Daniel and Kelly’s Extraordinary Universe - How stable is the Earth's orbit?

Episode Date: July 13, 2023

Daniel and Jorge talk about whether we can expect the Earth to continue in its path forever, or if our days are numbered.See omnystudio.com/listener for privacy information.

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so you can work, create, and boost productivity all on one device. December 29th, 1975, LaGuardia Airport. The holiday rush, parents hauling luggage, kids gripping their new Christmas toys. Then everything changed. There's been a bombing at the TWA. terminal, just a chaotic, chaotic scene. In its wake, a new kind of enemy emerged, terrorism. Listen to the new season of Law and Order Criminal Justice System

on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. My boyfriend's professor is way too friendly, and now I'm seriously suspicious. Wait a minute, Sam. Maybe her boyfriend's just looking for extra credit. Well, Dakota, luckily, it's back-to-school week on the OK Storytime podcast, so we'll find out soon. This person writes, my boyfriend's been hanging out with his young professor a lot. He doesn't think it's a problem, but I don't trust her. Now, he's insisting we get to know each other, but I just want her gone. Hold up. Isn't that against school policy? That seems inappropriate.

Maybe find out how it ends by listening to the OK Storytime podcast on the Iheart radio app, Apple Podcasts, or wherever you get your podcasts. Every case that is a cold case that has DNA. Right now in a backlog will be identified in our lifetime. On the new podcast, America's Crime Lab, every case has a story to tell, and the DNA holds the truth. He never thought he was going to get caught, and I just looked at my computer screen, and I was just like, ah, gotcha. This technology is already solving so many cases. Listen to America's Crime Lab on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. Hey, Daniel, did you see the recent launch attempt by Space X?

Oh, yeah, I did. A massive rocket with so many engines attached, really awesome to watch. Yeah, I hear the fireworks were great. It really popped. But the whole thing kind of has me worried a little bit. You worried the rocket's going to crash into your house? A little bit. I mean, I live in my house.

That would be a problem. No, but I guess I'm more worried about the effect it has on the Earth. Don't all those engines on the rocket also push on? on the earth? Yeah, I guess it's kind of like putting a rocket engine on the earth itself. A little bit, right? So we're letting Elon Musk steer our planet? I mean, he can't even steer Twitter. It would be pretty cool if a planet had a steering wheel. I guess that'd be fun. Although I would probably fall asleep. So maybe I shouldn't be driving the Earth. It would probably flies into the sun.

Hi, I'm Jorge, I'm a cartoonist and the creator of PhD comics. Hi, I'm Daniel. I'm a particle physicist and a professor at UC Irvine, and I don't want to fly into the sun. What do you want to do into the sun? Drive, walk, fall, dive. I guess I want to look into the sun of all the verbs. I think that's the least destructive one. I like hearing about the sun and feeling the sun. I don't know if I want to look at it. It's not dangerous? I want us to build new scientific eyeballs that let us peer into the sun

and understand the chaotic churning inside of it. You want to peer into the sun. Yeah, exactly. You want to spy on it. I consider the sun to be our peer in the solar system. I see. Are you saying you're like a sun god? No, I'm saying if we're ever accused of breaking a law of physics,

then I want a jury of our peers, which I guess would include the sun. And who else? Who else do you consider your peers in the cosmos? Jupiter is pretty good, yeah. It carries a lot of weight. Yeah. It would be a massive help on the jury. But anyways, welcome to our podcast, Daniel and Jorge,

Explain the Universe, a production of IHeart Radio. In which we try to thread the needle of understanding the entire universe without pissing it off too much. We try to pay attention to what's going on out there in the universe from the tiny little particles to the very massive objects swirling around each other. to try to deduce the laws that this universe follows as it moves forward through time towards its eventual end, whatever that may be. And we hope that before that end comes, we can figure out how it all works.

That's right because it is a massively cool universe full of amazing and incredible laws and mechanisms that seem to make the whole thing work like a giant clock, it seems, going around and around, taking away till the end of time. A clock makes it seem like very organized and stable. I see it more like a really complicated Rube Goldberg machine, you know, like ball rolls down a wheel and hits this lever which makes the cat jump

and then that knocks something else over. Sometimes it feels like the mechanisms on which our entire existence are based are very precarious. Like it knocks a ball, the ball rolls down a ramp and then out comes humans. And out of those humans, one of them bumps into another

and you and I are born. And this podcast is born. Exactly. It seems like it could have gone lot of different ways and in many of those ways we wouldn't be here so in some respects our existence here seems very very fortunate and i wonder sometimes about the future of our existence here how long these special cozy conditions will continue i know i feel pretty inevitable i feel like rhea chan was meant to be you feel like the whole project of the universe was to bring you

into existence why not at least my universe i don't know if my kids feel the same way Or my spouse. I'm an unfortunate byproduct sometimes, it seems. Well, one of the joys of understanding the universe is being able to predict its future, taking those laws of physics that describe what we have seen and also applying them to the future and thinking, what's going to happen, what's likely to happen in the next 100 years, million years, or a billion years.

Or the next hour. I mean, I don't know where this conversation is going, to be honest. The podcast does seem kind of unpredictable. It doesn't seem to matter too much what I write in the hour. line. Well, I think that's what happens when you put two unstable people and try to create a stable system here. But it is kind of an interesting question, how precarious our existence is and how likely it was that we are here in this place talking about the universe. It seems like the universe kind of could go either way at any moment. And there's lots of ways that things could go south

for us. But on the podcast, a few times we've talked about one in particular, which is the requirement that the Earth stay in orbit around the sun at just the right distance to keep water nice and toasty on our surface, but without bubbling it into steam or dropping it into a deep freeze. Yeah, the Earth is in what's called the Goldilocks zone of our solar system where it's not too hot and not too cold, which makes it just right for life to flourish on it and for fishes, birds, animals and humans, which I guess are also animals for them to come about. So you might wonder how long this Goldilocks situation can continue before the bears come home and ask for their porridge back.

