sun, 187 00:13:23,525 --> 00:13:26,259 this is the moment of their closest approach. 188 00:13:26,259 --> 00:13:30,999 At this point, what is going on? Well there's an attraction and as the 189 00:13:30,999 --> 00:13:35,217 inner planet has been catching up with the the outer planet the 190 00:13:35,217 --> 00:13:40,672 gravitational attraction between them has been attempting to distort the inner 191 00:13:40,672 --> 00:13:46,541 orbit this way, because the inner planet is attracted to the outer planet, so it, 192 00:13:46,541 --> 00:13:49,648 it, it acquires a slightly higher velocity. 193 00:13:49,648 --> 00:13:54,896 At the same time, it's slowing down the orbit of the outer planet, and so the 194 00:13:54,896 --> 00:13:59,991 outer planet's orbit is being distorted slightly in this direction and, of 195 00:13:59,991 --> 00:14:03,659 course, I grossly exaggerate what is going on. 196 00:14:03,659 --> 00:14:10,668 Now what I'm going to do now is allow the animation to run for a bit and we'll see 197 00:14:10,668 --> 00:14:17,515 that after a while as usual, the inner planet outruns the outer planet and if we 198 00:14:17,515 --> 00:14:22,487 wait long enough they come into conjunction again about here. 199 00:14:22,487 --> 00:14:28,077 Well, this time, again, in conjunction, there's a distortion of the orbit. 200 00:14:28,077 --> 00:14:34,270 The inner orbit is being distorted in this direction while the outer orbit is 201 00:14:34,270 --> 00:14:40,130 being distorted in that direction. and you can see that we can go do one 202 00:14:40,130 --> 00:14:45,835 more round of this crazy race. And what is going to happen is that they 203 00:14:45,835 --> 00:14:49,690 will come into conjunction again at some other 204 00:14:49,690 --> 00:14:54,121 position along their orbits. And I've got it timed so it's kind of 205 00:14:54,121 --> 00:14:57,276 close to where it was before, but not too close. 206 00:14:57,276 --> 00:15:01,371 This time, the inner orbit is being distorted into this shape. 207 00:15:01,371 --> 00:15:05,937 And of, again, I am grossly exaggerating, and the outer orbit into the 208 00:15:05,937 --> 00:15:08,622 perpendicular shape, something like this. 209 00:15:08,622 --> 00:15:14,060 You see that what's going on is that the net result of all these deformations is 210 00:15:14,060 --> 00:15:19,297 not going to be very much because at each conjunction, the orbit is deformed in a 211 00:15:19,297 --> 00:15:20,933 different direction. Aha. 212 00:15:20,933 --> 00:15:26,507 Now, I'm going to try the same thing, except, I'm going to set up the ratio of 213 00:15:26,507 --> 00:15:29,955 the radii of the two planets to be one to 1.59. 214 00:15:29,955 --> 00:15:35,676 If you check with Kepler's laws, this will make the ratio of their periods one 215 00:15:35,676 --> 00:15:39,918 to two. and we'll see that this changes things 216 00:15:39,918 --> 00:15:44,474 considerably. what's going on here, again, during this 217 00:15:44,474 --> 00:15:51,516 conjunction, the inner orbit is being stretched out in this direction while the 218 00:15:51,516 --> 00:15:55,161 outer orbit is being stretched out that way. 219 00:15:55,161 --> 00:16:01,361 and now, if we let the animation run we'll see that because the ratio of the 220 00:16:01,361 --> 00:16:07,156 orbits is two [COUGH] the next conjunction will happen precisely after 221 00:16:07,156 --> 00:16:12,637 the great, slower outer planet has completed one rotation and the inner 222 00:16:12,637 --> 00:16:18,902 planet has completed two and guess what, the deformation of the orbits this time, 223 00:16:18,902 --> 00:16:25,976 is in the same direction. What happens this time is that at each 224 00:16:25,976 --> 00:16:30,993 encounter, the orbit is further deformed in the same direction. 225 00:16:30,993 --> 00:16:36,820 When you have orbital periods, this was the situation when P2 was 2P1. 