The Rings of Saturn - Sixty Symbols

0:00 You're going a little bit outside your area of expertise today.

0:02 I am Freddy.

0:03 Yeah.

0:03 Yeah.

0:04 What we got?

0:05 Um inspired by a a show on the BBC,

0:09 a quiz show called Mastermind in which the contestants [music] um

0:13 are given two minutes to answer questions on their favorite topic.

0:17 Recently, I saw one on planets of the solar system.

0:20 So, I thought, okay, I'll I'll have a go at that.

0:22 I couldn't answer anything,

0:24 but there was a question that came up and when I heard the answer,

0:28 that was me finished for the show.

0:30 I just got went online and I'm just looking.

0:33 I was so amazed.

0:34 And the question was

0:35 in his essay on the stability of the motion of Saturn's rings,

0:38 published in the 1850s,

0:40 which scientists demonstrated that the rings could not be solid structures,

0:44 but must instead be composed of numerous

0:46 small particles [music] orbiting the planet independently.

0:49 And uh I'm thinking it's going to be an famous astronomer.

0:53 It's got to be.

0:54 And the guy didn't know.

0:57 And it was James Clark Maxwell.

0:59 Maxwell of electromagnetism fame.

1:02 Maxwell of thermodynamics fame.

1:04 I'd never thought of Maxwell of astronomy fame.

1:07 And he did it.

1:09 He's the one person that submitted this essay.

1:12 And in that essay, he explains the ring

1:15 structure of Saturn way before it was known.

1:18 Andy explained why it had to be made up of particles and not made

1:23 up of solids and a solid piece and not made up of a fluid.

1:27 And I just thought that's really neat.

1:30 A theoretical physicist came up with this prediction

1:33 that was finally confirmed well certainly in the 20th century.

1:37 But where it's Cassini going up between 2007 and 2017

1:42 that actually finally was able to get between the rings

1:45 and saw all of these particulates that James Clark Maxwell had

1:48 predicted must be there and I thought this is so neat.

1:51 And actually there's a nice little story about the Adams Prize

1:53 as well that I thought we could just bring it all together.

1:57 Go ahead, professor.

1:58 I'm all ears.

1:59 All right.

1:59 So Adams is John Adams, not the US President John Adams.

2:04 So in the 1840s he was busy trying to understand Uranus and the orbit

2:08 of Uranus around the sun and he was noticing that it wasn't fitting quite

2:12 with the equations be Newton's laws

2:14 and Kepler's laws and he predicted that there

2:17 needed to be something else there that something else turned out to be Neptune.

2:20 So he told two of his astronomy colleagues about this but nothing was done.

2:27 A few years later, Leier in in France did

2:31 a very similar calculation and came to the same conclusion.

2:34 He also predicted there should be another planet,

2:37 but he got in touch with a friend of his, a colleague in Germany,

2:41 an astronomer, and said,

2:41 "Can we go looking?" I think it was he was called Gallas and said,

2:44 "Could you go and find this?" And within a few days, he'd found it.

2:48 He'd found Neptune.

2:50 So Adams had had predicted it, but hadn't published anything.

2:53 and Levier had predicted it and it had been published and it had been spotted.

2:59 So there was a bit of a tussle as to who should get the credit.

3:02 But in Cambridge they were pretty determined to try

3:05 and make sure that Adams got some credit.

3:08 He was a member of John's College

3:10 and so the alumni of John's College clubed together,

3:13 put money in and said we're going to have a prize.

3:15 We'll call it the Adams Prize.

3:17 It'll be bestowed by the University of Cambridge and the prize

3:20 will be given to somebody who writes an essay in either mathematics,

3:25 astronomy or another area of natural philosophy.

3:28 It'll be a bannual thing and the title will

3:31 be given that the essay has to be about

3:34 before we move on professor to this essay and the prize

3:37 the Adams Prize who does history give the credit to for

3:40 well I hear of Leia that's getting it I have to admit

3:44 yeah I had I'd forgotten that Adams if if I knew I'd forgotten

3:48 that Adams was was associated with it and I had heard

3:53 of the Adams Prize because I know two prize winners of the Adams Prize.

3:56 Oh, it's still going.

3:56 The Adams Prize.

3:57 Oh, yeah.

3:57 It's still going strong.

3:58 Yeah.

3:59 So, two good friends of mine have have won the Adams Prize.

4:02 So, this was 1848 now that uh the Adams Prize was sort of instigated.

4:07 So, in 1855, the announcement was made that the next Adams

4:14 Prize would be on the title of the rings of Saturn.

4:18 So, why the rings of Saturn?

4:20 People think it's because there had been observations.

4:23 I mean, Galileo saw Saturn back in 1610 and then in 1650,

4:29 Higgins was able to make out that there were ring structures there.

4:32 Then in 1750 or something, Cassini realized that there were series of rings.

4:37 He saw a second set of rings.