So today on the podcast, we'll be asking the question. How stable is the Earth's orbit? Never thought about the stability of our planet's orbit, I guess. It seems so predictable and regular, right? I mean, nobody questions whether the sun will rise in the morning every day. We just assume it is. It's one of these really fun questions where the answer depends a lot on the time frame you're imagining. Nobody suspects that the Earth will fall out of its orbit tomorrow or next year or

in 100 years. And on the kind of timescales that humans are used to thinking about, the solar system is kind of static. We imagine it's looked the same way for 100 years, a thousand years, probably a million years. But when you look on longer timescales, hundreds of millions of years or billions of years, you see the solar system is actually quite chaotic. Planets have been lost. They've changed their orbit. They've moved from the outer solar system to the inner solar system and back. All sorts of crazy stuff has happened. So then you can ask like, well, how long will this phase of our solar system last? Yeah, I guess the solar system was just a giant cloud of dust and gas at some point, right? And then the sun formed and then the planets form. But

even after the planet's formed, the solar system kind of had to find its groove kind of, right? It's rhythm, its orbits. Things would crash into each other a lot before settling into planets, right? Yeah, that's exactly right. And you look at the surface of anything in the solar system, like the moon, and you'll see lots of evidence for collisions. Basically, anything that's out there is getting smacked into all the time. The Earth doesn't have a surface filled with craters because we have an atmosphere that mostly burns those things up before they hit the ground. But, of course, sometimes they don't. 65 million years ago or so, something really big hit the Earth. And billions of years before that, the moon was formed in an even more giant collision.

We've been hit around a lot. And yet we're still here. And if we look at Jupiter, for example, there's a lot of evidence that Jupiter and Saturn migrated to the inner solar system and then turned around and went back out, returning to the depths of the outer solar system. So planetary orbits are not as fixed as you might imagine. At least in large timescales, as you were saying. Well, as usually, we were wondering how many people out there had thought about this question and about the stability of our orbit, about how steady the solar system is. So as usual, Daniel went out there into the internet to ask people how stable. is the Earth's orbit.

I'm eternally grateful to everybody who answers these questions. If you want to be part of this segment, please don't be shy. Just write to me to questions at danielandhorpe.com. So think about it for a second. How stable do you think our orbit is? Here's what people had to say. So I would say that the Earth's orbit is very stable

over millions or maybe even billions of years. But perhaps when the sun turns into a red giant and expands, maybe that will change things and throw the Earth's further or closer in? Well, I think Earth's orbit is quite stable, but we are slowly drifting away from the sun because of the moon, and we might get hit by asteroids in the future,

but otherwise I think the Earth's orbit is stable. I don't think the Earth's orbit is stable forever. I think it looks pretty stable to us because the timescale of the universe of the solar system is pretty long. I would say it's like a metastable state, and maybe even an asteroid could kick the Earth out of Earth orbit. It's more like a castle of cards.

We remove one and everything falls apart. It seems pretty stable to me if humans had long enough to evolve, so hopefully it'll hang in there a bit longer. I know from your podcast about when stars collide that any object that's accelerating gives off gravitational waves because of its acceleration. So fundamentally, the orbit is not stable, and although it will take a really, really long time, eventually the Earth's orbit will fall into the Sun. I think the Earth's orbit is very stable. I have heard about studies that talk about Jupiter moving around in the ancient solar system and studies of sensitivity of Mercury and Venus to subtle perturbations, but I just think that the Earth's orbit is very stable. I think it's decaying, just like, you know, might expect it to, but, you know, not going into the sun anytime soon.

I think the Earth's orbit about the sun is very stable, at least over the timeframes that we're concerned with long-term millions or billions of years. There might be some drift in its position relative to the sun, just like there's some drift of the moon relative to the Earth over time. I think it's pretty stable in a human time scale, but on the long term, I think that either gravity or angular momentum will be more prevalent. All right. Seems like most people think it's kind of stable. Only a few dissenters. Not a lot of people worried about this out there, although maybe they got more worried after they read this question. Maybe they should be more worried.

That's what we're here for, isn't it? to make people think about all the different ways that the universe can kill them. Maybe we should be selling Earth orbit insurance somehow. There you go. If the Earth plunges into the sun, we will pay you any arbitrary amount of money. A bazillion dollars. Exactly. Just give us a million dollars a year.

That's right. Submit your request to this PO box. But yeah, it's kind of an interesting question. How stable is the Earth's orbit? Because I guess we're going around the sun pretty steadily, right? Is our orbit like, do we always go through this? the same spot in the, in the solar system, or is our orbit kind of wobbly? Well, our orbit around the sun is not perfectly circular, right?

It's an ellipse, and that ellipse can process a little bit, which means if you imagine an ellipse or like a football or anything oblong, then that orbit itself can rotate, right? The path of the ellipse itself can rotate. And is that the same for the whole solar system? Like everyone's orbits also kind of rotating? There are some changes in the eccentricity of the Earth's orbit that's deviation from it being circular over like 100,000 year time scale. And these things actually can affect like the climate.

These are called Milankovic cycles. We talked about it once in the podcast about ice ages. But that doesn't make the Earth's orbit stable or unstable. An elliptical orbit can be stable over very, very long time periods. So whether or not you're circular or elliptical doesn't change whether or not you're stable. I see. The orbit is changing a little bit. But I think maybe what you mean by stable or unstable is whether like if you move,

move the Earth a little bit, is it going to go back to its same orbit or is it going to spin out of control and shoot out of the solar system? That's kind of more what you mean, right? Yeah, by stability we mean, will it return to its current configuration if it's pushed a little bit? Say, for example, you jump. Every time you jump, you are pushing on the Earth, right? You're using your leg muscles to push yourself away from the Earth, but you're also pushing the Earth away from you. And Newton's laws tell us, you know, every force has an equal and opposite reaction. And so you're moving away from the Earth, and the Earth is also moving away from you. Now, of course, because the Earth has so much mass, your push doesn't really affect it

as much as it affects yourself. It's sort of like when you fire a rifle, the bullet gets going really, really fast, but the rifle itself also has a little bit of recoil. And so when you jump, the Earth recoils a little bit against you. And so if the Earth's orbit is stable, then a little push like that won't like send it spiraling into the sun, it'll like drift back to its original orbit. If the Earth is unstable, then it's more like a pencil balancing on its tip. Any tiny little touch will knock it out of its configuration and it won't come back. So stability tells you about whether you come back to your current orbit when you're given a little push. First of all, it's cool that every time I take a step, basically, I'm sort of moving to Earth

a little bit, right? Every step I take is Earth shattering, Earth moving. It sort of is, though, you return to the Earth, right? And the Earth returns to you. So in the end, the Earth's orbit isn't actually changed by that. To really change the Earth's orbit, you need to, like, take a rock and throw it into outer space and have it escape from the Earth. So the rock and the Earth are now, like, parting ways and going in opposite directions. Yeah, I guess that's what I meant. It's like, if I jump, I'm going to fall back down onto the Earth, unless I jump super duper high, but I'm not that fit, I guess.