226 00:16:36,820 --> 00:16:41,298 When the ratio of the periods is a fraction with small numerator and 227 00:16:41,298 --> 00:16:44,674 denominator, we'll get once every denominator number 228 00:16:44,674 --> 00:16:49,412 of periods a conjunction with extends the orbit in the same direction. 229 00:16:49,412 --> 00:16:53,242 And the orbit over time will become more and more deformed. 230 00:16:53,242 --> 00:16:57,721 This is called orbital resonance. What we saw then is this phenomenon 231 00:16:57,721 --> 00:17:01,746 called orbital resonance. from a distance, the gravitational 232 00:17:01,746 --> 00:17:06,160 interaction between two planets might perturb their orbits slightly. 233 00:17:06,160 --> 00:17:12,091 If the periods of the solar orbits are resonant, what does resonant mean? 234 00:17:12,091 --> 00:17:19,011 That means that nP1 is nP2 where n and m are sufficiently small integers because 235 00:17:19,011 --> 00:17:25,684 this means that if P2 is the larger orbit so that n is the larger number, every n 236 00:17:25,684 --> 00:17:30,203 orbits of this one conjunction happens at exactly the same place. 237 00:17:30,203 --> 00:17:33,029 And so, every n orbit, the effect is enhanced. 238 00:17:33,029 --> 00:17:36,946 If n is not too large, then we get this resonant perturbation. 239 00:17:36,946 --> 00:17:42,339 And the net result is that the orbit will be elongated in a particular direction. 240 00:17:42,339 --> 00:17:47,219 And notice that as it's elongated in that direction, the distance of closest 241 00:17:47,219 --> 00:17:52,498 approach only gets closer and so this again is a nonlinear process that can 242 00:17:52,498 --> 00:17:55,474 continue and so success of perturbations add. 243 00:17:55,474 --> 00:18:00,885 Now, there's two things that can happen in the details of that dynamic, is beyond 244 00:18:00,885 --> 00:18:03,590 the kind of math that we're want to, going to do. 245 00:18:03,590 --> 00:18:09,136 one possibility is you get meta-stable resonances, not quite stable orbits that 246 00:18:09,136 --> 00:18:13,059 could go on forever, but orbits in which two things can 247 00:18:13,059 --> 00:18:18,528 continually orbit for a long time and a great example of that is Earths mosrt 248 00:18:18,528 --> 00:18:23,588 famous other moon, it's name is Cruithne or whatever the pronunciation is and it 249 00:18:23,588 --> 00:18:29,043 actually orbits the sun in a solar orbit that is one to one resonance with that of 250 00:18:29,043 --> 00:18:32,000 the Earth. The objects will never collide, the 251 00:18:32,000 --> 00:18:37,521 orbits are tilted and the timing is off. But what happens is that Cruithne orbits 252 00:18:37,521 --> 00:18:42,933 in a more elliptical orbit than the Earth does but its period is precisely one to 253 00:18:42,933 --> 00:18:45,969 one. You will see that every time the two 254 00:18:45,969 --> 00:18:51,628 objects or arrive at this sort of intersection, from our point of view in, 255 00:18:51,628 --> 00:18:57,208 in right ascension of the orbits. they arrive there in precisely the same 256 00:18:57,208 --> 00:19:00,834 configuration. This is orbital locking or resonance. 257 00:19:00,834 --> 00:19:06,073 And what this looks like from Earth is if you imagine fixing the earth in one 258 00:19:06,073 --> 00:19:07,752 place, so this is the sun, 259 00:19:07,752 --> 00:19:13,260 the slight wiggle in the Earth's orbit about the sun is due to the ellipticity 260 00:19:13,260 --> 00:19:16,892 of the Earth's orbit. And here's Cruithne orbiting the sun but 261 00:19:16,892 --> 00:19:21,462 as we see it from Earth, Cruithne goes around the sort of bean-shaped orbit. 262 00:19:21,462 --> 00:19:25,446 This is often very confusing. People describe this bean-shaped orbit 263 00:19:25,446 --> 00:19:30,017 and try to figure out why anything would orbit the sun in a bean-shaped orbit. 