Image credit: NASA/JPL

Image credit: NASA/JPL

How much energy is needed to blow up the sun? How is this connected to the idea of binding energy? Where is all the energy in the universe? I discuss these questions and more in today’s Ask a Spaceman!

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Music by Jason Grady and Nick Bain. Thanks to WCBE Radio for hosting the recording session, Greg Mobius for producing, and Cathy Rinella for editing.

Hosted by Paul M. Sutter, astrophysicist at The Ohio State University, Chief Scientist at COSI Science Center, and the one and only Agent to the Stars (http://www.pmsutter.com).

 

EPISODE TRANSCRIPTION (AUTO-GENERATED)

Let's talk about energy. Of course, there's the common everyday sense of the word energy, and of course, there's the physics jargon definition of the word energy. And for once, lucky for us, the common everyday sense of the word is actually close to the physics jargon sense of the word. This it's almost never happens. It's always the opposite.

So I found that remarkable, and so I just wanted to get that out there is is when you use the word energy in everyday conversation, that's actually pretty close to the way a physicist uses the word energy to explain something about the world. Like like, why did you eat your cereal for breakfast? Because you needed the energy. Why did you need energy? Because you have work to do.

In the physics definition of the word energy is the ability to do work. Okay. Okay. So I guess we have to define that word. It's not like digging ditches or pushing paper.

I mean, yes, that that is work, but the way you would use the word work isn't the same way a physicist would use the word work. Work is force applied over a distance. That's it. If you want to apply a force over a distance, imagine pushing a box across the floor. That is work and that requires energy.

And that energy is transferred from you to the box as you push it across the floor. And energy comes in so many delicious flavors and if you haven't tried them all, you really should. There's the kinetic energy, the the energy of something moving. If by definition, if a thing is moving, it has kinetic energy. It can do work if it were to, I don't know, hit something.

There's also potential energy. This is based on an object's position in a force field like the gravitational field of the earth. Where you are in that gravitational field, are you close to it? Are you far away from it? That defines your potential energy.

This is energy that you can use if you so choose to do so. Like a ball sitting at the top of a hill can do some work if it were to fall off the hill. There's also thermal energy, AKA heat. This is just really an expression of kinetic energy, the the energy of motion, but it's the motion of all your little subatomic bits and pieces wiggling all over the place. They each have their own speed.

They're all moving around. They all have their own kinetic energy, and we just add that up all together in a macroscopic sense and call that thermal energy or heat. And it can do work on another object. If you if you're hot, you can do work on something else. You can transfer that energy.

Like, you can touch a cold thing, and the wiggling molecules in your hand will start wiggling the molecules in the cold thing and heat it up. That's doing work. Right? It counts. There's also radiant energy.

There's there's light. Light itself, radiation carries with it energy, and it has the ability to do work. There's also raw mass energy. This is the wonderful thing about special relativity. If if you are a massive thing, there is energy associated with that.

If we were to somehow reduce your mass, we could liberate some energy out of that. But that's that's a different discussion. And energy can be transmitted and stored and transformed, and one of my favorite things about physics is the ability to view our complex, messy world through some very simple lenses and still get amazing insight. Like like, it's just at first glance, the world seems impossible to comprehend, but we can write down some very, very simple laws, some relatively straightforward equations, some some very simple things, and we can make sense of this crazy world. In this case, we can view so many physical processes as just exchanges of energy.

Like, follow follow energy from the sun. The sun is emitting radiation. That's radiant energy blasting out of the sun. Some of it hits the earth. Plants store some of that energy in the form of chemical bonds.

Then we take those plants and grind them up and turn them into cereal. We eat the cereal. We store that energy in a different set of chemical bonds and then later on release that energy to think our thoughts and move our muscles and our muscles now have kinetic energy. That energy gets applied to the environment surrounding us. Some of that energy goes into moving things.

Some of it goes into heating up the atmosphere. Eventually, that hot mat atmosphere radiates that energy back into space. Look at that story. There's a lot of storing of energy. There's a lot of transfer of energy.

That's the wonderful thing about energy, which basically makes all of modern civilization possible is that you don't have to immediately use up all your energy. You can store it. You can put it somewhere else. You can transform it. I can put energy into the chemical bonds of a cereal and it will stay in the cereal for a very long time.