But if I jump, but the Earth pulls me back. and then it sort of recovers, right? Like, as it's pulling me back down into Earth, it's also moving a little bit towards me. Exactly. You come back together, and so there's no effective change. That's why I was talking about Elon Musk

instead of you and your ripped thighs jumping off the surface. You know, if Elon Musk launches a rocket away from the Earth, then he really is giving the Earth a push. Now, if that rocket ends up in orbit, then it isn't because it's still in the Earth's gravitational system. But if he launches a rocket to Mars or to deep space or something like that,

so it really leaves the Earth's gravity, system, then it's given the earth a push. And if the earth was in an unstable situation, like a pencil balanced on its tip, then even a tiny push would knock it out of orbit. Yeah, I guess maybe an analogy is that sort of like tossing a coin or like rolling a coin. That's a system that's kind of unstable, right? Like if you tip the coin just a little bit to the right, it's the whole coin is going to veer off to the right a lot. Or if you tip it a little bit to the left, it's going to veer off to the left a lot. That's what you mean by sort of unstable or kind of sitting on the edge of something. Exactly. Or imagine you have a ball in a glass, right? You shake the glass

a little bit, the ball moves from the bottom of the glass, but it comes back to where it was. When it deviates from its preferred location, there are forces to push it back to where it was. Or if you have the situation upside down, like ball balance on the top of a hill, for example, if it's precariously balanced there and you give it a push, then the forces are going to pull it away from that configuration place. So another way to think about stability is, are there forces that are restoring you back to your original location or are there forces that are pushing you away? So in the stable case, their forces restoring you to where you were. And in the unstable case, their forces pushing you away. Right. I guess it's kind of what you mean by balancing a pencil or

like if you take a long rod or stick and you try to bounce it on the palm of your hand. Like there is a way for you to like move your hand around a lot and not have this stick fall over. But That's sort of an unstable situation. Like if you deviate a little bit from that path, then the stick will fall. Exactly. And in physics, we call that equilibrium. There is a configuration for the stick to be balanced, for all the forces to be equal and for it to just stay there. But it would be unstable.

Like a tiny fly lands on it and pushes it in one direction. Now the forces are going to keep it going in that direction rather than pushing it back. Whereas if you have a ball and a glass and a fly lands on it and pushes it a tiny little bit up the glass, the glass is going to return it back to the equilibrium location. So you're going to have stable and unstable equilibrium. And the difference really is whether you have forces pushing you back towards the equilibrium or away from it. Right. And so that's what we're talking about here for the Earth. I mean, we're going around the sun in a circle or a semicircle, sort of a circle.

And it seems stable, but it could be an unstable orbit, meaning like we're going around this path and we just got lucky to get into this groove. But if we actually sort of step away from the groove or fall a little bit to the one side, then maybe it'll take us into a completely different orbit or even away from the solar system or into the sun, I guess. Yeah. And you might be worried like that if you jump too high, you're going to push the earth out of orbit. Because if you imagine that the earth like deviates a little bit towards the sun, gravity gets stronger and it pulls on it harder. So you might worry that like if you jump on the wrong side of the earth, you could actually push the earth into the sun,

like a fly toppling that balanced pole on your hand. Although I guess it would depend on which way you jump like you just said like if I jump in the direct like if I jump off of the north pole maybe I'll just move the orbit up and down a little bit right yeah exactly or if I jump sort of like trailing the earth in the in the direction where behind the earth I guess then I will give it a little boost or if I jump in the front it'll slow down the earth a little bit or if you have a friend on the other side of the earth and you time your jumps together then it doesn't matter right so really this question is about can you do exercise whenever you like or do you need to coordinate it with the rest of humanity?

That's right. And or do we have any friends? All right. So that's what stability means for an orbit and for our planet. And now let's get into whether or not it is a stable orbit or if it's a precariously balanced orbit. And we are just here out of sheer luck. But far as, let's take a quick break.

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All right, we're asking the question, how stable is the Earth's orbit? We talk about how we are in orbit around the sun, right? The Earth is being pulled by gravity towards the sun, but we have a certain velocity, which makes the whole planet kind of go around in a circle, right? Yeah, that's right. We're moving in roughly a circle, it's essentially in the ellipse,

But we'll talk about the difference there in a minute. And the question is like, is the orbit stable? If we deviate from this situation a tiny little bit, are we going to spiral into the sun or drift out into deep space? Which makes you worry, not just for like everyone jumping at the same time, is that going to knock the Earth out of its orbit? But if something else comes out from space and hits us, right? Yeah, exactly, because we are hit all the time by asteroids and meteors, right?

Every time you see a meteor shower, those are objects from other places in the solar system smashing into the Earth's atmosphere. And a minute ago, we talked about it in terms of forces. Are there forces restoring you back to your orbit or are there forces pulling you away from your equilibrium? And in this situation, the only relevant force is gravity, right? Gravity pulls us towards the sun. There's no electromagnetic force.

