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Saul and Mike tally up how much energy Earth actually has – solar, fossil, nuclear, wind, geothermal, tidal – and work out whether any of it is enough to get the Project Hail Mary ship to Tau Ceti.
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Saul: Hello, and welcome to Mag World, where we like to ask big questions, make wild guesstimates, and quantify literally everything on a magnitude scale. If you’re new here, you should know that on a magnitude scale, every mag 1 means times 10. To multiply mag numbers, you simply add them together. So 100 is mag 2, and 1,000 is mag 3, and multiplied together, that’s mag 5, which is 100,000. That’s all the math you need to know to understand what’s going on in Mag World. Just remember that every order of magnitude is a big deal, because as we say in Mag World, quantity has a quality all of its own. If you wanna learn more about Mag World, come visit our website at magworld.pw. I’m Saul Pwanson, your guide to Mag World, and I’m here with my friend Mike, who doesn’t always turn off the power when he’s doing electrical work.
Mike: I like stakes when I work.
Saul: Well, today’s e- episode is Mag Energy, where we’ll be talking about how much energy is available on Earth, and if it’s enough to travel to another star.
Mike: Bang, boom, straight to the moon.
Saul: Yeah. Well, we’re gonna be trying to go to another star this time, which is Tau Ceti.
Mike: I’ve heard of that place.
Saul: Yeah. So “Project Hail Mary” is both a book and a movie that’s come out recently.
Mike: Oh, question, Saul.
Saul: Yeah?
Mike: Uh, should we give a spoiler alert?
Saul: Oh, good call, Mike. Yes. Spoiler alert, if you haven’t seen the book or read the movie, then now is the time to back out of this and go either read or see it, if you care about spoilers, because we’ll be talking about some of the plot points in this, in this book.
Mike: And more importantly, the math-
Saul: And-
Mike: … which is the most exciting part.
Saul: It is a very exciting part. So The main conceit behind “Project Hail Mary” is that Andy Weir has come up with the perfect fuel. It is called astrophage, and it basically converts almost all of its mass into energy directly. And this is the fuel that’s used for a spaceship that has to get to another star in order to save our sun, basically, and hence Earth, right? And so they need 2 million kilograms of this fuel get to this, to, to Tau Ceti, which is 12 light years away. Because of the tyranny of the rocket equation, the more fuel that you have, the more fuel that you need because ma- fuel has mass.
Mike: … the more fuel you need to push the fuel that you needed to push you.
Saul: Right. And so in this particular thing, Hail Mary is the ship. The Hail Mary, just the, the, the ship itself is, I think, 100,000 kilograms, about 100 tons or so. It’s a very small ship, but it needs 2 million kilograms of this perfect fuel to get to another star in any kind of timely fashion.
Mike: So several times more mass of fuel.
Saul: 20 times more mass of fuel, yes. Yeah, an order of magnitude more fuel. And this is true of all the rockets. Every rocket on its– when it’s on the launching platform has more than 10 times the fuel just to go up for, for this exact reason.
Mike: Mm-hmm.
Saul: So we’ve got this astrophage that converts almost perfectly from mass into energy, and then that’s the, basically that’s the main conceit of the book. Given that now, how does everything fall out? And it’s a very interesting story. It’s got a lot of action and a, a friendship bond that can’t be surpassed, et cetera. But I wanna dig into the math today about this because he has done a lot of math, and this is, uh, in a genre called hard science fiction. And I wanna point out that it’s not just hard like hard as a rock, but also difficult. It is hard science fiction. It is difficult to get to another star with the fuel that we have here on Earth. And so we’re gonna be diving into that and talking about all the different energy sources we have here on Earth and which of them could possibly take us to another star.
Mike: Fascinating.
Saul: So first of all, I want to talk about astrophage and how much energy there literally is in there. So I have a quote from the book here. And he talks about having a gram of astrophage and how much energy there is in just one little gram, which is a very tiny amount, right?
Mike: Mm-hmm.
Saul: And so I wanna do the math live here. So the main equation, of course, is-
Mike: E equals MC squared.
Saul: E equals MC squared, the classic Einstein equation, the mass-energy equivalence. And so we’re gonna be converting from the mass, one gram, to energy and seeing how much energy there is in one gram. So-
Mike: At, I would say we should probably define our…
Saul: Our units.
Mike: Yes.
Saul: That’s a great idea, Mike. So the main units we have in Mag World, there’s two of them. There’s energy, which is in joules, and there is power, which is in watts. And a watt is basically a joule per second, or a joule is a watt for one second.
Mike: in the equation for energy-
Saul: Mm-hmm. Mm-hmm
Mike: … we also have MC squared.
Saul: Right. So mass is going to be in kilograms because kilogram is the base unit for SI units and Mag World, and E is the energy in joules, and then C
Mike: It’s, uh, the speed of light.
Saul: Speed of light, right. That is mag 8 and a half. Now, in outside of Mag World, we think of it as 300,000 kilometers per second or 300 million meters per second, and 300 million is around mag 8 and a half meters per second.
Mike: Mm-hmm.
Saul: And so if we’re gonna do this live here, E equals MC squared. Let’s do this. We’ve got one gram of astrophage, which is something they’ve, they’re using at some point here. How much energy is in that?