264 00:19:30,017 --> 00:19:34,528 It looks to us as though Cruithne is orbiting the sun in a bean-shaped orbit. 265 00:19:34,528 --> 00:19:39,215 That is really just the point of view from Earth because we're moving along our 266 00:19:39,215 --> 00:19:41,969 orbit. And indeed, there are three or four other 267 00:19:41,969 --> 00:19:45,250 objects that are locked into resonant orbits with Earth. 268 00:19:45,250 --> 00:19:50,948 And so, we have more than one sort of moon, but only one that is both naked eye 269 00:19:50,948 --> 00:19:56,528 visible and actually in Earth's orbit. But this is sort of a bound orbit between 270 00:19:56,528 --> 00:19:58,680 the Earth and the sun, where 271 00:19:58,680 --> 00:20:03,522 together, controlling the motion of this piece of rock, Cruithne which is also 272 00:20:03,522 --> 00:20:06,465 quite small. This is not the standard outcome of 273 00:20:06,465 --> 00:20:09,652 orbital resonance. Typically, what happens in orbital 274 00:20:09,652 --> 00:20:14,250 resonance is that because the orbit is deformed in the coherent way in a 275 00:20:14,250 --> 00:20:18,235 particular direction, the entire situation become, because of this 276 00:20:18,235 --> 00:20:22,464 nonlinearity, the entire situation becomes unstable and the orbit is 277 00:20:22,464 --> 00:20:25,836 destabilized. This is probably best characterized in 278 00:20:25,836 --> 00:20:30,042 the asteroid belt. The asteroid belt, remember, lies between 279 00:20:30,042 --> 00:20:33,455 two to four astronomical units from the sun. 280 00:20:33,455 --> 00:20:40,047 and in this region fall all of the resonances with, with small numbers of 281 00:20:40,047 --> 00:20:45,554 periods with Jupiter and with Saturn. And what we observe indeed is the 282 00:20:45,554 --> 00:20:51,294 distribution of asteroids as a function of their distance from the sun. 283 00:20:51,294 --> 00:20:54,029 And so this is the position of Jupiter. 284 00:20:54,029 --> 00:20:58,622 the fact that there are asteroids in Jupiter's orbit that's a resonance 285 00:20:58,622 --> 00:21:00,581 situation. There's other Trojans. 286 00:21:00,581 --> 00:21:05,113 In fact, how those Trojans fall into a stable resonance is again, something 287 00:21:05,113 --> 00:21:09,338 that's a little bit beyond us. But there are these Lagrangian points 288 00:21:09,338 --> 00:21:14,115 around which there's an unstable resonance and these asteroids orbit that 289 00:21:14,115 --> 00:21:15,856 unstable position. 290 00:21:15,856 --> 00:21:21,558 And so, they end up being locked for long terms into these positions, 60 degrees 291 00:21:21,558 --> 00:21:26,724 away from the planet along its orbit. But more importantly, in the more inner 292 00:21:26,724 --> 00:21:30,212 reaches, this is the main asteroid belt, over here 293 00:21:30,212 --> 00:21:33,500 is Earth orbit. And what we see, is that there's a 294 00:21:33,500 --> 00:21:36,273 distribution of asteroids and then there are gaps. 295 00:21:36,273 --> 00:21:39,951 There are distances from the sun at which nothing orbits. 296 00:21:39,951 --> 00:21:44,690 These are called Kirkwood Gaps. And what they correspond to is distances 297 00:21:44,690 --> 00:21:49,757 from the sun at which the period of an asteroid, were it to orbit there, would 298 00:21:49,757 --> 00:21:54,921 be a third or a half or 2/5 and so on of the period of Jupiter. These are objects 299 00:21:54,921 --> 00:21:59,543 which would be coming into orbital resonance with Jupiter that would distort 300 00:21:59,543 --> 00:22:04,465 their orbits into eccentric orbits and if there were a little bit of a tilt to 301 00:22:04,465 --> 00:22:08,487 their orbit, that too would get accentuated, and eventually they get 302 00:22:08,487 --> 00:22:11,008 completely ejected from the asteroid belt. 303 00:22:11,008 --> 00:22:15,809 So, nothing orbits at these orbits and in particular, not only are these guys, 304 00:22:15,809 --> 00:22:20,734 or are, is there nothing orbiting there now, but in the original asteroid belt as 305 00:22:20,734 --> 00:22:25,475 Jupiter and Saturn were forming, they started to distort the motion of things 306 00:22:25,475 --> 00:22:29,292 in the asteroid belt. This lead to these objects not moving in 307 00:22:29,292 --> 00:22:33,663 the nice circular orbits into which everybody was trying to settle. 