There's no weak force. There's no strong force. It's really just gravity here. And so from that simple perspective, you might think, hmm, the only force is pushing us inwards. So if we got hit, like from just the right angle, like an asteroid fall in, in from the outer solar system and pushing us towards the sun, it might make you worried because the force of gravity would get stronger as you get closer and then pull you harder

plummeting the earth into the sun. But it's a little bit more complicated. And also you just made me think like if an asteroid falls to Earth and it gets burned up in the atmosphere, does it actually pushes or does it just get converted into, you know, fire and smoke and light? It definitely pushes us. It doesn't matter if it gets burned up or not. It's sort of like a bullet entering your body, right? It's still going to push you back even if it doesn't leave your body or if it gets shredded inside you. It doesn't really matter whether it turns into heat or not. You've absorbed the momentum of that object. Doesn't some of the energy of an asteroid also like leave maybe as light? Yeah, a little bit, although that actually might have a bigger impact

because that's more like the asteroid bouncing off of the earth, which would be a larger momentum transfer. Or doesn't somebody get transferred into heat? Like it heats up to Earth, but that doesn't necessarily push the Earth, does it? If the Earth totally absorbs it, then it's going to absorb all of its momentum. If it bounces off the atmosphere, then it's going to get twice its momentum because it's changing direction entirely. The way for it to actually minimally affect the Earth

would be like pass through the Earth out the other side to maintain its momentum. So if it like grazed the atmosphere somehow, then it wouldn't affect the Earth as much. All right. Well, let's get into the stability of our orbit. Maybe step us through the basics. Like what makes an orbit and what would make it stable or unstable?

Yeah. So there's only gravity at work. here, which is pulling us towards the Sun. And first you might wonder, like, how do you get equilibrium at all? How is it possible to have an orbit where your radius is basically constant? Again, just thinking about it in terms of circular orbits for now. How is that even possible if all you have is a force towards the center? Well, it's true you only have one force, but it's a little bit more complicated than that.

There's another apparent force because we're talking about circular motion, which is not inertial frames, like there's an acceleration here. Then there's an effective force that appears. It's not a fundamental force like gravity or electromagnetism or whatever. It's the effect of working in a rotating frame of reference. The way, for example, if you're on a merry-go-round and it spins, you feel a force pushing you towards the edge of the merry-go-round. It's not gravity, it's not electromagnetism. It's an effective force due to the rotation.

Right. It's not like a real force. It's more like you feel like something's pushing you towards the middle of the merry-go-round, but really it's just a merry-go-round trying to make you go in a circle, right? Yeah, exactly. And so there really are two effective forces to consider there. There's gravity pulling you in, and then there's this centripetal force pushing you out. So there is the possibility to have a balance there.

That's where the equilibrium comes from. When those two things balance, then you have an orbit. When the force of gravity pulling in and the centripetal force pushing out balance, then you have circular motion. So that's why you can have an equilibrium at all. But equilibrium doesn't necessarily mean it's stable. You can have stable or unstable equilibrium, like the example of a pole balancing in your hand, And all the forces are balanced there, but as soon as you deviate from it, it falls over.

Whereas a ball in a cup is at stable equilibrium because the forces are restoring. So now we understand why the Earth can be an equilibrium in an orbit, but we still have to answer the question of whether that's stable or unstable. Yeah, I guess I've always thought about it as like, let's say I'm flying through space and I have a velocity vector pointing in front of me. I'm going forward. And the sun is to exactly to my right. Now, the sun is pulling me towards the right, but it's sort of not affecting my velocity that I have going forward because it's pulling me perpendicular to that velocity. So it's going to kind of change the direction of my velocity, but it's not going to slow me down

or speed me up. And if you keep doing that, it traces out a circle, right? Yeah, that's right. There's a couple of things going on there. You have the constant total velocity, right? Your overall velocity, the overall magnitude of your velocity doesn't change, but the direction of it does. And that confused people sometimes, that still counts as acceleration because you're changing like the different components of your velocity.

So moving in a circle, you're right. It doesn't change your overall velocity. That can be constant, but the direction of the velocity changes. And that requires acceleration. And that's what the force of gravity is doing. It's changing the direction of your velocity, not the overall value. Right. And I think you're saying that an orbit is when that's perfectly balanced, like the force of gravity pushing you towards the sun, but then also you have enough velocity.

to kind of resist that motion. That's when you get an orbit, which is a circular kind of path around the sun. But there are, I mean, there are many other paths, right? Like if I'm near a big object like the sun, I don't have to fall into an orbit, right? I could just, for example, fall straight into the sun or spiral into the sun, right?

Exactly. There's also parabolic trajectories and hyperbolic trajectories, right? Things that fall in from the outer solar system can get slingshotted by the sun and then leave the solar system. So there's lots of different trajectories around the sun. This is sort of a very special arrangement.

You have the right direction and the right velocity at the right radius, then everything settles in and you can just keep doing it. Right. And it kind of seems lucky that we are stuck in an orbit that does go around in a circle, but that's because that's kind of what survived the chaos of the solar system, right? Like the solar system probably had a bunch of rocks flying all over the place. And over the millions of years, maybe billions of years, anything that wasn't in an orbit basically fell into the sun or got thrown out.

And so anything that remains after all that time, it should be in an orbit, right? Yeah, that's right. We only see the things that didn't fall into the sun. And so we see the bits that have the right radius and velocity match, right? At a given radius, you need a certain velocity to have that orbit work. Or it's another way, if you have a certain velocity, you have to be at a specific radius. So you have to have those pair match. You can't just have an arbitrary velocity and an arbitrary radius and expect to be in an orbit.

For a given radius, you have to have a very specific velocity to be in an orbit. But that seems like almost impossible, right? It seems like, well, if your velocity has to be exactly some number, then how did anything end up in orbit? Because what are the chances that two, like, real valued numbers exactly match each other? Right. Like, I wonder if there could have been a planet early in our solar system's history that they were, you know, floating around the sun. And they were like, oh, we're in an orbit. This is pretty cool.

But it turns out they weren't in a circular orbit. They were in a spiraling orbit. Exactly. But if you look at the energy dynamics of it, it turns out. that these orbits actually are stable. Meaning if you don't have exactly the right value, the physics of it tends to push you towards having the right value.