It may not taste very good after a couple years, but that's a different issue. I can put a book, I can take a book and put it up on a bookshelf, and now I've stored energy. It now has greater potential energy that I've stored by virtue of putting it higher up, and it can release that energy if it were to ever fall down. And energy can be stored, and energy can be liberated. My my digestive system, my guts, and the biologists and animists among you can fill in the details here for everyone else, break down chemical bonds in the cereal, then rearrange them into new bonds, and there's a difference in energy levels there that my body can extract to do all the wonderful things that my body likes to do.

I can walk over to my bookshelf and I can knock that book over, letting it fall to the ground, and I convert that juicy potential energy back into kinetic energy for a while, and then it hits the ground and the energy gets converted into sound and heat. You can contribute to Patreon and liberate all that stored science. Think of all the amazing science that's just waiting to happen, and you can liberate it at patreon.com/pmsutter. It's how all all of my education outreach happens. Thank you so much to all my contributors.

It's because energy can be stored and released, energy doesn't always have to be positive. And at first, it feels so wrong to say the phrase negative energy. If you're uncomfortable, if you're uncomfortable with that, you can just whisper it at first so you can do it right now. I won't tell anyone. Just just just see how it feels.

Negative energy. It feels a little weird, doesn't it, to say it out loud. Like that shouldn't be a thing. It shouldn't be a thing to have negative energy. But in fact, it's very common in physics.

It's just a matter of accounting. It's to make sure that all the numbers come out right in the end to make sure you know where you're getting energy from and when you're giving energy to something. You wanna keep that separate. You wanna keep all the accounting straightforward so you can keep track of how the energy flows in a system. And the reason I'm making a big deal about this is I'm gonna spend a good amount of time talking about a particular kind of energy called binding energy, and this energy is negative.

What is binding energy? Why is it negative? Why am I talking about this in a show entitled, how do we blow up the sun? We're gonna get there. Don't worry.

We're on a journey together. You may not see the end of the path, but don't worry. The end of the path is there. If we wanna talk about blowing up the sun, we have to talk about binding energy. And binding energy is negative, so we have to talk about why it's negative.

Let's look at something like the solar system, the whole solar system. Billions of years ago, it was just a giant nebula of gas and dust and it was all thin and all spread out and it was really big and brawly really beautiful. Then it that cloud of gas and dust collapsed and shrank and became the solar system in a process described in a different episode. That cloud of stuff had a lot of potential energy. It was separated from itself.

It was very large. It was gravitationally attracted to itself but hadn't quite hadn't started that process of collapsing in. So it started with so much potential energy. Just think of the potential like, oh, man. That nebula could be amazing someday if it would just apply itself.

It would just work a little bit harder. It has so much potential. But as it collapsed, that potential energy was liberated and it was transformed into other things. Some of the energy went into the kinetic energy of motion, creating planets that are in orbit around the star. The central star, our sun, has a lot of angular momentum.

That's all kinetic energy that came from that potential energy. Some of the energy went into heating up the components. So as the Earth collapsed, it got really, really, really hot, and it's still hot today. That heat that was transferred from imagine just imagine all that gas and dust collapsing in on itself, rubbing up against each other, the heat. Hot Earth, and that is glowing.

It's emitting radiation back into space. So some of the potential energy that our presolar nebula started out with all that potential energy. Some went into kinetic. Some went into heat, which is still trapped in the core of the earth and the other planets. Some escaped from the solar system altogether.

If some of that heat got transformed into radiation, that radiation blasted off into the interstellar void, it's gone. You're not getting it back. Just give it up, man. The solar system lost energy as it formed. Some energy that it did have is no longer available for us to do work.

The energy that was lost in forming the solar system is called binding energy And because it's gone, because it's removed, it must be negative. Here's an example. Here's an example. Let's say you let's go back to that quintessential ball on the top of a hill. It has a lot of potential energy.

You kick it, it rolls down the hill. It wiggles back and forth a little bit at the bottom of the hill, but then it stops. What happened to its potential energy? Some of it went into kinetic for a while, but the ball was rubbing up against the grass. It was heating up the grass from that friction that made the grass a little bit hotter, that made it emit a little bit more radiation into the atmosphere, and it's gone.