Mike: Well, we start with the gram, so the scientific… So the unit is a kilogram.
Saul: Mm-hmm.
Mike: So one gram is negative three.
Saul: Mag negative three for a gram.
Mike: … the energy equals mag negative three kilograms times the speed of light squared.
Saul: Right. So the speed of light is mag 8 and a half.
Mike: Mag 8 and a half squared. So that means mag 8 and a half times mag 8 and a half. Those get added together.
Saul: Right. So mag 17.
Mike: Mag 17 times mag negative three.
Saul: Mm-hmm.
Mike: Subtract three from 17, mag 14 joules.
Saul: Mag 14 joules, and in fact, the quote from the book is exactly that. That gram of astrophage has 100 trillion joules of energy. Mag 14 is thousand, million, billion, trillion. Mag 12 is trillion. Mag 14 is 100 trillion. So 100 trillion joules of energy in one gram of astrophage. And they have 2 million kilograms of this stuff on the spaceship.
Mike: Explosive.
Saul: So let’s calculate how much energy there is on that ship. How much energy they need to go to another star. So they have 2 million kilograms
Mike: Million is mag 6.
Saul: So if they’ve got mag 6 kilograms…
Saul: Times mag 17, basically the speed of light squared.
Mike: Is mag 23 joules.
Saul: Mag 23 joules.
Mike: Wow. That’s-
Saul: Actually, they’ve got double that, so it’s actually mag 23.3 joules, but we’re not gonna quibble about that. We’re just gonna try to find mag 23 joules.
Mike: So that’s one with 23 zeros after it.
Saul: Oh, gosh.
Mike: I don’t-
Saul: Are we gonna do that now?
Mike: Well, I don’t even know what-
Saul: Oh, what, what the-
Mike: … how to say that.
Saul: Yeah, no, I, it’s true. I think some people start doing, like, a trillion… It’s not even quite a trillion trillion, is it? It’s like a billion trillion joules, ’cause you got mag 9 times mag 12 is 21. 100 billion trillion joules. I’m, like, I’m already lost, right? I just wanna think of it as mag 23 joules is what they’ve got aboard this ship.
Saul: By the way, I wanna say that I really appreciate that Andy Weir used kilograms in this. He could’ve said 2,000 tons, like most people would’ve expected, but he said 2 million kilograms, and that is exactly right. You wanna be talking about kilograms.
Mike: Well, if I recall the book, uh, the main character actually does math on some of these calculations.
Saul: Oh, yeah.
Saul: Okay. So, so the thing is, mag 23 joules is a lot of energy, and I wanna talk about how much energy that actually is. So if we look at how much energy there is available to us on Earth, so the standard metric that I, I found in, uh, a lot of different research here is they talk about terawatt hours per year of energy production and consumption. So 180,000 terawatt hours per year. And we’re just gonna do this math once and for all just to get it out of there. We’re never gonna use terawatt hours again, terawatt hours per year again, at least not in this episode. So 180,000 terawatt hours. So let’s, let’s go through this. So a terawatt is mag 12.
Mike: Mm-hmm.
Mike: So terawatt hours, the SI unit for time is seconds, so we’re going to have to convert from hours to seconds, right?
Saul: Yes, exactly, right. And then we’re gonna have to convert from years back down to seconds also.
Saul: So let’s do 180,000 terawatt hours per year. So 180,000 is mag 5-
Mike: Mm-hmm
Saul: … and some. A terawatt is mag 12, so that’s mag 17 right there. And then an hour is mag 3 and a half, so mag 20 and a half per year joules. And that’s ac- it’s actually mag 20.8 ’cause it’s almost 200,000 joules. So it’s mag 20.8 joules per year.
Mike: Okay.
Saul: So if you think about this, mag 23 compared to mag almost 21, if we’re gonna give ourselves some headroom here, that’s 100 times.
Mike: That’s two orders of magnitude more energy on a single ship than produced by the entire world in a year.
Saul: Yes.
Mike: Two full orders of magnitude just contained.
Saul: Yep. And the question is, so they were, they’re, they do all this great science to figure out how to build a rocket or build a ship that can go to another star and sustain the, every people and everything, and they’ve had this perfect fuel, and we still have to figure out how to power that fuel. The fuel doesn’t come from anywhere. It’s actually more of a battery. So we have to get the energy into the fuel. Where are we going to get mag 23 joules to put into that fuel?
Mike: That’s a good question. In the book, they get it from the sun.
Saul: It’s true.
Saul: I wanna explore all of the other options and see if anything else could do the same.
Mike: So if everyone just put their phone charger into-
Saul: Exactly
Mike: … the right place?
Saul: Right.
Mike: Yeah.
Saul: Maybe, and actually, so here we’ve got 10 cards labeled out here. Um, we’ve got fossil fuels and biomass and geothermal and explosives So we’re gonna dive into each of these to talk about how much energy there is on the Earth available in these forms.
Mike: Great. That’s a lot of different forms of power.
Mike: Mm-hmm. Well, do we want to start with solar?
Saul: That’s great. Let’s start with solar. So the Earth receives mag 17 watts all told from the sun.