Or if you have the right value and somebody gives you a push, or he jumps off the planet, or an asteroid hits us, or Elon Musk launches a super heavy rocket, so we deviate a little bit from having the right pair of velocity and radius, that actually the forces will push us back towards having the right velocity and radius. Turns out that just from a gravitational point of view, using Newtonian physics, these orbits are stable.

Wait, wait, wait. Are you basically answering the question of the episode? So orbits are stable. In the simplified universe that we don't live in, where we have only one planet and the only thing happening is Newton's gravity, then yes, these orbits are stable. But of course, there's lots of other things going on. The sun is losing its mass. The Earth feels a solar wind, et cetera, et cetera.

There are other planets tugging on us. So it's a little bit more complicated. But in the simplified view of just a single planet orbiting a star, then yes, those orbits, are stable. Oh, I see. Wait, wait. So like, if the solar system only had one planet, us, then no matter what we do, we would be in an orbit. If the solar system had only one planet and the sun lasted forever and there was no solar wind and no gravitational radiation and nothing else from outside the solar system affected us, then yes, we would be in an orbit that would be stable basically forever. But like, it has to be one particular orbit? Or like, let's say we're this

single planet around the sun. There's nobody else. Nothing changes. in terms of how big it is or what happens to the sun. We're with one planet in the solar system and something comes and knocks it or gives a sudden boost in one direction. It's going to move out of the orbit we're in, but is it going to then get into another different orbit? It depends a lot on how it gets hit.

If the Earth speeds up a lot, for example, it gets hit from behind, then there's another radius that it needs in order to have a stable orbit. But it's actually likely to slide over into that radius because the energy configuration is stable. If the Earth has too much velocity, then the balance of the forces will tend to push it towards the radius it needs for that velocity. On the other hand, if it gets pushed like from the side that it gets kicked out a little bit, then it might actually oscillate and move from a circular orbit to an elliptical orbit, which is sort of like a circular orbit, but you're like sloshing back and forth a little bit.

There's like a harmonic motion around a circular orbit. So like, let's say I have the Earth and we're the only planet in the solar system and I attach some rockets to the back of the Earth. and I fire them up, I'm going to speed up. Is that going to get me into like an electrical orbit then around the sun? Or is it going to be like a totally chaotic orbit? Like I feel like the only reason we tend to think of orbits as stable is because they're pretty circular, right? But you can also go around the sun for a long time going around in like big ellipsis, right?

Like you're really far from the sun and then you fly towards the sun but you get really close but you fly really fast and then you shoot past the sun and then you come back and you do the same thing over and over and maybe that big ellipse is not always the same. You're sort of going around and around the sun, but you're still sort of, you're not falling into the sun. Exactly. That ellipse can also be a stable orbit. It's not circular, but it can be stable. And you can think of it as having two components. You can think of it as a circular orbit plus motion relative to that circular orbit where you're sloshing in and out and in and out. And that whole arrangement can be stable. You can be in a circular orbit forever around a star,

without ever falling in. And the reason is something you just mentioned, which is that your speed and your radius vary. Say somebody comes along and pushes us towards the sun, for example. So now we fall in a little bit towards the sun and gravity is getting stronger, but we're now also going to speed up. So when we come around the curve,

we're going to be going fast enough to go further out than we used to. That's going to slow us down. And gravity is going to pull on us, slowing us down. We're going to use up our energy climbing out of the gravitational well, and then we're going to come back. And we're going to slosh back and forth around that original circular orbit. That's what I mean when I say

that it's stable. There's forces of gravity pulling you back towards it and then there's this centripetal force effectively pushing you back towards your orbit. And those two forces are encouraging you to stay in that orbit. To that new elliptical orbit, right?

Like if I put some booster rockets on the Earth, it's not going to maybe make the Earth spiral in. It's going to make it just, it's just going to change the shape of the orbit. Or is that true? Or is there a possibility for me to fall into the sun? There's a possibility for you to fall into the sun. There's a possibility for you to fall into the sun.

Absolutely. If you push hard enough, right? Stability is always approximate. It's always possible to get out of the orbit. If you put enough energy in that rocket, you can escape the sun's gravity, or if you turn really, really hard, you can drive right into the sun. But small deviations will return to the stable orbit. To a stable orbit, right?

Not necessarily the one we're in right now. Yeah, that's right. And it might be circular and it might be elliptical. It depends exactly on the kick that you give it. You can also change your circular orbit to another circular orbit, that that's basically an ellipse with zero eccentricity, and so that's a little bit less likely to happen. So if you're in a perfectly circular orbit, I think the most likely thing if you get a kick is to end up in a slightly elliptical orbit.

Or if you're in a slightly elliptical orbit, if you get a kick, then you're saying the most likely thing is that it'll just change the shape of that ellipse, right? It might twist or in my turn, it might get, you know, rounder or narrower, but it will still be in an orbit that the Earth will want to stay in. Yeah, exactly. So there's lots of different stable configurations. Circular orbits are like a special condition. of elliptical orbits.

Really, circles are like a special kind of ellipse than ellipse with zero eccentricity. So if you think about all orbits as elliptical and circular ones are like one particular kind of elliptical orbit. But yes, elliptical orbits are a stable. And I think a big reason we're here, alive full of animals and plants around us,

is that our orbit is pretty circular. Like, if you look at a picture of it, you couldn't probably tell that it's not a perfect circle. Yeah, the eccentricity is not huge. And you're right, if it was much greater, we would have more dramatic seasons. Yeah, like, you know, you think about just how different summer and winter are, and that's just because of our tilt. But like if our orbit was elliptical and we flew a lot closer to the sun in some parts of the year, I mean, we basically beat toast, right?

And we would freeze the other parts of the year. Yeah, that's right. And there are very elliptical orbits that would in principle be stable, but would not be survivable. So stable and survivable are not the same thing. So it's not just about the Goldilocks zone, right, being at the right distance from the sun. And it's also about having a pretty circular orbit, right? So that things are stable. Yeah, that's important.