It's gone from the system. Now if I want to take that ball and put it back up to the top of the hill, I have to add energy. And if I have to add energy to get something back to where it started, then right now it has negative energy. Going back to the solar system, if I wanted to remove the earth from the solar system, let's just say, okay, you know what? Earth, let's pick a different planet.

Let's let's pick a planet nobody cares about, Mercury. Let's remove Mercury from the solar system. Gone. We're sick of it. If you want to remove Mercury from the solar system, you have to add energy to Mercury.

You have to attach big rockets to it or something else. It's an engineering problem. You just get rid of Mercury. You have to add energy to Mercury. You have to add positive kinetic energy, which means right now it must have negative energy associated with it.

It has binding energy associated with it is bound to the sun. It is Gravitationally glued to the sun that binding energy is negative and if I want to return to its original state, you know if I want to Remove mercury for away from the sun. I have to add positive connect energy. Make sure it all balances out. To return a system to the way it started, large and spread out, you have to add energy.

So by definition, to make everything balance out, the binding energy must be negative. I'm going on and on and on and on and on about this because, personally, I find it weird to have negative energy, and so I'm trying to convince myself it's okay. And by extension, I'm trying to convince you it's okay. I'll do another take. What the heck?

Let the the presolar nebula, the nebula that would eventually become our solar system, had a certain level of energy. Let's call it zero for the sake of convenience. It could be any number we want. Then it collapsed and became bound together, so now it's in a negative energy state. And if you add energy back to the system, it's back to normal, back to zero.

It's an accounting trick. The binding energy is negative just to make the numbers come out cleaner in the end. So let's talk about blowing up the sun. But I feel like blowing up the sun is gonna be really, really challenging, so let's do a slightly easier problem, and let's just blow up the earth. We're gonna destroy the Earth.

We'll get our master's degree there, then we'll go on to the doctoral program of blowing up entire stars. If we wanted to blow up the Earth, the Earth is bound together with the force of gravity just the same way that our solar system is bound together with the force of gravity. So there's negative binding energy associated with the Earth. And if we wanna rip it apart, we have to add energy to it. How much?

Well, imagine taking a handful of dirt. You reach down, you grab a rock, a bunch of dirt. To unbind that handful of dirt from the Earth, I have to send that dirt as far away as possible, so far away that would never even get a glimmer of a hope of a chance of returning back to earth. I have to give it escape velocity. I have to make it go so fast that it will forever escape the gravitational clutches of the earth.

It will never return. There is a speed associated with that. That is the escape velocity. I have to make that dirt go that fast, so I have to put it on a rocket, and I have to blast away. Then I do it for another handful and another handful and another handful by handful, rock by rock, boulder by boulder, I will unbind the earth.

It is a bound system, and I'm gonna undo it. And I have to do it one piece at a time, and I'll count up all the energy I'm spending to do it. But at first, it's really tough, but it tends to get easier. With every handful that I remove from the Earth, the Earth gets a little bit smaller. It's a little bit smaller, a little bit less massive, slightly weaker gravity, so the next handful isn't as hard to send off.

I don't need as much rocket fuel to get the job done. I don't have to fight as hard to unbind the next batch. You can actually come up with a very simple formula that encapsulates this whole process. Imagine imagine strip mining the Earth. Like we're gonna take the top one meter layer off the Earth.

You know, just shave off all the trees, the mountains. We'll we'll get a bunch of water, everything, and we're gonna pack that into rockets and we're gonna send it away. Then we're gonna do the next layer and the next layer and the next layer, getting easier as it goes all the way down to the core. Imagine writing down that process in the form of a mathematical equation. It'd be a pretty crude estimate because you say, okay, maybe the maybe it's gonna be each layer is gonna be three feet and and, you know, that that misses some nuances.

You know, it doesn't get the whole picture not quite accurate. So you say, okay. Maybe it's gonna be one foot, you know, a tenth of a meter, a hundredth of a meter, a centimeter, a millimeter thick. Imagine wanting to make this mathematical estimate more and more accurate. You take thinner and thinner strips at a time, which is more and more strips.

