Ep. 714: Orbital Resonances

Several of the planets and moons in the Solar System are in orbital resonance, orbiting in a geometric lockstep. And not just the Solar System, astronomers have found the same resonances in other star systems.


(This is an automatically generated transcript)

Fraser Cain [00:01:19] Astronomy Cast episode 714 Orbital Resonance. Welcome to Astronomy Cast, your weekly facts based journey through the cosmos, where we help you understand not only what we know, but how we know what we know. I’m Fraser Cain, I’m the publisher of Universe Today. With me, as always, is Doctor Pamela Guay, a senior scientist for the Planetary Science Institute and the director of Cosmic Quest. Hey, Pam, how are you doing? 

Pamela Gay [00:01:39] I am doing well. If you are watching this live, or perhaps even in recording, and things aren’t going entirely the way you would like, the audio will be perfect. There is something screwy going on with the internet right now. Apologies if the video and audio and everything is a little bit glitchy. 

Fraser Cain [00:01:59] We recorded a local version completely separate, and it gets edited and processed and it sounds beautiful and you should be experiencing these things via podcast. That way you can be out on a walk or a bike ride or, or gardening or doing the dishes. Yeah, yeah. 

Pamela Gay [00:02:15] Get out today outside. 

Fraser Cain [00:02:17] Right. Don’t don’t sit in front of a computer screen on a tiny phone watching us. No, let’s do a podcast. And then you can increase the speed to like 1.5 and one. We’re talking really quickly. 

Pamela Gay [00:02:29] Yeah. I’m not all those people. 

Fraser Cain [00:02:30] I’m more I’m totally one of those people. I listen to all my podcast super fast. Who has time for this? My brain can handle it at top speed. I watch all my YouTube videos at double speed. I review my own videos at triple speed because like, I don’t want to take 30 minutes to sit through my video. Yeah, then I know what I’m really just looking to catch mistakes as opposed to engaging with the content. But who knows? Who knows, maybe they’re just living in in some sort of fast forward future. Right. So some of the planets and moons in the solar system are in orbital resonance, orbiting in a geometric lockstep and not just the solar system. Astronomers have found the same resonance at other star systems. All right. So before we get into all of the crazy examples of where this happens, I want to just like just understand what is orbital residence, what’s going on here? 

Pamela Gay [00:03:24] The idea is compared to the stars, two or more objects will go around so that the alignment between the thing they’re orbiting them and the thing they’re in resonance with will in an integer number of orbits repeatedly line up with the stars so that you get object being orbited object or orbiting object orbiting stars lined up perfectly integer number of orbits. 

Fraser Cain [00:03:55] And so like, how do these integer numbers tend to fall like is it always the same number or does it differ. 

Pamela Gay [00:04:02] So it it can be all over the map. And different kinds of things can be in resonance for different reasons. So the the example that everyone starts out learning is the orbits of the Galilean moons, which even Galileo was like, oh, that’s weird. Where it where what we see is, Ganymede is the furthest out and Ganymede will go around once, and, Europa will go around twice, io will go around four times. And, so you have with, with these three worlds, this, this resonance in how they go around Callisto. Callisto decides it’s it’s not going to play any part in these memory games. Right. But with the other three. Yeah, yeah. Ganymede, Europa and innermost io have this integer resonance, which is really cool to look at top down in terms of you, you have just this periodic alignment of all three of them in Jupiter in a line. And when this occurs, you end up with more gravity affecting tidally pulling apart the worlds. And then when you have them most apart, you have the least tidal tugging. And this constant change on the forces on the worlds are what are driving Io’s volcanism are what is driving, we believe Europa’s crust slowly migrating, spiraling, changing. All of these forces generate heat inside the worlds, and it also has the ability in other cases to move things around. Now these worlds are locked in place. They’re going to stay in orbital resonance. But sometimes when objects sneak into orbital resonance. For instance, with the asteroid belt that repeated tug that they get every time they line back up with that other world. If it’s a significantly different size, for instance, if they end up in resonance with Jupiter, that’s going to actually change their orbits, and you can end up with either bands inside the rings of Saturn, you can end up with bands inside the asteroid belt where fewer objects are able to accumulate. 