308 00:22:33,663 --> 00:22:38,404 But into these eccentric orbits, this leads to violent, destructive collisions 309 00:22:38,404 --> 00:22:42,810 between the asteroids or the planetesimals and protoplanets that are 310 00:22:42,810 --> 00:22:47,460 forming in the asteroid belt. This is one of the ingredients into why a 311 00:22:47,460 --> 00:22:52,897 planet never managed to form the larger objects were colliding destructively at 312 00:22:52,897 --> 00:22:58,595 high speed rather than sort of overtaking each other very slowly with slow relative 313 00:22:58,595 --> 00:23:03,639 velocities as was the case in the inner solar system farther from Jupiter. 314 00:23:03,639 --> 00:23:09,240 And this process of resonant emptying of the asteroid belt eliminates most of the 315 00:23:09,240 --> 00:23:13,327 stuff that was there. Astronomers estimate there were between 316 00:23:13,327 --> 00:23:19,133 one and three Earth masses of material in the region from the sun between two and 317 00:23:19,133 --> 00:23:25,371 four astronomical units and most of that has gotten kicked out less than a tenth 318 00:23:25,371 --> 00:23:31,163 of a percent is now present, and we attribute this to the, the gravitational 319 00:23:31,163 --> 00:23:37,030 effects of Jupiter and partially, Saturn. Now, that we understand that orbits can 320 00:23:37,030 --> 00:23:43,268 change we can understand something about the currently accepted, and I should say, 321 00:23:43,268 --> 00:23:49,071 it's relatively recent and might still change understanding of the early 322 00:23:49,071 --> 00:23:53,776 evolution of the relevant part of the solar system, mainly the outer solar 323 00:23:53,776 --> 00:23:56,637 system. This is called the Nice model, it was 324 00:23:56,637 --> 00:24:02,042 formulated in a sequence of papers that came out of the University of Nice. 325 00:24:02,042 --> 00:24:05,475 These are where the simulations, the simulations were done. 326 00:24:05,475 --> 00:24:09,990 And the idea is this, remember out at 30 astronomical units where 327 00:24:09,990 --> 00:24:13,482 Neptune orbits today, there is no way to form a giant. 328 00:24:13,482 --> 00:24:18,687 In this model, the four giants form at distances between five, were slightly 329 00:24:18,687 --> 00:24:23,496 away from where Jupiter is today, 5.5 astronomical units out to seventeen 330 00:24:23,496 --> 00:24:26,923 astronomical units so closer in than they are today. 331 00:24:26,923 --> 00:24:31,930 And here, four giant planets form and they completely exhaust the gas in the 332 00:24:31,930 --> 00:24:38,845 disk beyond this orbit all the way out to 35 astronomical units, planetesimals are 333 00:24:38,845 --> 00:24:42,573 formed. There are ices, methane, water farther 334 00:24:42,573 --> 00:24:46,382 out even more and they do form planetesimals. 335 00:24:46,382 --> 00:24:52,570 And so, there's about 35 Earth masses worth of planetesimals in a disk outside 336 00:24:52,570 --> 00:24:57,522 the orbits of these giants. Now over, 337 00:24:57,522 --> 00:25:03,922 time the outer giants, it seems that probably Uranus was formed farther from 338 00:25:03,922 --> 00:25:09,810 the sun than Neptune and they cross. So, Uranus will encounter some of the 339 00:25:09,810 --> 00:25:14,526 inner part of this disk. So, when Uranus which is in an inner 340 00:25:14,526 --> 00:25:19,524 orbit meets these fragments in the outside of the disk, then it slows them 341 00:25:19,524 --> 00:25:22,510 down. And Uranus slows down the fragments, 342 00:25:22,510 --> 00:25:27,378 shifting them inwards and acquiring a little bit of their energy, it shifts 343 00:25:27,378 --> 00:25:31,208 slowly outwards. Now, this is a very slow process because 344 00:25:31,208 --> 00:25:35,590 planetesimals relative to Uranus, here in this orbit doesn't change much, 345 00:25:35,590 --> 00:25:40,030 but there's this constant rain of planetesimals moving inward propelled by 346 00:25:40,030 --> 00:25:43,854 collisions with the other giants, where they, they, they encounter Uranus. 