And if you get it so thin that the strips are infinitely thin, congratulations. You've just invented calculus, and you've come up with a single number. It's a very simple relationship between the mass of a planet or gravitationally bound structure, its radius, and the binding energy needed to deconstruct it. That is the binding energy. What do you need to apply to that object to totally blow to smithereens?

This does not take into account, say, molecular binding energy or nuclear binding energy. These are the molecular and atomic and nuclear bonds that hold tiny stuff together. We're not gonna try to rip apart every molecule we'll be content for taking whole molecules and sending them off into space individually, just trying to over overcome gravity, not any of the other forces. So this formula, this calculation doesn't apply if I wanted to say blow you up, only blowing up the planet. So it's nothing personal here.

And you can calculate it for the Earth. It's a relatively rough estimate. It's around 10 to the 32 joules. 10 to the 32 joules is how much energy you need to obliterate the Earth. So any budding mad scientist out there, if you feel like blowing up the Earth or threatening to blow up the Earth if you wanna be taken seriously, you better have 10 to the 32 joules in your back pocket.

If that means absolutely nothing to you, and it probably does, for comparison in 02/2013, all of humanity, all of us, consumed about 10 to the 20 joules of energy. So all of our electricity, all of our nuclear power plants, and coal power plants, and solar panel farms, and wind farms, just the whole deal. All the energy that humanity as a species generated and used was 10 to the 20 joules or one trillionth the amount needed to evaporate our planet. So if you were to rely purely on human made sources of energy, you would have to wait a trillion years. Yes.

The Earth would still be around by then, but our sun would be long gone. So I don't know exactly what the point of that would be, and that's not gonna be a very good threat. Here's another comparison, though. It's about one week of the sun's total energy output. The sun is really energetic.

One week. If you could collect all of the sun's energy output, all of it, 100% of it, 100% efficiently for one week, you would gather about 10 to the 32 joules. You can do whatever you want with it, including blowing up the Earth. Of course, if you're stuck out here on the Earth and you can actually, you know, capture all of the sun's output, then let's say you coated the entire Earth's surface in perfectly efficient solar panels. Because the Earth is relatively small and relatively far away from the sun, it hardly captures any of the solar output, so it would take you about eighteen million years to collect enough energy to blow up the Earth.

That is a lot of binding energy. That's just the Earth. With the sun, it's more massive. It's bigger. It's about a billion times more binding energy than the Earth.

So it's a billion times harder to blow up the sun than it is the Earth. If you could capture all of the sun's output for a billion weeks or twenty million years, you could collect enough energy to unbind the sun. And in an interesting twist here, all that solar energy, all that hot thermal radiation coming from the sun, it's from binding energy, but not gravitational binding energy. Binding energy itself is just a very generic term. It doesn't really care about whether you're dealing with nuclear forces or gravitational forces.

It's just if something is glued together somehow, it has a binding energy associated with it. And in the sun, the sun takes a bunch of hydrogen, shoves it together to make helium, and changes the binding energy, releasing a little bit in the form of radiation. Because the sun is constantly converting hydrogen into helium and the helium has less energy, has more negative binding energy than the individual hydrogen atoms that went into it, they have less mass, so you actually don't have to blow up the sun. The sun is losing mass with time. About 4,000,000 tons per second, it's losing mass from the nuclear furnace in its core.

So it's kinda eating itself alive from the inside out. And you know what? The Earth might be losing mass too. So maybe you don't have to work so hard. Don't worry about collecting all this energy so you can blow up the sun and the Earth.

They might be doing it to themselves. The Earth is a little bit harder to count. We're we're steadily gaining mass. There's a rain drizzle of micrometeorite dust that's just constantly sprinkling into space, but we are losing some stuff constantly. The upper reaches of our atmosphere, the very tippy tops, they're only loosely tied to the Earth.

You know, in a technical term, their binding energy is only slightly negative compared to the very negative binding energy that we have here on the surface. They're just they're just kinda, you know, acquaintances with the Earth. They're not besties like we are. So the upper reaches of our atmosphere are are just there. They're on the Earth.