Mike: Mm-hmm.
Saul: And that’s year-round, like it’s j- it’s, it’s somewhere on the Earth, this mag 17 watts impinging on it. if we compare that to how much energy civilization uses, we’ve already said that civilization uses mag 20.8 joules a year. How many watts of power is that, basically? So a year has mag 7 and a half seconds in it.
Mike: Mm-hmm.
Saul: So if we subtract seven and a half from 20.8, what is that?
Mike: That’s 13.
Saul: Mag 13.
Mike: Point three.
Saul: 13.3, something like that. Yep. We are a 10 terawatt civilization, mag 13. We hit that in the ’70s, and we hit, the 1970s, and we hit a mag 12 wattage in like the 1890s. And before that, it’s, we kind of don’t know exactly how much energy we were using, but it was a lot less than this.
Mike: Mm-hmm.
Saul: This is the Industrial Revolution got us to mag 13 watts. And so compared to the amount of sunlight that comes to the Earth, there’s mag 17 sunlight, and mag 13 is what we’re using.
Mike: So that’s mag 4 difference.
Saul: Mag 4 difference. That is 10,000 times more sunlight than we use coming on Earth.
Mike: Well, that makes solar power sound like a wonderful thing.
Saul: Yeah. There’s only one challenge, which is that it doesn’t come all at one point. It comes down at around 300 watts per square meter. So if you wanna capture that, you’ve gotta cover more and more and more of the Earth to do so. So what they did in “Project Hail Mary,” and this is not, as far as I can tell, in the movie, this is only in the book that they talk about how they did this. They try to do that. They have to do that. This is how they, they collect the energy with solar power. If we have 300 watts per square meter, how many square meters are we gonna need in order to get this mag 23 joules?
Mike: And I feel like there was a timeline that they gave.
Saul: Yeah. So they basically have only a couple of years to send, to build this up, build the ship, go to the other star, and then come back. And then they have a, like a year, I guess, to implement the solution here on Earth. So yeah, they’ve only got a couple of years. So let’s say that it is, um, I don’t know, some three years. Three years is a nice round number in mag world, right?
Mike: Mm-hmm.
Saul: Because if we’re gonna say there’s mag 7 and a half seconds per year, then three years is around mag 8 seconds.
Mike: Mm-hmm.
Saul: And so if we have 300 watts per square meter, that’s mag 2 and a half watts. Actually, in the book, he actually says there’s 1,000 watts per square meter if you go to like a really, uh, sunny place, and he’s right, except for that doesn’t go all day long. It, on average, it’s still only 300 watts per square meter. But we’ll just go with his number ’cause it’s a nice round number. So mag 3 watts per square meter times the mag 8 time that we’re gonna have, we can get mag 11 joules per square meter per, for this, uh, three-year timeframe we’re talking about.
Mike: So we have mag 11 joules per square meter.
Saul: Yep.
Mike: And we need to get how many joules?
Saul: Mag 23.
Mike: So mag 23-
Saul: Mm-hmm
Mike: … divided by mag 11.
Saul: Uh-huh.
Mike: So 23 minus 11 is 12.
Saul: Mag 12.
Mike: So mag 12 square meters.
Saul: Yep. How many is mag 12?
Mike: That’s a trillion.
Saul: A trillion square meters.
Mike: Wow.
Saul: Yeah. he even calls out in the book that the… Well, first of all, the entirety of all Earth area is mag 14 square meters.
Mike: Mm.
Saul: So it’s 100th of the entire Earth, and that includes all the water too.
Mike: Yeah.
Saul: So we have to get-
Mike: So 1% of the surface of the Earth.
Saul: Yep. So what they wind up doing is looking at the Sahara Desert, because the Sahara has, as they say in the book, 10 million square kilometers. And as we know, a square kilometer is a million square meters.
Mike: Mm-hmm.
Saul: So a mill- 10 million, million square meters is mag 13 square meters, and we need mag 12. So there’s actually 10 times the amount of space in the Sahara if we can cover it with a trillion of whatever these things are that make the stuff. we’re allowing that you can just do this. You can just make things to the trillions.
Saul: As I was doing this research, I was like, “What have humans made a trillion of that are about the size of a square meter?”
Mike: A trillion of?
Saul: A trillion. We’ve made a trillion screws.
Mike: There’s, there’s not even 10 billion people.
Saul: Right. Right.
Mike: And, uh, to have a trillion of something means each– for each person there’s-
Saul: 100-
Mike: Yeah
Saul: … of this thing. Yeah. That’s ev- that’s been made. And so if you look at over all of history, what have we made a trillion of? So what do you think, Mike? What have we made a trillion of?
Saul: Mm-hmm
Mike: … I can’t even imagine what we would have a trillion of.
Saul: That are about a meter in s-
Mike: Yes.
Saul: Yeah. So it turns out there’s only two things that I could find that we’ve made that much of around that size.
Mike: Mm-hmm.
Saul: And they are cloth and cardboard. Yep.
Mike: Of course.
Saul: I mean-
Mike: Yeah
Saul: … I’ve seen a trillion pieces of cardboard come through my garage when I’m getting packages, right?