All right. Well, as you said, this stability and this ability to stay in orbit is only good if in a perfect universe where we're the only planet in our solar system. Unfortunately, as most kids know, having siblings is kind of a hard thing to deal with. And you can really throw your household in this array. So let's get into what could maybe knock us out of our orbit or at least make that orbit unstable and whether we have any control over those things. But first, let's take another quick break. Ah, come on. Why is this taking so long? This thing is ancient. Still using yesterday's tech,

upgrade to the ThinkPad X1 carbon, ultra-light, ultra-powerful, and built for serious productivity with Intel core ultra-processors, blazing speed, and AI-powered performance. It keeps up with your business, not the other way around. Whoa, this thing moves. Stop hitting snooze on new tech. Win the tech search at Lenovo.com. Lenovo, Lenovo. Unlock AI experiences with the ThinkPad X1 Carbon, powered by Intel Core Ultra processors

so you can work, create, and boost productivity all on one device. December 29th, 1975, LaGuardia Airport. The holiday rush, parents hauling luggage, kids gripping their new Christmas toys. Then, at 6.33 p.m., everything changed. There's been a bombing at the TWA terminal.

Apparently, the explosion actually impelled metal, glass. The injured were being loaded into ambulances. Just a chaotic, chaotic scene. In its wake, a new kind of enemy emerged, and it was here to stay. Terrorism. Law and Order Criminal Justice System is back. In season two, we're turning our focus to a threat that hides in plain sight. That's harder to predict and even harder to stop.

Listen to the new season of Law and Order Criminal Justice System on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. My boyfriend's professor is way too friendly, and now I'm seriously suspicious. Oh, wait a minute, Sam. Maybe her boyfriend's just looking for extra credit. Well, Dakota, it's back to school week on the OK Storytime podcast, so we'll find out soon. This person writes, my boyfriend has been hanging out with his young professor a lot. He doesn't think it's a problem, but I don't trust her. Now, he's insisting we get to know each other, but I just want her gone. Now, hold up. Isn't that against school policy? That sounds totally inappropriate.

Well, according to this person, this is her boyfriend's former professor, and they're the same age. And it's even more likely that they're cheating. He insists there's nothing between them. I mean, do you believe him? Well, he's certainly trying to get this person to believe him because he now wants them both to meet. So, do we find out if this person's boyfriend really cheated with his professor or not? To hear the explosive finale, listen to the OK Storytime podcast on the IHeart Radio app, Apple Podcasts, or wherever you get your podcast. I'm Dr. Scott Barry Kaufman, host of the psychology podcast.

Here's a clip from an upcoming conversation about exploring human potential. I was going to schools to try to teach kids these skills, and I get eye rolling from teaching. teachers or I get students who would be like, it's easier to punch someone in the face. When you think about emotion regulation, like you're not going to choose an adaptive strategy which is more effortful to use unless you think there's a good outcome as a result of it if it's going to be beneficial to you. Because it's easy to say like go you, go blank yourself, right? It's easy. It's easy to just drink the extra beer. It's easy to ignore to suppress seeing a colleague who's bothering you and just like walk the other way. Avoidance is easier. Ignoring is

easier, denial is easier, drinking is easier, yelling, screaming is easy. Complex problem solving, meditating, you know, takes effort. Listen to the psychology podcast on the Iheart radio app, Apple Podcasts, or wherever you get your podcasts. All right, we're asking the question, And how stable is the Earth's orbit? And it sounds like in a perfect world, orbits are pretty stable. Yeah, universes in which you have three directions of space like X, Y, Z, have stable gravitational orbits if you have nothing else going on. What's fascinating to think about is that other universes with like two-dimensional space or four-dimensional space don't actually have the same kind of balance. This balance you talked about where gravity pulls you with just the right strength to bend your velocity.

That perfect balance only happens in three-dimensional space. In 4D and 2D space, centrifugal force and gravity both change and they don't balance each other. There aren't stable orbits in 2D or 4D space. Wait, what? Like, isn't the Earth basically going around a flat ellipse? Aren't we technically in 2D? We're not technically in 2D because gravity gets dispersed in three dimensions, right? So if there was only two dimensions of space, then the dependence of gravity would be different.

Oh, interesting. All right. Well, as you said, this is only in a perfect world, but we don't live in a perfect world. world. There are other things in the solar system. There's things that things can change in the solar system. So let's talk about some of the things that could maybe knock the earth out of its orbit. So, of course, the sun is the source of our gravity and the gravity of the sun comes from its mass, but the sun's mass is not actually constant. The way that the sun lights up our skies and heats up our days is that it burns its fuel. It's converting mass into energy in order to send it to us.

And so it's actually dropping its mass, which means the sun's gravity is actually fading. It's burning up. It is burning up because the fundamental process inside the sun that produces that light is fusion, which converts mass into energy. Like if you take four protons and you convert them into helium four, which is two protons and two neutrons, they don't have the same amount of mass as those four protons. Remember, mass is not a measure of the amount of stuff. It's actually measured the internal stored energy.

And that arrangement of all those corks in a helium-4 nucleus has less stored energy than four individual protons by about 0.7%, which means that every time fusion happens, the sun loses mass. Well, it's basically burning away itself, right? Like it's sort of like a log eventually burns down into a pile of ashes. Yeah, now, of course, the sun is really massive. And even though it burns like 4 million tons of mass every second, right? Every single second, the sun loses 4 million tons of its mass. That energy flies away in photons and in the solar wind. But over the lifetime of the sun, that only adds up to like the mass of Saturn,

which is a tiny, tiny fraction of the mass of the sun. Wait, over billions of years, the sun is only going to lose the equivalent of one Saturn's worth of mass? Yeah, that's right. That doesn't seem like a lot. I mean, Saturn is big, but it's tiny compared to the sun. Yeah, that's right. Saturn is tiny compared to the sun.