They're attached to the Earth. They're gravitationally bound to the Earth, but not very much. And if you have any gas, like an atmosphere, at a certain temperature, that temperature represents all the wiggling and jiggling and zipping around of the particles in that gas, but not all the particles are gonna have the same speed. Some are gonna be a little bit slower, some are gonna be a little a little bit faster than average. Just at any temperature, there'll be some particles in the gas that just have a mind of their own, and some of them go fast enough that they randomly reach escape velocity.

Just whoop. One day decide they have enough kinetic energy, they can overwhelm the binding energy, and they're gone. It happens to the lightest elements, easiest, like hydrogen and helium. There's still some in our atmosphere left over from formation, but we're leaking somewhere around a hundred thousand tons per year. Sometimes, also, we humans literally take a handful of rocks, put it in a rock, and blast away.

That's but that's only, like, a hundred tons per year or so. The difficult thing is it's very hard to estimate just how much the Earth is gaining from the micrometeorites constantly raining down somewhere between 30,000 to a hundred thousand tons per year. If that's on the low end, if we're only getting around 30,000 tons of micrometeorites dust sprinkling in, then we're actually losing mass with time. And if it's more, then we're actually gaining. So it's it's a little bit tough to tell, but you might be able to just wait.

Although, we're not gonna lose everything. Right? It's hydrogen, helium. Yeah. It's gonna go.

It's gonna do its own thing, but oxygen and nitrogen and carbon, they're pretty heavy. They have a lot more work to do if they wanna overwhelm the binding energy of the Earth and escape. So even though right now the Earth is losing mass, it's not gonna lose mass for a very long time. There's an interesting side note here, and I totally skipped over because I wanted to I wanted to emphasize it right now. The conclusion of could we blow up a star?

Could we blow up our sun? Yes. It but it would take a really long time. Like, there is the energy available in the universe to be able to unbind stars. Yes.

That energy is available. Good luck trying to actually collect it and apply it. But where does that energy come from? What's the most the best source of energy nearby in the solar system? It's the sun itself.

And in fact, it's only twenty million years of the sun's energy output that you would have to collect to unbind it. Twenty million years, that sounds like a long time, but our sun total lifetime is like, what, nine billion years? That's more, way more than enough energy. The sun itself, through nuclear fusion, generates way more energy than needed to destroy itself. So why doesn't our sun or any star just blow up instantly?

Because at any one moment, our sun is not generating enough energy to blow itself up, but that can change. If the energy production rate gets too high, if the fusion rate gets too hot in the core, well, then it can overwhelm the binding energy and it can destroy itself. Or if for some reason the binding energy itself drops, if if the mass of the sun or the size of the sun changes, it can can lose some of its layers. And, in fact, in the last stages of its life, our Sun will inflate and become a red giant. It will be swell.

It'll become huge. It won't change its mass, but it'll become much, much wider. And because of that, it will be easier for the outermost layers to leave because their binding energy has dropped. You could strip mine the red giant sun. In fact, in this stage, our sun will lose almost all of its mass and form a planetary nebula, which is, hey, a big cloud of gas and dust, which is just how it started.

Why is it able to do that? Because it will self inflate. Its binding energy will drop where the interior core of that red giant star will definitely generate enough energy to blow itself up. In the biggest stars, the biggest stars do it even more dramatically. They convert themselves into proto neutron stars and neutron stars or even black holes in their cores at the very very ends of their lives.

They ramp up the energy production orders upon orders of magnitude, which is more than enough to unbind it, AKA an explosion. So we humans couldn't blow up a star, but stars are perfectly capable of blowing up themselves. Thank you at bat crew run five over on Twitter for asking the question for today's episode. Could we blow up a star? And of course, make sure you read and enjoy my book, pmsutter.com/book for links to how you can buy it.

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Started to keep all my education outreach activities alive, Especially, big thanks to Robert r, Dan m, Matthew k, Evan t, Justin g, Kevin o, Chrissy, Helga b, Barbara k, and Matt w. You're the best. All of you are the best, but some are more best than others. Go to askaspaceman.com. Leave a review on iTunes, and you can keep asking me questions.

That's askaspaceman@gmail.com. You can also follow me, Twitter, Facebook, and Instagram at paulmattsutter. And I will see you next time for more complete knowledge of time and space. Space.

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