Mike: Uh-huh.
Saul: And cloth, we all have bought. We do kind of buy at least a dozen articles of clothing over our life, if not, you know, every couple years, right?
Mike: Yeah. Mm-hmm. Okay.
Saul: And so-
Mike: I guess, so what you’re saying is that… So is it, is that per year or is that over humanity’s-
Saul: That’s o-
Mike: … span?
Saul: We make 100 billion square meters of textiles a, of cloth a year. A year.
Mike: A year?
Saul: And so that’s 10 years’ worth of total textile production to do just that in terms of cloth.
Mike: I presume that solar collectors for astrophage energy are slightly more complicated than-
Saul: He makes the point that they’re made out of foil, ceramic, and something else that are very common on Earth, and he’s looking at the raw materials, but not necessarily for the production, the manufacturing capacity, which I– as far as my numbers look, uh, it’s at least an order of magnitude too small, and that’s if we’re using cloth.
Mike: Mm-hmm.
Saul: Wow. So I am gonna say that in the book, they use, uh, sunlight, and this is how they use sunlight. They do cover some huge portion of the Sahara Desert and do it that way. I’m gonna say I don’t think this is actually workable on the timeframe that we have here, because it, we have to build up our manufacturing capacity for whatever, and that will take more than a year-
Mike: Mm-hmm
Saul: … just by itself. And then you have to do the actual manufacturing.
Mike: To build the glass and the foil and all the things to make the trillion square meters of-
Saul: Yep
Mike: … collector.
Saul: Yep. A trillion is a really large number. Mag 12.
Mike: Yeah.
Saul: So that’s how black panels work, or work in the book anyway.
Mike: Black panels being the Hail Mary collectors.
Saul: Yes, exactly. That’s what they’re called in the book.
Mike: So even given this perfect energy source, charging it up-
Saul: With the best source we’ve got, the sun.
Mike: Mm-hmm.
Saul: Mm-hmm.
Mike: Is still a stretch.
Saul: Yeah. And I, I’d say by an order of magnitude.
Mike: Mm-hmm.
Saul: So before we move on from solar though, I wanna talk about the Kardashev scale. So this Russian fellow, astrophysicist, Um, he came up with a system for categorizing civilizations, but on a, on a, on a sci-fi level, basically, right? There are three, he says Type I, Type II, and Type III civilizations. So Type I is a civilization that can harness all of the energy available to a single planet, and Type II can harness all of the energy available to a sun, and Type III can harness all the energy in an entire galaxy.
Mike: Hmm.
Saul: And so that’s tho- that’s a huge spread, right?
Mike: So harvest all the energy available, one, a planet, two, a sun, and three, a galaxy.
Saul: Yep.
Mike: This is some deep nerd stuff, Kardashev.
Saul: Yeah.
Mike: Because I don’t even think we’re at one yet, let alone know of any civilization beyond that.
Saul: Absolutely. This is aspirational. and so Carl Sagan formalized this. Carl Sagan’s like, “Okay, it turns out that it’s around mag 16 watts for Type I, mag 26 watts for Type II, and mag 36 watts for Type III.” So it’s very clean, mag 16, mag 26, mag 36 for planet, sun, galaxy.
Mike: Mm-hmm.
Mike: So the space vessel in “Project Hail Mary” uses mag 23 watts.
Saul: Hmm. No, no, it uses mag 23 joules.
Mike: Mag 23 joules.
Saul: Mm-hmm.
Mike: Okay.
Saul: But it’s taking us on the order of mag 16 watts, or mag 15 watts anyway, to charge up that battery.
Mike: Mm-hmm.
Saul: we’re using almost all of the energy available to a planet-
Mike: Mm-hmm
Saul: … to power this single ship.
Mike: So in order to have a single ship to get to o- one of the closest stars, you’re needing to bump up your civilization to type one.
Saul: Yes, exactly.
Mike: Almost definitionally.
Saul: Yeah. And that’s with the miracle of the perfect fuel.
Mike: Yes.
Saul: Yeah. So that’s where we’re at. We’re trying to become a type one civilization here. What does, what does type one look like if we have the whole array of fuels available to us or of energy sources available to us? Okay, so we’ve done solar.
Mike: Well, we’re talking about this fictional perfect power source in Hail Mary, right?
Saul: Mm-hmm.
Mike: The closest I feel like we come in real life is nuclear power in getting the most power per gram, right?
Saul: Okay. Yeah.
Mike: So why don’t we look at that?
Saul: So let’s move on to nuclear power. Good choice. So we’ve basically got two different kinds of nuclear power. We’ve got fusion and fission, but we basically don’t have the ability to do fusion here on Earth yet. We can do it in the very, very, very small, but it’s not even worthwhile. So we can talk about fission power. Fission power is still quite good, right?
Saul: If we were to do all the fuel once through, which is basically dig it out of the ground, get it all together, whip it up so it’s in the right general form, and then use that, it’s mag 21.4 joules in that uranium.
Mike: Mm. Mm-hmm.
Saul: And that’s if we just do the simple thing that we’ve already currently doing. If we want to expand, and people have been talking about this for decades, using breeders to make better fuel and trying to get more and more of the fuel out of it, it’s mag 23.2, and that’s all of the uranium that we have, used as well as we can use it.