347 00:25:43,854 --> 00:25:47,505 And the next, they encounter Neptune, and next, they encounter Saturn. 348 00:25:47,505 --> 00:25:51,864 And eventually, they encounter Jupiter. And yeah, this slowly shifts the giants, 349 00:25:51,864 --> 00:25:57,530 other, over millions of years, all of these giant orbits are slightly growing. 350 00:25:57,530 --> 00:26:02,318 Now, this is very slow, until after about 600 million years, something happens. 351 00:26:02,318 --> 00:26:07,043 And what happens is that this motion brings Jupiter and Saturn, who are not 352 00:26:07,043 --> 00:26:11,705 too far from that right now, into a two to one orbital resonance where, the 353 00:26:11,705 --> 00:26:15,360 period of Saturn is precisely twice the period of Jupiter. 354 00:26:15,360 --> 00:26:18,710 At this point, we have problem the problem that we discussed. 355 00:26:18,710 --> 00:26:23,121 There's this instability. The orbits are both elongated, one in, in 356 00:26:23,121 --> 00:26:28,389 orthogonal directions, in a coherent way but these are two massive objects. 357 00:26:28,389 --> 00:26:32,221 The gravitational impact on each other is nontrivial. 358 00:26:32,221 --> 00:26:35,299 They both get deformed into eccentric orbits. 359 00:26:35,299 --> 00:26:38,378 They, that in turn, influences the rest of the 360 00:26:38,378 --> 00:26:41,662 giants. And what one sees in the simulations, and 361 00:26:41,662 --> 00:26:47,409 you can I'll post a link and you can see these simulations yourself, is that once 362 00:26:47,409 --> 00:26:53,430 this point is reached, then very rapidly, the planet planetary orbits change, and 363 00:26:53,430 --> 00:26:58,030 Uranus and Neptune swap places and move, get pushed farther out. 364 00:26:58,030 --> 00:27:03,726 Jupiter gets moved a little bit inwards as a result of all of this and in the 365 00:27:03,726 --> 00:27:07,669 process the entire outer asteroid belt is depleted. 366 00:27:07,669 --> 00:27:13,146 all of those planetesimals beyond the disk are scattered either, either into 367 00:27:13,146 --> 00:27:18,550 higher orbit trans-Neptunian orbits beyond 30 astronomical units where 368 00:27:18,550 --> 00:27:24,100 Neptune today resides, and they form what we think of now as the Kuiper belt. 369 00:27:24,100 --> 00:27:28,957 Or some of them are rejected into very eccentric off-access, off-plane 370 00:27:28,957 --> 00:27:32,547 trajectories. And we think of that as the origin of 371 00:27:32,547 --> 00:27:38,277 what we now see as the Oort cloud. And notice that as Jupiter and Saturn are 372 00:27:38,277 --> 00:27:44,931 moving resonantly, they apply a resonant and shifting a influence on the asteroid 373 00:27:44,931 --> 00:27:51,428 belt, and this really is what completely depletes it and prevents the formation of 374 00:27:51,428 --> 00:27:54,972 anything there. Also, the nearest planet to this whole 375 00:27:54,972 --> 00:27:59,987 mass is Mars and the perturbations applied by Jupiter and Saturn, to the 376 00:27:59,987 --> 00:28:05,336 orbit of Mars are what prevent, we think, Mars from becoming a planet, the size or 377 00:28:05,336 --> 00:28:10,752 mass of Venus or the Earth the main difference is that it was subject to more 378 00:28:10,752 --> 00:28:15,300 perturbations as it was trying to grow. Moreover, 379 00:28:15,300 --> 00:28:19,763 following this resonant, the resonant period, Saturn moves out. 380 00:28:19,763 --> 00:28:25,617 it, it, it collides in the sense of orbital encounter with Uranus and 381 00:28:25,617 --> 00:28:29,202 Neptune, pushing them out into eccentric orbits. 