4:39 And then closer to the 1850s,

4:41 it was realized there was a like a darker ring near the center of Saturn.

4:46 And I think that led to this interesting,

4:49 you know, what are these rings made of?

4:51 And so they they issued this essay challenge and um well there

4:56 was one submission [laughter] and of course it was from James Clark Maxwell.

5:00 So you might think well he's going to win anyway but what was

5:03 quite remarkable about this submission from James

5:06 Clark Maxwell was a the timing.

5:08 He'd been a graduate at Cambridge.

5:10 It's open to all Cambridge alumni.

5:12 It still is.

5:13 But he was busy thinking about electromagnetism speed of light.

5:16 His father had been taken ill.

5:18 He had to look after his family.

5:19 And then he was also applying for jobs in Scotland.

5:22 But this project kept going.

5:25 He he began it around 1855 and he actually published the final essay which

5:32 is now regarded as you know the definitive work from him on it in 1859.

5:38 So he worked on and off this [snorts] project for for quite a while

5:42 even after he'd won the prize.

5:43 Even after he'd won the prize because he got the prize in the summer of 1857.

5:47 They awarded him the prize.

5:49 People who've heard of Maxwell will know

5:50 of Maxwell's equations and he's he's very famous scientist.

5:54 Yes, it's as famous as they come.

5:55 But he wasn't super famous when he won the prize.

5:58 Had he'd already done his equations then?

6:00 No.

6:00 No, he hadn't.

6:01 He he was building up to them.

6:02 He'd obviously done good things and he was beginning to think about

6:05 kinetic theory of gases which fed into actually to some of this work.

6:09 But he wasn't anything like the superstar that he that he did become.

6:14 But let me just make one point about the the approach

6:16 he took which I think makes this even more interesting.

6:20 He he devel he basically was one of the first to develop

6:23 a technique called dynamical systems which is used all the time in mathematics.

6:27 It plays a big part in my work as well.

6:29 And what a dynamical system does is it says okay

6:33 I know what the equilibrium situation should be you know

6:36 if the if the with the orbits of of the planets

6:40 for example but then it asks the following question.

6:42 He says, "Imagine I just perturb them a little bit.

6:45 Will the planets go back into their original orbits

6:48 or will they shoot off?" Because if they shoot off,

6:50 then even though it's a solution of the planets going around,

6:53 it's an unstable solution because anything small

6:56 pertubation will cause it to go off.

6:59 And Maxwell realized that he could apply this technique

7:03 to models of the ring structure of Saturn.

7:06 And that's exactly what he did.

7:07 He found the equilibrium solutions and then he perturbed them.

7:12 mathematically and he solved the perturbed evolution equations.

7:15 The ones that just now trying to understand what happens to that perturbation.

7:19 If the perturbation grows, it means that that equilibrium solution isn't stable.

7:25 And if the perturbation sort of oscillates and dies down again,

7:28 then you've got an an equilibrium a stable equilibrium solution.

7:32 And so he introduced this for this technique.

7:35 And he asked the following questions.

7:36 He he considered three possibilities.

7:38 The first was that the ring itself was a solid.

7:42 Like a big hula hoop,

7:42 a big hula hoop.

7:43 And he quickly demonstrated that that couldn't be stable.

7:47 So we have Saturn and then we have a ring around it which is now a solid.

7:51 And he perturbed it.

7:52 He just moved it.

7:53 And he what he found was that that movement

7:56 itself was enough that the gravitational pull

7:59 from Saturn on one side of the ring was enough to sort of just pull it all in.

8:05 And so it wouldn't simply go back to where it was.

8:07 So then he said, okay, if it's not a solid, then maybe what it is is a fluid.

8:12 You know, maybe there's somehow the fluid is is been trapped in there.

8:15 One way you could trap it in principle is if you force

8:18 it to the the ring to be going around in a circle, right?

8:21 Then you have a c centrifugal force

8:23 going out matching the gravity pulling it in.

8:26 So you've got a wave like a like a a weird river or a big lake.

8:31 Yes.

8:31 Yes.

8:32 Exactly.

8:32 And so he so he did this.

8:34 He had it going around with some angular momentum and he

8:37 has it that's an equilibrium solution that will do that.

8:39 And he perturbs it again.

8:40 He he says okay now let's imagine a section of this ring and I'll just pump it.

8:46 I'll so that I'll I'll make it bulge slightly.

8:50 And is that representing collisions or gravitational influence?

8:54 Exactly.

8:54 But probably more collisions the impact of a collision on it but it

8:58 could be gravitational pull you know on on one region of it.

9:02 And so he he pulled so he gives it a bulge.

9:05 And now what you would hope is that as it's going around that bulge

9:08 will die back down again and it'll go back to its original shape.

9:12 But what actually happens is as it goes up that bulge goes up.