Mike: So mag 23-
Saul: .2
Mike: … .2.
Saul: Yep.
Mike: Is using all the fissionable material.
Saul: All the uranium.
Mike: All the uranium that we have on Earth.
Saul: Turns out we’ve got three times as much thorium, which we’ve never used in any kind of plant. There was kind of a fork in the road some 50 years ago where we could have done one or the other. We chose to use uranium ’cause we were already using uranium for bombs, and so we went that route. But we could go use the thorium route, and then we would have mag 23.7 fuel available, joules available. But that’s it.
Mike: That’s it.
Saul: That’s mag 23.7 energy in all of our nuclear stocks, and we’re looking for mag 23, mag 23.3 joules.
Mike: So it would be possible to fuel the Hail Mary once using all our nuclear material.
Saul: So because it’s mag world, 23.7 is a little bit more than twice mag 23.3, so we can do two ships.
Mike: Oh, that’s great.
Saul: All of the nuclear material, fissile nuclear material we have.
Mike: I actually think that might be a good decision for the world.
Saul: Although th- this is within a human lifetime.
Mike: Mm-hmm.
Saul: You don’t have to spend that much energy if you’re willing to go really slow.
Mike: Well, what human has the patience for that?
Saul: And it’s true. What civilization even have, has the patience for that, right?
Mike: But if we use it all for star travel, there’s none left for the weapons.
Saul: Well, do you wanna talk about weapons next?
Mike: Absolutely, I do.
Saul: Because that’s one of the cards So the deal with explosives is that they are power dense, not energy dense. They have, a 10th of the energy of an equivalent energy dense thing. And so if you get a, uh, um, nuclear weapon that’s got so much uranium, yeah, you’re gonna get about a 10th, and actually sometimes even a 100th of the energy out of it. But-
Mike: That you would in a power plant, say?
Saul: Ex- uh, exactly, yes.
Mike: But you’re getting it so much quicker.
Saul: Getting it all at once, exactly. It’s explosive, right?
Mike: Mm-hmm. Well, it, poison’s in the dose.
Saul: Uh-huh. Yep, and the rate. Exactly.
Mike: Yeah.
Saul: How much conventional explosive has ever been made?
Saul: All conventional explosives ever manufactured is mag 18.
Mike: So then my guess for all nuclear explosives-
Saul: Mm-hmm
Mike: … is mag 18.
Saul: All nukes ever detonated is the same amount as all conv- conventional explosives ever manufactured. All nuclear explosives ever detonated.
Mike: Detonated.
Saul: Mm-hmm.
Mike: Oh. So two in anger and a whole bunch in test.
Saul: Yep.
Mike: That means, oh my gosh, the ratio of test to actual holdings is-
Saul: Mm-hmm
Mike: … what? You test 1% of your stocks?
Saul: Mm-hmm.
Mike: Oh, no. So it’s mag 20?
Saul: Mag 20 in– was our peak Cold War ar- ars- arsenal.
Mike: Mm-hmm.
Saul: That was in the ’60s. Yeah. So mag 20 joules, that’s a huge amount. That is almost the entire… No, it’s actually, it’s a tenth of all current energy usage in bombs alone, nuclear bombs alone.
Mike: Wow. And that won’t even get you a percent of the way to, uh, Episilon Eridani [sic]
Saul: Not on the timeframe we’re looking at, no. No. Now, the nice thing about nuclear bombs are, well, the nice thing that we know now is our peak was mag 20 in the 1960s, but we are actually about 1% of that now. We have taken our stocks down that much in terms of, uh, the actual energy contained in those bombs.
Mike: Mm-hmm.
Saul: We have the number– The actual number has fallen from 20,000, well, 20 to 50,000 depending on if you’re calling the whole Earth, whole Earth or just the US, um, down to about 5,000. So the number has been reduced to a quarter, but the total energy in them has been reduced by a hu- two orders of magnitude because we don’t have– There was the largest bomb ever
Mike: Tsar Bomba
Saul: Tsar Bomba, yeah. 50 megatons of energy, and that was exploded in the ’60s, but… And so for a while in the ’60s, we had d- many of those things laying around. We basically decommissioned those, and now we have very small nuclear weapons, and we have more of them.
Mike: Relative sense.
Saul: So yeah, exactly, in a relative sense. There’s still like a kilo- a kiloton, 1,000 tons of TNT in a single bomb.
Saul: So yeah, the peak Cold War arsenal was mag 20 joules of energy, and now there are fewer bombs, but a lot fewer of the actual amount of energy in those bombs.
Mike: Mm-hmm.
Saul: So for reference, uh, yeah, Tsar Bomba was mag 17 joules, and, uh, Hiroshima was mag 14. About 1,000 times more energy in Tsar Bomba as opposed to the first bomb that we set off. Uh, a ton of TNT is about mag 10 joules, mag 9.6, and a barrel of oil is actually mag 9.8. There’s actually less energy in a ton of TNT than there is in a single barrel of oil.
Mike: Wild.
Saul: The last thing I wanted to talk about with regard to, um, explosives and nuclear explosives, there was a Project Orion back in the ’60s. Have you heard of this?