382 00:28:29,202 --> 00:28:33,812 They encounter the planetesimals, as I said, destroying the disk. 383 00:28:33,812 --> 00:28:38,130 Scattering things into either trans-Neptunian orbits or 384 00:28:38,130 --> 00:28:41,997 higher orbits. Some of the planetecimals that they 385 00:28:41,997 --> 00:28:46,167 encountered, in fact, slowed. And if they're slowed down sufficiently, 386 00:28:46,167 --> 00:28:49,030 they rain down into the interior solar system. 387 00:28:49,030 --> 00:28:54,360 this means that there will be a time period in the history of the inner solar 388 00:28:54,360 --> 00:28:59,296 system, a time, and the outer solar system actually, where there will be this 389 00:28:59,296 --> 00:29:04,211 barrage of things coming from this outer disk of planitesimals, and raining down, 390 00:29:04,211 --> 00:29:09,077 all the way down into the inner solar system this period, and we see its traces 391 00:29:09,077 --> 00:29:12,282 in the history of cratering in the inner solar system. 392 00:29:12,282 --> 00:29:14,775 It's called the time of heavy bombardment. 393 00:29:14,775 --> 00:29:19,523 And when we talk about cratering in the inner solar system, in our moons, we will 394 00:29:19,523 --> 00:29:23,572 be able to trace a timeline that matches up with this, and 395 00:29:23,572 --> 00:29:28,956 then, the remnants of the disk create enough friction to settle everything down 396 00:29:28,956 --> 00:29:34,341 into the circular orbits which are essentially stable, which we find them 397 00:29:34,341 --> 00:29:37,408 today. So, here is a graphic representation. We 398 00:29:37,408 --> 00:29:46,560 start out with the four giants note that light blue Uranus is farther out than 399 00:29:46,560 --> 00:29:51,558 dark blue Neptune, and then Jupiter and Saturn are inside. 400 00:29:51,558 --> 00:29:54,570 Then after a, a few hundred million years, 401 00:29:54,570 --> 00:29:57,971 just before the resonance the orbits have shifted. 402 00:29:57,971 --> 00:30:03,105 They're a little bit more eccentric. Neptune and Uranus have exchanged places. 403 00:30:03,105 --> 00:30:07,598 And Neptune is starting to plow through this disk of planetesimals. 404 00:30:07,598 --> 00:30:11,063 And indeed, the disk is thinning out on the inside. 405 00:30:11,063 --> 00:30:16,262 And some of these planetesimals are being blown down into the inner solar system. 406 00:30:16,262 --> 00:30:20,112 Some are being scattered out into the outskirts of the disk. 407 00:30:20,112 --> 00:30:23,450 And then, very rapidly, once resonance is achieved 408 00:30:23,450 --> 00:30:28,923 the disk is completely emptied, we see a scattering of population beyond Neptune's 409 00:30:28,923 --> 00:30:32,014 orbit. Some of them have been scattered entirely 410 00:30:32,014 --> 00:30:37,360 out of the plane to form the Oort cloud and the giant has settled into their 411 00:30:37,360 --> 00:30:44,535 accepted orbits that we've seen today. And this is what we our models predict, 412 00:30:44,535 --> 00:30:50,433 was the history of the solar system. This is how we got to where we are. 413 00:30:50,433 --> 00:30:54,904 We've answered, at some level, the question, the last question we asked, 414 00:30:54,904 --> 00:30:58,786 where it all came from and when? And in the process, we've learned 415 00:30:58,786 --> 00:31:03,742 something about how orbits change, though we haven't addressed the question of will 416 00:31:03,742 --> 00:31:08,400 planetary orbits change in the future, I can tell you that the solar system is 417 00:31:08,400 --> 00:31:13,416 stable on time scales of hundreds of millions of years at least as far as the 418 00:31:13,416 --> 00:31:17,357 planets are concerned. what happens after a few hundred million 419 00:31:17,357 --> 00:31:21,088 years, it is hard to predict. But as we'll see, there are other issues 420 00:31:21,088 --> 00:31:24,124 that are going on in the solar system on those time scales. 