But, of course, it has an effect on the sun's mass, which has an effect on the sun's gravity. And so every year, the sun loses enough mass so the Earth's orbit gets larger by about a centimeter and a half every year because the sun's gravity is getting weaker. Whoa. Every year. Every year, we've got a centimeter and a half further from the sun. We're like slowly spiraling out. So is our orbit then just getting bigger our orbit? Yeah, that's right. Every time the sun loses mass, there's a new radius where we would have a stable orbit. So if you took like a scoop of stuff out of the sun and the sun lost its

mass, the earth would slide out a little bit into a new stable orbit. In reality, it's happening on a continuous basis. The sun is losing its mass and the earth is sliding out. So at any moment, it's in a stable orbit, but the stable orbit is actually changing with time because the sun is losing mass over time. But I think on average humanity is gaining weight in general, right? So wouldn't that mean that our gravity is stronger. I'm just thinking like a five-year-old year. If you eat the earth, you gain weight, but the U plus Earth system doesn't get any more massive.

Although, wait, are we getting energy from the sun? And isn't some of that energy being converted into, I don't know, things and plans for us to eat? Yeah, that actually does have an effect. All the photons hitting the Earth and all the energy hitting the Earth does have an effect on the Earth. And it actually pushes it, right? The Earth is like a big solar sail. Remember we talked about how photons can push on things, even though they don't have mass,

they have momentum, and you can like fly a spaceship if you have a huge solar sail which catches those photons. So the Earth is kind of like a big solar sail. And that's another effect we didn't include when we thought about just the simple Newtonian view. So all the photons hitting the Earth do push it a little bit. The effect is super duper tiny because the Earth is pretty massive. The calculation suggests that over a million years, that increases, the Earth's orbital radius by about the width of a proton.

Wow, that's tiny. Yeah, that's basically something we can ignore. But I wonder, like, we've talked about how, like, you know, mass is really just energy and that concentration of energy is what affects your gravity and how you bent space around that with that energy. So does that mean, like, the hotter the Earth gets, the more gravity we have? Yeah, as the Earth heats up, you have more mass. Like, when you put a rock in the sun and it absorbs photons, it doesn't just get hot.

hotter. It has more internal stored energy. It has more mass. It has more inertia. It bends space more. The same way, like if you take a box of mirrors and you shine a flashlight in it and then slam it closed, you've trapped those photons inside. That box gains mass. Interesting. I'm guessing it's not, maybe not enough to counteract or to change our orbit around the sun, or is it? No, that's not enough. The overall effect from the sun's energy hitting the earth is to push it to transfer our momentum, but really these effects are totally negligible. Compared to the sun losing its mass, this is basically something we can ignore. Although it depends on how hot you make the earth, isn't it?

Like if you make it super duper hot, it is going to be heavier. Yeah, that's right. And the sun actually is getting hotter every year and it's growing. Something else to think about over these very long times is whether the earth is going to get gobbled by the sun, right? As the sun burns its fuel and gets a helium core, then the fusion starts to have. happen in the outer edges and it puffs out and the radius of the sun grows really, really large. The estimates are that eventually the radius of the sun will be 200 times its current

radius, which puts it right about where the Earth's orbit is today. Which will be bad news for anyone on Earth at that time, right? Because it'll be way too hot. It'll be way too hot. It's actually a really interesting and complicated calculation because the sun gets larger and it would be very bad for the Earth, obviously to get enveloped by the outer layers of the sun. Because not only would it be super hot, but it would drag on us. It would tend to slow us down and then we're very likely to fall into the sun. But at the same time, the sun is losing mass. So the Earth is spiraling out as the sun grows.

So it's kind of a close race. Like the Earth is drifting away and the sun is like trying to catch us. But wait, even as the sun grows, as long as it doesn't grow more than the orbit of the Earth, doesn't it feel the same to the Earth? Like, you know, it feels like a point mass. Exactly. As long as the sun is contained within. the Earth's orbit, then you're right.

It doesn't matter how that's distributed big or small, a point mass, the black hole, the current sun, it's all the same gravitationally. But if it does pass the Earth, then any parts of the sun that are outside of our orbit no longer contribute gravity to pulling on us. And then we feel a drag because we're flying basically through the sun's outer atmosphere. And that would just kill the stability of our orbit. I feel like if we're flying through the sun, we have other things to worry about. Yeah, exactly.

Or like if we're still on Earth at that time, it seems like it wouldn't matter if you're going to fall into the sun or not. Like you're already in the sun. But because as the sun gets bigger, it also gets less massive. It's losing its mass. The Earth is going to be sliding away from the sun as it gets puffy. So the estimates are like the sun will grow to a few hundred times its current radius and the earth will drift out to like a little bit further than that.

But the calculations are very uncertain. And so it's not clear whether the Earth is going to get engulfed by the outer atmosphere of the sun or if we're going to like escape that in orbit at a new distance. But I feel like maybe neither of those things is making our orbit unstable. You know what I mean? Like neither of those things is enough to either make a spiral into the sun or kick us out of the solar system. They won't kick us out of the solar system. If we do enter the upper atmosphere of the sun, then the orbit's unstable because the drag is just going to surf all of our energy.

And it's like a satellite orbiting in low Earth orbit getting slow. down by the atmosphere and eventually plummeting to Earth. All right. What else can disturb our orbit in space? Well, another big problem are the other planets, right? It's not just the Earth and the Sun. Jupiter and Saturn are very tiny compared to the Sun, but they're not something we can totally ignore.

And the problem is that while two objects can be in very stable orbits for a very long time, three objects are chaotic. We talked about this on our episode about the three body problem. It's not just a cool science fiction novel. It's actually a real thing in physics. that three objects have a hard time being stable for long periods of time. And so as Jupiter and Saturn tug on us, they basically disturb our orbit. It's sort of like romantic relationships.

Like two is barely stable, but three, that's just asking for trouble. And if they push hard enough or they get lucky or we get unlucky, then they can disturb our orbit in a way that like ejects us from the solar system. And we think that this has happened. We think that there have been planets in our solar system, which were ejected by Jupiter and Saturn. I guess it's kind of a wonder that it hasn't happened, right? Like, Jupiter's there.