Mike: No.
Saul: So this was a project to explore whether nuclear weapons could be used to propel a spacecraft.
Mike: Oh, no.
Saul: If you just take those bombs and, uh, explode them behind a spacecraft, you can get it going pretty fast. And that was Project Orion. They, they thought it would take, um, 300,000 nukes, 300,000 nukes-
Mike: Oh, my
Saul: … to get to Alpha Centauri in 133 years.
Mike: Wow, that’s not fast.
Saul: Not fast. It took 300– the 10 times as many nukes as we had at our peak to do this.
Mike: And how much lead were they, uh, pushing just to protect the occupants?
Saul: So actually, the real problem is that the, i- if you do… A nuclear blast is a lot of power all at once.
Mike: Uh-huh.
Saul: And that’d be about 100 Gs that it would push the ship. That’s not gonna work, so what you have to do is you have to put a little dampening spring or something in, in the back of the ship so that the nuclear blast does that, pushes that into the ship, and then the ship can go only go two Gs or whatever. And so you can kinda see this bomb going off, and then the spring compressing, and then the other thing kind of going in front of it, and that was the plan. I mean, you know, it was not a real, it wasn’t a serious plan, but that was what they were exploring.
Mike: Mm-hmm.
Saul: Yeah. That was Project Orion.
Saul: what other mechanism do you wanna look at here? What other energy source?
Mike: Well, you just compared one ton of TNT to one barrel-
Saul: Uh-huh
Mike: … of oil.
Saul: Uh-huh.
Mike: There’s a bunch of oil.
Saul: We-
Mike: So why don’t we look at that?
Saul: Let’s look at fossil fuels. Absolutely. Okay.
Saul: So the, uh, amount of coal that we use per year is mag 20.3.
Mike: Mm-hmm.
Saul: That’s also the same amount of oil that we use per year.
Mike: Mm-hmm.
Saul: Mag 20.3. And the amount of natural gas we use is mag 20.2. Basically, they’re all the same order of magnitude.
Mike: Wow.
Saul: And so if you’ve got three things of the same order of magnitude, that’s gonna add a half magnitude, right?
Mike: Mm-hmm.
Saul: ’Cause times three. And so we actually use about mag 20.7 joules per year in terms of fossil fuels.
Mike: So nearly all of the energy used by humans.
Saul: Bingo, is fossil fuels right now. Yeah. And of course, that last .1, that’s actually a, quite a large amount still.
Mike: Mm-hmm.
Saul: But yes, the lion’s share of energy is done by fossil fuels. So if we talk about the reserves, the amount… So this is what we, what we currently use. That’s every year, right?
Mike: Mm-hmm.
Saul: If we talk about the reserves, the amount that’s left in the ground that we know we can access, we’re like, “Well, we’re ready to pull this out if we need to,” is mag 22.6 joules in total across all three sources. It’s mag 22.4 joules of coal, mag 22 joules of oil, and mag– basically mag 22 joules of natural gas.
Mike: So less than mag 23.
Saul: Less than mag 23.
Mike: So even if we tore up the entire Earth, you-
Saul: No, no. This is all-
Mike: Oh.
Saul: This is recoverable. This is the stuff-
Mike: Recoverable.
Saul: This is the reserves. This is stuff we know we have access to and can get.
Mike: Oh, got it.
Saul: If you wanna look at all of this, we have mag 23.5. So yes, if we were to tear up the entire Earth and get to all the coal and everything, then we could get mag 23 and some.
Mike: We could get to Tau Ceti twice.
Saul: We can almost get it twice. Not quite. I mean, you guys, we were pulling at multiple things, but yeah, we can’t even do it twice.
Saul: There is a thing though here that I wanna talk about with regard to fossil fuels. So have you– do you know about the EROI, the energy return on investment?
Mike: Tell me.
Saul: So when we talk about reserves, we’re talking about the, uh, things that are economically gettable. It’s like it’s worth it to get those-
Mike: Mm-hmm
Saul: … that kind of coal-
Mike: Yeah
Saul: … that kind of oil.
Mike: If oil is selling for $100 a barrel, you want to extract it for less than that.
Saul: Yes. And if it costs $1,000 per barrel, well, you can– there’s, there’s more things you’ll be willing to do because you can make more money off of it, right?
Mike: Mm-hmm.
Saul: But there’s a thing called the energy return on investment, which is even more important and insidious. it takes energy to get the oil out of the ground. Like time was, 100 years ago, you kind of stuck a, uh, a shovel in the ground and maybe some oil would bubble up, and that was a certain thing, right?
Mike: Mm-hmm.
Saul: It was almost like negative energy to get it, but that’s not the case these days. All that easy stuff is already gone. So it takes energy to get the oil out, for instance, right?
Mike: Mm-hmm.
Saul: Or to dig up the coal. And there is a, it’s a ratio. Basically, it takes so much of a fraction of a barrel of oil to get a barrel of oil out. When that fraction is over one, it doesn’t matter how much energy you put into it, you’re not making anything off of this transaction. If it’s 0.99, you can still get a little bit of energy from this, and you’re using a sh- a ton of energy to get a single barrel of oil, but you can do it and it’s still worthwhile. But-
Mike: Mm
Saul: … over that, it’s not. And some of the coal that we have buried that’s part of the all metric here is in that category where it, it is not feasible for us to get it out with the, at least with the techniques we have today.