421 00:31:24,124 --> 00:31:26,954 We know why there's no planets where the asteroids are. 422 00:31:26,954 --> 00:31:29,630 we understand why there are two kinds of planets. 423 00:31:29,630 --> 00:31:32,049 We know why the asteroids didn't form a planet. 424 00:31:32,049 --> 00:31:35,239 We know why things are round and why thing, some things aren't. 425 00:31:35,239 --> 00:31:38,687 And we understand why all planetary orbits are circular in a plane, 426 00:31:38,687 --> 00:31:42,598 friction slowed them down to circles. The plane is the original plane of the 427 00:31:42,598 --> 00:31:46,817 rotation of the solar nebula, and comets move on whatever orbits they happen to 428 00:31:46,817 --> 00:31:50,590 have been thrown into. Because they are the result of some near 429 00:31:50,590 --> 00:31:54,221 collision with a heavy object of some old planetesimal. 430 00:31:54,221 --> 00:31:56,987 So, wWe've made some progress though there 431 00:31:56,987 --> 00:32:01,712 are still questions we need to ask. It might be a good time to summarize what 432 00:32:01,712 --> 00:32:05,729 we've learned about the history of the solar system with a timeline. 433 00:32:05,729 --> 00:32:10,040 So, we started our clocks at what I call time zero, 4.56 billion years ago. 434 00:32:10,040 --> 00:32:14,765 Something triggers the collapse of the molecular cloud that will form the solar 435 00:32:14,765 --> 00:32:19,372 nebula within a 100,000 years in the inner solar system and less in the outer 436 00:32:19,372 --> 00:32:24,159 solar system, we have planetesimals. within 10 million years the inner system 437 00:32:24,159 --> 00:32:28,615 has formed protoplanets and is beginning to start the accression of planets. 438 00:32:28,615 --> 00:32:31,740 The outer planets by this time are pretty much formed. 439 00:32:31,740 --> 00:32:35,853 The T Tauri winds start to sweep away the gas and the dust, 440 00:32:35,853 --> 00:32:39,902 leaving planetesimals that are more massive and dense objects. 441 00:32:39,902 --> 00:32:45,517 And so, the inner planets have take about till a hundred million years from this 442 00:32:45,517 --> 00:32:49,761 event to complete their formation and settled into their orbits. 443 00:32:49,761 --> 00:32:55,312 This includes the massive impacts that formed the moon and stripped Mercury of 444 00:32:55,312 --> 00:32:59,034 its outer layers and so on. After about 600 million years 445 00:32:59,034 --> 00:33:03,957 we hit the Jupiter Saturn resonance. And this is the time that the asteroid 446 00:33:03,957 --> 00:33:08,563 plates, belt is depleted, the outer planets migrate out pretty much out to 447 00:33:08,563 --> 00:33:11,053 their current orbits. And in the process 448 00:33:11,053 --> 00:33:16,389 some of the material from the planetesimals beyond Neptune's orbit gets 449 00:33:16,389 --> 00:33:21,610 ejected out into the Kuiper belt. Some into off-access orbit, off-plane 450 00:33:21,610 --> 00:33:27,260 orbit, producing the Oort cloud farther out, and a lot gets thrust into the inner 451 00:33:27,260 --> 00:33:31,336 solar system and we find the period of heavy bombardment. 452 00:33:31,336 --> 00:33:36,835 So, we should expect lots of 3.8 billion year old cratering, right, because that 453 00:33:36,835 --> 00:33:42,175 is the time of the heavy bombardment and by about 700 million years, the stable 454 00:33:42,175 --> 00:33:46,798 configuration has basically been achieved, planets exist and of roughly 455 00:33:46,798 --> 00:33:51,877 their current mass, in pretty much their current orbits and not coincidentally, 456 00:33:51,877 --> 00:33:55,720 the first signs of life appear on the planet we call Earth.