Fraser Cain [00:06:37] That’s that’s really interesting, and I definitely want to get to that. But I but I kind of want to go back and get a sense of, of what is the mechanism that’s going on here. I mean, I think when we think about the, the interior, how io is this volcanic moon and how Europa has its liquid water and that we know that they’re being heated this tidal heating. The moons are playing a big part in this tidal heating. But what is, I guess, what is causing if you see, IO goes around once and Europa goes around. Oh, sorry. Yeah. So Ganymede goes around once. Yes. Goes around, goes around twice, and io goes around four times. Yes, but what is what is like causing them to lock up into this residence? Like they didn’t start out that way? Probably. 

Pamela Gay [00:07:25] Probably. It’s, you know, that that is kind of weird to think about. Now, if things like this don’t happen accidentally, they happen. Because if you’re very close to lining up, you’re going to get pulled forward as you get closer to that other object you’re in orbit with. If you’re a little bit ahead, you’re going to get slowed down so the forces will actually cause the objects to want to line up like this icy. And so over time, this, this torquing that occurs on the orbits will force them into alignment. It’s it’s very similar to the kinds of situations that happen that cause worlds to get tidally locked. In this case, instead of locking the rotation, it’s locking the orbit. And you can actually and I’m sure we’ll get to it, have a combination of the rotation and the orbit get locked together. There’s all different ways to fall into resonance. 

Fraser Cain [00:08:25] Right? Right. I mean, we think about the moon being tidally locked to the Earth. I guess that’s a form of residence. 

Pamela Gay [00:08:33] It’s we don’t usually talk about that as being a resonance. But for instance, if you look at the planet Mercury, we had thought for decades that it would probably be tidally locked to the sun. And then back in the 1960s when they finally did radar observations of it. And it’s not perfectly round this works. They were able to see that for every two times it goes around the sun, it spins three times. Right. And this particular spin orbit resonance is super rare. We think there is only a 26% probability that this could happen. But I’ve read this really cool paper preparing for this show. It’s it’s a paper in Mercury from 2011 by Mark White Sturrock that talks about how it’s possible. And we’re going to be able to figure out if this is true, probably from the BAP of Colombo data, that Mercury was once tidally locked, high probability event, and then got the bejesus smacked out of it by some sort of an impacting event, and that knocked it into the 3 to 2 resonance that we see today. And if that’s true, we will see differences in the two sides of it, how they appear. And this may explain some of the features that we’ve already been able to make out. We just need more data. We always need more data. 

Fraser Cain [00:10:06] All right. So we’ve looked at the famous moons of Jupiter and this really interesting situation of Mercury’s spin versus its orbital resonance. What other what are some other examples of things inside the solar system that have some kind of orbital resonance there? 

Pamela Gay [00:10:28] There are so many different moons orbiting so many different worlds that it seems like it’s just kind of ultimately, when you have multiple moons going around an object, you’re going to end up with this kind of a thing. We have cases of asteroids. We have moons of pretty much every world that do this. So there there are moons in residence scattered all. Throughout our our solar system. And there’s also worlds in resonance. Earth and Venus have an 8 to 13 resonance. Venus to Mercury has a 9 to 23 resonance. Yeah. 

Fraser Cain [00:11:23] That’s amazing. So? So sorry. What were the numbers for Venus again? 

Pamela Gay [00:11:28] Earth to Venus is 8 to 13. 

Fraser Cain [00:11:31] So for every 13 times of Venus goes around the sun, Earth goes eight times around the sun. Yeah. That’s bonkers. 

Pamela Gay [00:11:39] Yeah. So? So there’s all of these different things going on. Deimos and Phobos are a 1 to 4 resonance. And. Then the Jupiter versus asteroids like Jupiter versus the really large asteroid Pallas is a 7 to 18 resonance. And I figured there must be some one out there. Now that just runs software. Every time a new world is discovered to find that, the resonances. 

Fraser Cain [00:12:11] Find the resonances. Yeah. That’s interesting. 

Pamela Gay [00:12:14] But once upon a time, it was people doing all of this by hand, trying to figure out what exactly is and isn’t in resonance. And we see all sorts of different resonances with your Uranus’s satellites, with Neptune satellites. And it just seems to be the talks will naturally, if worlds are left alone, allow resonances to occur. Even Pluto, with all of its little satellites, Styx and Sharon or one, two, three Nix and Sharon is 1 to 4. Kerberos and Sharon is 1 to 5. Hydra and Sharon is 1 to 6. 