Mike: Because the energy it takes to tear apart that mountain is going to be more energy than the coal inside of it.
Saul: Yep. Yep.
Mike: Mm-hmm.
Saul: So that’s a little insidious. So even though we’ve got these max numbers, doesn’t mean we can use that in any capacity ever, no matter how much the price of oil or the price of coal is.
Mike: Mm-hmm. I think I’ve heard of energy ROI when it comes to biofuels,
Mike: But how much biomass fuel is there?
Saul: Well, that’s the next one. Let’s, uh, first of all, I wanted to say that the all fossil fuels ever burned are mag 22.4 joules.
Mike: Ever.
Saul: Ever. All human energy ever used is mag 22.6, and that includes biomass.
Mike: Mm-hmm.
Saul: So basically almost everything that we’ve ever used in energy has come from fossil fuels.
Saul: You wanna talk about biomass next.
Saul: How much biomass, if we were to just take it and burn it, how much joules are there in all of the biomass?
Mike: The everything?
Saul: Everything. Well-
Mike: You-
Saul: You wanna, you wanna start with everything, or you wanna start, you wanna start with trees?
Mike: Uh, trees are what I usually think of burning.
Saul: Okay. Let’s start with trees.
Mike: In this context.
Saul: Of course. Yes.
Mike: Uh, I’m gonna put all trees at 10 times the coal consumption.
Saul: Oh, so that’s mag 21.
Mike: Mag 21.
Saul: Times 10?
Mike: Mm-hmm.
Saul: You’re correct.
Mike: So mag 22.
Saul: It’s mag 22 joules in terms of trees.
Mike: Yeah.
Saul: And that is almost the entirety of the biosphere. Almost all of the energy available is in trees.
Mike: So even if we scraped and dried out everything else-
Saul: You can get twice as much.
Mike: Oh.
Saul: That’s it.
Mike: Wow.
Saul: Yeah. I was surprised to find out myself, too. Yeah. Basically it’s trees, and then all plants are mag 22.2, and then everything is mag 22.3.
Mike: Wow.
Saul: So yeah, it’s basically half of all of the biomass available to burn is trees. So turns out that just burning everything is not that much worth it, more worth it. But even burning all trees, you’re not gonna get very close-
Mike: No
Saul: … to getting to Tau Ceti.
Mike: So I mean, even though I advocate for less fossil fuel consumption, I’d, I’d rather do that than burn all the trees.
Saul: Right. Yeah, I think that’d be a little better. Okay, so that was biomass. What do you wanna try next?
Mike: Let’s go, let’s look at the Earth. I, all the rest of the things here are some sort of Earth power, so-
Saul: Natural phenomena
Mike: … natural phenomena-
Saul: Yeah
Mike: … like wind.
Saul: Yeah. Try wind. our current installed wind base windmill is about mag 19 joules per year, which is a lot higher than I thought actually.
Mike: Really? That’s only 1% of total energy generation.
Saul: Well, when you put it that way, now it doesn’t sound like that much. Yeah, but mag 19’s a big number. I was surprised it was that much.
Mike: Mm-hmm.
Saul: That’s about a mag 11 and a half watts.
Mike: Because?
Saul: Because there are mag 7.5 seconds in a year.
Mike: Right.
Saul: So mag 19-
Mike: Minus seven and a half-
Saul: Yeah
Mike: … equals 11 and a half.
Saul: So mag 11 and a half watts are what we’re using of wind, and there are about mag 14 watts that are recoverable for wind. About mag 14.4 watts total that you, is, is in the wind, and if we really pushed ourselves, we could get mag 14 watts. And so that’s, uh, on the order of, again, if we’re gonna add mag 7 and a half to that or-
Mike: Mm-hmm
Saul: … multiply by mag 7 and a half, that’s mag 21 and a half. That’s still 30 times less than what we need for this mission. 50 times less even.
Mike: So even if you covered the Earth in wind turbines-
Saul: Yep
Mike: … much less efficient than covering it with solar.
Saul: Yep.
Mike: Hmm.
Saul: Yep. And it might disrupt weather patterns, sucking all that energy out of the wind system.
Mike: True.
Mike: Uh, well, let’s look at geothermal.
Saul: Geothermal. This is one of my favorite ones here.
Mike: Oh, tell me.
Saul: I learned a lot from this. So where does geothermal energy come from?
Mike: Uh, it-
Saul: Do you know?
Mike: Ultimately?
Saul: Yeah.
Mike: Well, the heat in the mantle of the Earth.
Saul: In, in the core. There is still a molten ball of iron-
Mike: Mm
Saul: … from when the Earth was formed, but still quite hot. It’s got mag 31 joules hanging out in there.
Mike: So wait, you’re saying that we could be a spacefaring society if we could just find a way to cool the core?
Saul: Uh, if we could find a way to tap into that, yeah. We gotta go down thousands of kilometers. That’s tricky. And in fact, all of the geothermal measurements are about what can we get in the top five kilometers, which is already still pretty deep. Right?