Like, we're not just a three-body system in our solar system. We're like a, you know, 10 or 10 million body problem because of all the asteroids. Isn't it kind of a wonder that we are in a stable orbit, given everything that's flying out there? Yeah, it is kind of amazing that we're left here, right? We think that Jupiter traveled in towards the inner solar system and then back out. There might have been another gas giant that had got to do. ejected. It's sort of amazing that any planets survive that sort of chaotic motion. And especially in the future, we think that as the sun gets weaker, Jupiter and Saturn's orbits will become

more chaotic because they're not going to be as tightly held. And then in turn, they will add more chaos to the rest of the solar system. So in some simulations I looked at, Jupiter ends up being the only planet. Like even if the Earth escapes being engulfed by the sun's atmosphere as it grows. It gets injected by Jupiter. And in the long-term future, the solar system, it's just a big puffy sun and Jupiter. And this is due to the sun losing mass. Yeah, the sun loses mass. And so it doesn't pull on Jupiter as hard and it makes Jupiter more chaotic. But again, this is in a few billion years, right? This is in a few billion years, exactly. So you should buy your Earth stability insurance now and pay your premiums every single year until then. No, you should wait

a few billion years. If you know, if something's going to happen, you should buy it right before it happens. That's how insurance works. We're not going to be offering this insurance in a billion years. This is your one-time offer. To pay us a billion dollars for a billion years. All right. What are some other things that could maybe knock our orbit out of orbit? Well, other sources of chaos are things outside the solar system, right? Like other stars can pass kind of nearby our solar system and give it a little kick, like a little perturbation. This already happens. Like other stars come close enough that they can like tweak stuff in the

word cloud, this vast system of trillions of icy objects in the very distant solar system, some of them then get knocked in and become comets, which burn their way into the solar system and whip around the sun. But if other stars come closer, for example, then they could perturb the orbits of planets themselves. Right. Yeah, we had that object, oh, Muwa, right, come through our solar system from out of space a few years ago. Yeah, that's right. Nobody really knows what that thing was. Or how to pronounce it correctly. or if it was actually alien space junk, but it's a cool example of how we're not the only things out there, right?

We do bump into stuff from other solar systems, and the galaxy is chaotic. You know, the stars are all moving in different velocities relative to each other, so we get further and closer to other stars. There's another star called Glees 710, which is expected to pass near our solar system in about a million years, and that could have a gravitational impact on all the orbits. And remember, if it tugs on Jupiter, Jupiter could then. tug on us, it can all become very chaotic very quickly. But I guess stars are easier to see coming.

Like you say, we know this one's going to fly by in a million years. Yeah, they're easier to see coming. They're harder to do something about. We talked once about building a star-sized rocket ship, like flying in the sun into a different spot in the galaxy to avoid oncoming stars. It might take us a million years to figure that out. Or just wait for the insurance premium 2 p.S. That's right.

Sit back and relax. You're covered. All right. Now, what's the last thing that could maybe push us out of orbit? So even if you don't worry about Jupiter and you assume the sun is going to be there forever and all sorts of chaotic things are not something to worry about, there's still a gravitational issue. The reason I said that a Newtonian system is stable over long periods of time is that Newtonian gravity ignores gravitational radiation. Anytime you have an object that's accelerating and moving in a circular orbit counts as acceleration,

it gives off gravitational waves because gravity is not actually a force. it's actually the curvature of space affecting how things move. And when things accelerate, they create ripples in that space. These are gravitational waves. We've seen gravitational waves from orbiting objects like black holes orbiting each other give us those gravitational waves. They radiate away energy. So that means that as the Earth is going around the sun,

it's also generating gravitational waves and losing energy. So in principle, over a very long amount of time, the Earth will radiate away its energy and fall into the sun. But that's not going to happen for a while, right? Yeah, we estimate that it loses about one proton width and radius every thousand years. So if you do the calculation, it's like 10 to the 26 years before the Earth spirals into the sun, which is about 10 quadrillion times the current age of the universe. So yeah, not something to worry about.

But in principle, over very, very long times, gravitational radiation will cause us to lose our energy and spiral into the sun. All right. Well, it sounds like the message. or the answer to the question is that the Earth's orbit is pretty stable at least in the short run. It sounds like most orbits are stable and

the fact that we are in a stable orbit probably means that we're going to be here for a while. But of course the universe has a lot of surprises and we are in a sort of chaotic system with other planets in our solar system. So something could happen in the near future but it's unlikely.

That's right. So in a Newtonian system, in principle, it's stable. An object orbiting the sun can do that forever. But once you add gravitational radiation for Einsteinian gravity, then eventually it's going to fall into the sun. And once you add other things in the solar system, then you add chaos, which are going to perturb those orbits. And once you consider the fact that the sun itself is losing its mass and changing its gravitational pull on the earth, then over those very long time scales, the Earth's orbit is not stable. but over short time scales, we don't have anything to worry about.

So I guess maybe you don't need that insurance after all. So the next time you jump, feel free to jump as high as you can or want. The Earth is going to stay where it is going around the sun and the sun will rise tomorrow, most likely. All right, well, we hope you enjoyed that. Thanks for joining us. See you next time. that Daniel and Jorge Explain the Universe is a production of IHeartRadio.

For more podcasts from IHeartRadio, visit the IHeartRadio app, Apple Podcasts, or wherever you listen to your favorite shows. To the ThinkPad X1 Carbon, ultra-light, ultra-powerful, and built for serious productivity with Intel Core Ultra-Processors, blazing speed, and AI-powered performance that keeps up with your business, not the other way around.

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December 29th, 1975, LaGuardia Airport. The holiday rush, parents hauling luggage, kids gripping their new Christmas toys. Then, everything changed. There's been a bombing at the TWA terminal, just a chaotic, chaotic scene. In its wake, a new kind of enemy emerged, terrorism. Listen to the new season of Law and Order, Criminal Justice. system on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. My boyfriend's professor is way too friendly, and now I'm seriously suspicious.

Wait a minute, Sam. Maybe her boyfriend's just looking for extra credit. Well, Dakota, luckily, it's back to school week on the OK Storytime podcast, so we'll find out soon. This person writes, my boyfriend's been hanging out with his young professor a lot. He doesn't think it's a problem, but I don't trust her. Now he's insisting we get to know each other, but I just want her gone. Hold up. Isn't that against school policy? That seems inappropriate. Maybe find out how it ends by listening to the OK Storytime podcast and the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. This is an IHeart podcast.