Fraser Cain [00:12:54] I think. But but the Pluto to Neptune one is really interesting. People always ask like, why is it if if Neptune hasn’t cleared its orbit? I’m sorry if Pluto hasn’t cleared its orbit, right. If, if if it crosses orbit with Neptune every I forget some number of years. Why does it sometimes crash into Neptune? But in fact Neptune in Pluto or any two three orbital resonance. So? So they never can. They are always orbiting in their exact way, so that the paths of Neptune and Pluto never cross and they will never collide because of this orbital resonance. 

Pamela Gay [00:13:35] And these are the things that allow us to say, yeah, our solar system has been around in the form it’s in currently long enough to allow all of these resonances to accumulate. And that’s one of the cool things to think about is when solar systems form, you have mass chaos. You have things that form in all sorts of different orbits. You have things that form in elliptical orbits and go off and smash into other things. And over the fullness of time, worlds get captured by bigger worlds. Things evolve into resonance, things rotate into resonance, and it’s simply the gravity wins. Gravity always wins, including in forming resonances. 

Fraser Cain [00:14:26] That’s interesting if you think about this. I mean, I like this idea that you find a new object, and then it’s this question of finding it’s, you know, once you’ve calculated its orbit, try to figure out what the influence is. And eventually it may turn out to be some integer. Oh, what do you know? This newly discovered dwarf planet has a 364 to, I don’t know, 197 orbital resonance with some other object that that these objects have been orbiting each other and the sun for billions of years. They have made millions, tens of thousands. Or even billions of orbits. And those tiny perturbations just add up over time. Everything wants to settle into the most stable residence that it can. So you brought up Saturn’s rings earlier in the night? Yeah. Brutally cut you off. So can you continue that thought? What do we see in terms of residence in the rings of Saturn? 

Pamela Gay [00:15:29] So? So with with both the asteroid ring and the, rings of Saturn, there are times where larger moons are able to fling objects out of gaps. And, Saturn’s rings and Jupiter’s able to fling things out of certain orbits in the asteroid belt. And this is simply a matter of the thing that you’re in resonance with, is significantly larger than you are. And and so it’s able to simply move you about at its whim and whimsy until you, cease to be there. 

Fraser Cain [00:16:11] Really interesting. So astronomers don’t just see resonance here in the solar system. I mean, obviously, if everything is in resonance, then you would expect to see resonance wherever you look across, you know, across the cosmos. Yeah. So we but but it’s one thing to propose. Of course, this is everywhere. The. But finding it. Astronomers have made some incredible examples of finding resonance out there around other star systems. So can you show me some examples of that? 

Pamela Gay [00:16:39] I think the one that people talk about most is a six planet system that is, given the license plate address, HD 11 0067. And this world is basically designed like it feels like musical strings. The innermost world to the next is a 3 to 2 ratio. That one and the one furthest out is a 3 to 2 ratio. That one and the one further out is a 3 to 2 ratio. So we have three 3 to 2 ratios in a row. And then we have two 4 to 3 ratios. And and so it’s this really cool set of three things that are identical sort of two things that are identical and six different worlds. They’re not all that hugely different in size. And of course they’ve done all sorts of cool infographics showing what are basically spiral graphs of the motions of this system. It’s called a resonant six top list of sub Neptune’s that are all orbiting one star. 

Fraser Cain [00:17:51] Wow. And in fact, a pretty big percentage of multi planetary systems are in resonance. I mean, I think it’s something, you know, it’s like it’s above 10% of just all of the, you know, whenever they find a system that has at least two planets in it, there’s a pretty good chance that they’re going to be in residence again, A12. Yeah. So they’re everywhere. 

Pamela Gay [00:18:16] And and so we see it again. The Trappist system of seven planets has resonances. And there’s been some really cool. Sonia Graf is the wrong word. 

Fraser Cain [00:18:27] Like to like to hear it? 

Pamela Gay [00:18:28] Yeah. What’s the name of the thing where they make it to the. Here? 

Fraser Cain [00:18:31] It’s on a fram. Yeah, I know what you mean. It’s like an acoustic version where they give a different musical note to each planet, and then they play them at the cadence that they’re going around. And it sounds kind of like music. Yeah. 