9:16 Its angular velocity decreases and the bulge rather than sort of just

9:21 spreading back out it builds up behind because it's going slower.

9:25 The rest of the ring's going faster.

9:26 It's going slower.

9:28 and you just get this buildup and it grows and grows

9:30 and grows and it becomes unstable again and it breaks the ring.

9:34 So he's demonstrated it can't be a liquid.

9:37 So he said perhaps what it is is a series of particles.

9:40 He initially starts with an idealized case.

9:42 He says right I'm going to have these particles they're all going

9:45 to be the same and and I'm remember this is all theory right?

9:49 It's [laughter] there's no observations.

9:51 I'll put them evenly around the ring.

9:54 So that now what forces have they got?

9:57 Well, they've got the force of gravity because because Newton's

10:00 laws are telling you that the Saturn's pulling on them,

10:02 but they've also got interactions between themselves.

10:05 So, here's two particles separated.

10:07 He kicks one towards the other.

10:09 Okay?

10:10 So, now what happens is this particle gets

10:13 accelerated towards this one because gravity is pulling it.

10:17 And you think, okay,

10:18 this is clearly going to be unstable because it's it's going to pile up.

10:21 You're just going to get these piles up.

10:23 But it's not what happens.

10:25 What happens is as it's coming in, it

10:27 builds up speed and as it builds up speeds, it moves to an outer orbit.

10:32 It moves to an outer orbit.

10:34 It slows down and it sort of drifts back again.

10:38 And so you've got this system where a perturbation of the particles goes out.

10:44 It builds up speed.

10:45 It slows down as it's gone to a higher a further out orbit.

10:48 And so it gets pulled back behind.

10:50 And so this is a system where these particles they're moving.

10:53 There's effectively a wave going around,

10:56 but they're just vibrating backwards and forwards.

10:59 Sort of self-correcting.

11:00 It's a self-correcting system.

11:02 It's exactly that.

11:03 And so what he then did,

11:05 so he done it for these even these very similar particles.

11:10 He then did two more complicated things.

11:12 He said, "What happens if I have two rings,

11:14 which because by then it was already known that there

11:16 were two rings and he demonstrated that there was additional

11:20 interactions between the rings and that there was one possible

11:23 case where you could have what they call a resonance effect,

11:27 you know, where like pushing a swing.

11:28 If you hit the right resonance, it can suddenly become really big swing.

11:32 There was a one possible case where you'd have a wave

11:36 going around one and a wave of a different frequency or wavelength

11:40 going around the other and they could combine in such a way

11:43 that it would cause them both of them to grow rapidly.

11:47 But he decided that that is such a rare

11:49 phenomena that it's in the age of the solar

11:53 system it will not have happened and and all

11:57 of the combinations of these waves were perfectly stable.

12:00 There was just this one.

12:01 And he then went and did a fourth, a third.

12:04 So he did the all the particles being the same.

12:06 He then did these two rings.

12:08 And then what he did was he allowed for a distribution of particles.

12:11 And he it's a bit more complicated the mathematics,

12:13 but that principle of them going out into an orbit

12:16 and coming back self-correcting as you put it, but applied in each case.

12:20 And so he concluded his essay by saying Saturn's rings couldn't be a solid,

12:26 couldn't be a fluid, and had to be made up of particulates of varying sizes.

12:31 He got the prize.

12:32 The prize was£100 or £130, which is about £14,000 today.

12:38 It was a significant prize and probably one of the reasons he applied.

12:43 We had a discussion before this when when was this first confirmed and and yeah,

12:48 clearly people knew of the ring structure from then on.

12:52 Well, Voyager was sent up in the 1980s

12:54 that that went past Saturn and took detailed pictures.

12:57 So, you certainly knew there were particles in there,

13:00 but Cassini went out to Saturn and then went through

13:03 these rings and it was able to do all sorts of things.

13:06 It was able to actually look at the trajectories of the individual particulates.

13:10 It showed that the particulates had sizes that went from micrometers,

13:14 microns up to meter size.

13:16 And these are these shephering boulders.

13:18 It also was able to see some of the moons

13:20 coming by the rings and distorting the rings so that then

13:23 a wave would go around the rings as predicted

13:26 by Maxwell with exactly the same frequency that Maxwell had suggested.

13:31 and they were able to look at the gaps between the rings and see

13:35 that the structure was as Maxwell was suggesting

13:37 in terms of the distribution of the particles.

13:40 So, I think it's just such a nice little story and it's one of those at a time

13:45 when um theoretical ideas sometimes get a bad

13:49 press because you can't necessarily solve everything.

13:52 Here's a guy that came up with a purely theoretical

13:55 idea that was then verified a hundred or so years later.

14:01 They have to have a mechanism by which they can

14:03 decide whether or not an event is useful or not.

14:06 Given all the billions that are shooting out every second,

14:13 how does all that energy decide?

14:15 Okay, I'm going to reconstitute into a Higs boson