Pamela Gay [00:18:45] And so with Trappist one, seven worlds, this is totally what they are finding. 

Fraser Cain [00:18:52] So, you know, we’ve talked about planets, we’ve talked about moons. But then do we get other things like if we had a multi star system. Yeah. Would we get some kind of residence going on. 

Pamela Gay [00:19:04] Yes. And we have seen stars and multi multi stellar resonances. The trick is with stars the most likely thing that’s going to end up happening is you end up with two in the center going around each other, and a third going around the inner to or some version of that. You might end up with one in the center and then the other two going around it. So you really have to start to get to the four star systems where it’s not two binaries. But it is possible. So it’s, it’s all a matter of how do they go around. But to get resonance the vast you have large mass in the center, things of similar mass going around. If you have large thing in the center, small thing, big thing, big thing, remove small thing. Gas in Saturn’s rings. Gap in orbit. Right. If you have things of similar size like this, set six to split of sub Neptune’s. I cannot say that fast, but is my challenge to all of you. 

Fraser Cain [00:20:10] Six couple of separate tunes. 

Pamela Gay [00:20:12] Okay. All you then you start to see more and more of these resonances occurring. And so it is. It is a matter of what is the ratio of masses? How long have they been there to get to move each other around? And, given the fullness of time. Resonances will occur where the masses allow it. 

Fraser Cain [00:20:39] And then I wonder if you have even weirder things. I mean, could you have three black holes in some kind of of interaction where or even. 

Pamela Gay [00:20:51] No, because they’re you’re looking at three equal mass objects. So with star. 

Fraser Cain [00:20:55] No. Well let’s say they’re not. No. Like say you’ve got one supermassive black hole and it’s being orbited by two other smaller black holes. And they’re destined to merge in the future. 

Pamela Gay [00:21:03] Yes. Then you can get a resonance. 

Fraser Cain [00:21:05] Yeah. Like, would you see the residents like, right now we see the resonance in that we we can can track them. But imagine if you could see that resonance in the gravitational waves as opposed to tracking them then visually. And it should all just at the end you’ll get the same numbers, but with black holes they don’t have. Yeah, things that they don’t have gravitational handles in the same way. And so I wonder if black holes would, would end up with the same kinds of resonances that, that objects that are not perfectly mathematically, I guess oblate. 

Pamela Gay [00:21:41] There’s no reason that that can’t occur, but I can’t see why we would be able to detect it in the gravitational waves with current technology. That’s where it gets tricky. Story is we generally see currently the the waves only at that last moment of of collision. But technology will change over time and who knows what will be possible. Although it does sound rather like a low probability kind of thing. 

Fraser Cain [00:22:14] Yeah. And then I guess, should we also see that the larger scales, when you imagine galaxies orbiting around galaxy clusters, I mean, I guess they’re getting torn apart by tidal forces because they’re not. But I wonder. 

Pamela Gay [00:22:28] So there you have the added force of drag, which we don’t really have within the solar system. So yeah, orbital resonances can occur because of that. Orbit is defined by by GMM over r squared. Then it’s getting affected by that larger mass that it’s also in orbit with. But no drag is being involved. Once you add in drag, that changes all of the physics. 

Fraser Cain [00:23:00] Right. And can you think of anything else like. Where this could be useful for science. In terms of like, are there interesting ways that they can use or like, I know, for example, they use orbital resonance to try to predict the existence of other worlds in the solar system, dwarf planet, planet nine, things like that. Right? That you’re you’re seeing what should be an orbital resonance, and that allows you to infer that there must be some object affecting gravitationally. Yes. 

Pamela Gay [00:23:34] And so we can assume that the best places to go looking for things is where the resonance points are. We can look at slightly elliptical orbits and say what kind of a resonance would create that ellipticity? Things are extremely complicated. So. That doesn’t always help. We are learning with the search for Planet nine or whatever you wish to number it. I leave the numbering up to you. I’m going to be agnostic. 

Fraser Cain [00:24:11] But you’re right. This Alan Stern gives this a strongly worded email. 

Pamela Gay [00:24:15] Yeah, yeah. Yeah. It’s so there are so many interesting explanations for why there isn’t a Planet Nine out there. There are so many interesting explanations for why there must be. And this is why we haven’t found it. We need to have an observatory to do Lsst survey as quickly as possible. And yes, I know the word survey is in the acronym Lsst, but it sounds stupid to just say Alice s t. 

Fraser Cain [00:24:43] All right. Very interesting. 

Pamela Gay [00:24:45] Thanks, Pamela. Thank you, Fraser, and thank you to any of you who made it through all of our internet difficulties. As I see, we are now streaming live once again. Apologies for all the chaos my computer and Chrome’s desire to spawn AI is causing us this week. 

Fraser Cain [00:25:04] Well, the podcast listeners don’t have a problem with that. Don’t listen to the nicely edited version. Listen to the podcast. 

Pamela Gay [00:25:11] It’s true. Listen to the podcast. And, all of you, whether you know it or not, are extremely grateful to these people and many others who are our patrons. These folks have joined our. Pamela will mispronounce my name here and we are grateful. This week I would like to thank Cooper, Benjamin Mueller, Peter Don Mundus, Aaron Zagreb, Philip Grand, Cami Ross, Ian James, Roger, Sean Matz, Sam Brooks and his mom Nate Detweiler, Dean, Jeff Wilson, Kimberly Reck, disaster. Cheena, Tim Gerrish, John Drake, Philip Walker, Paul de Disney, Janelle aka Veronica Cure, Michelle Cullen, Benjamin. Davies, Dwight. Ilke, Brian. Kilby, Sydney. Walker, David. Bogard, Robert. Cordova, Justin S, Maxim Levitt, Howe McKinney. Bebop. Apocalypse Ruben McCarthy, Larry. Dots, Frank. Stewart, Jason. Caduceus, Gordon. Turner, Christiane. Golding, Bob. Czapski, Ron. Thorson, Daniel. Donaldson. Thank you all so very much. 

Fraser Cain [00:26:23] Thanks, everyone, and we’ll see you next week. 

Pamela Gay [00:26:26] And I’m going to stop the recording and save. And then they saved and then they saved and then they saved and then they saved and then they saved and then they saved and then they saved. And be safe. 

Fraser Cain [00:26:52] And they saved. 

Pamela Gay [00:26:54] All right. And then they saved. 

Fraser Cain [00:26:57] And then they saved. Our dogs are really losing their minds. 

Pamela Gay [00:27:02] I don’t know what’s going on. I’m sorry. We’re just gonna have to pause for a moment. There’s howling and barking and more howling. I don’t understand it. This normally is what happens when someone comes over, but I don’t think anyone’s coming over today. Astronomy cast is a joint product of Universe Today and the Planetary Science Institute. Astronomy cast is released under a Creative Commons Attribution license. So love it, share it, and remix it, but please credit it to our hosts, Fraser Cain and Doctor Pamela Gay. You can get more information on today’s show topic on our website. Astronomy. Cars.com. This episode was brought to you. Thanks to our generous patrons on Patreon. If you want to help keep the show going, please consider joining our community at Patreon.com Slash Astronomy Cast. Not only do you help us pay our producers a fair wage, you will also get special access to content right in your inbox and invites to online events. We are so grateful to all of you who have joined our Patreon community already. Anyways, keep looking up. This has been Astronomy Cast. 

Show Notes

Orbital resonance (Wikipedia entry)

What is orbital resonance? A dance between heavenly bodies (EarthSky)

Orbital Resonance: Planets Have a Gravitational Dance With Aligning Orbits (Discover Magazine, Chris Impey of University of Arizona)

Resonant Effects (NASA Science)

ESA’s Cheops helps unlock rare six-planet system (ESA)

Found super-Earth and mini-Neptune in orbital resonance (Universe Magazine)

Astronomers from the University of Liège discover a key planetary system to understand the formation mechanism of the mysterious ‘super-Earths’ (University of Liège ExoTIC)

Mercury’s spin–orbit resonance explained by initial retrograde and subsequent synchronous rotation (Nature Geoscience)

Orbital resonance in the solar system (S. J. Peale, University of California Santa Barbara; archived by NASA ADS)

Orbital resonances in planetary systems (Preprint) (Renu Malhotra, Lunar and Planetary Laboratory, University of Arizona)