Mike: Mm-hmm.
Saul: And so it’s about how much, uh, available to us, and it turns out that it’s mag 26.2 joules are available in the mantle, like you were saying. So what happens is the molten core has this energy, and it radiates out, just heat radiates out from it, right?
Mike: Mm-hmm.
Saul: And it heats up the mantle. So the mantle is actually, and the, and the crust is actually warmed by this.
Mike: Mm-hmm.
Saul: And it’s warmed at a certain rate, and there is mag 26 joules in that whole thing that’s available to us. And, but it’s actually kind of a battery itself. Like, we can tap into that, but then it cools down, and it gets replenished at about a rate of mag 13.6 watts
Mike: If you could somehow extract the heat from the entire crust of the Earth.
Saul: Right. That’s the challenge. It only happens in certain areas, and you still need to be able to convert heat into power somehow.
Mike: Mm-hmm.
Saul: Into electricity or energy.
Mike: So in a realistic sense, it’s much less than that, I expect.
Saul: So we use about mag 18 joules per year.
Mike: Mm-hmm.
Saul: Which is actually more than I thought, too. Like, that’s actually 0.1% of our total energy consumption.
Mike: Mm-hmm.
Saul: But yeah, it’s actually, you know, mag 18 joules a year. It’s, we’re currently doing that.
Saul: So if I was to play hard sci-fi author here-
Mike: Uh-huh
Saul: … what I would wanna do is say, “Well, the sun is going away.” Oh, that sucks. What if we tapped into geothermal? There’s this huge battery there. All we gotta do is live underground and tap into the radiating heat out, and we’ve got enough energy for ourselves. It’s, it’s no problem. So- I mean, look, look at this. The replenishment rate is mag 13.6. It’s actually double what we’re currently using. We kind of have an industrial civilization if we could tap into all that energy,
Mike: if you could live underground and not worry about plate tectonics.
Saul: Mm-hmm.
Mike: Speaking of which.
Saul: Speaking of which.
Mike: We get power from earthquakes.
Saul: Could we get power from earthquakes?
Saul: So all of the earthquakes ever are around 19.3 joules. Almost all of the energy released in earthquakes in recorded history comes from one single earthquake in 1960-
Mike: Really?
Saul: … in Chile. Yeah. It was a magnitude nine and a half earthquake, which released mag 19.1 joules of energy, and that is the largest earthquake that we’ve ever had. It was a really big deal. And yeah, that accounts for most of the earthquake energy. Now, how do we capture that and send it into a spaceship? I don’t know. That’s the major challenge.
Saul: But still, mag 19 ever, we’re no, we’re, we’re nowhere close.
Mike: Yeah.
Saul: Like, it’s not gonna get us anywhere. Okay.
Mike: Well, we have one potential source of energy left.
Saul: Yep, and that is tides.
Mike: Tides.
Saul: So Mike, when we talked earlier, you thought that the energy in tides would be pretty significant.
Mike: Yeah. This was originally, you had nine things-
Saul: Mm-hmm
Mike: … that we were going to talk about, and I said, “What about tides?” It’s-
Saul: Mm-hmm
Mike: … a daily movement of the entire ocean-
Saul: Mm-hmm
Mike: … up and down twice a day.
Saul: Mm-hmm.
Mike: That seems like a lot of energy.
Saul: Yep.
Mike: What did you find?
Saul: So we– Let, let’s talk about what we’re using first. We’re using about 500 megawatts of tidal energy currently. It’s, uh, mag 8.7 watts.
Mike: Mm-hmm. Very small.
Saul: And that is actually only in two, they call them barrages. They, we have dammed up an estuary, and we basically, you know, the water comes in, goes out. We, we are, can use that.
Mike: Mm-hmm.
Saul: And there’s only two of them. Uh, well, there’s actually several of them, but there’s, there’s two that account for almost all of this power.
Mike: Mm-hmm.
Saul: They are in South Korea, Sihwa Lake, and France, La Rance. Uh, 250 megawatts a piece. Everything else is a pittance.
Mike: Hmm.
Saul: And so that’s the one thing. So mag 8.7 is what we’re using. And then there are something, it’s, uh, underwater turbines that we could be using, so it’s actually capturing the moment, movement in the water, not damming up an estuary.
Mike: Mm-hmm.
Saul: And there’s a pilot project in Scotland that produces six megawatts for that. This is the pilot. But we think we could get 10, maybe 100 times more from that, uh, in the, in the short term. The total theoretical tidal amount is, that, that we think we could possibly get to, is 14,000 terawatt-hours per year. That’s the number I came out to. It is mag 12 watts or mag 19 and a half joules per year.
Mike: Hmm.
Saul: That is all of the tidal energy theoretically we could have access to. So no, it is actually not the-
Mike: That’s very small.
Saul: It’s, it’s, it’s, it’s not, it’s not nothing.
Mike: Mm.
Saul: But it’s, uh, not gonna be enough to send our ship there.
Mike: So in Hail Mary-
Saul: Mm-hmm
Mike: … Andy Weir really did hit on probably the only potentially feasible energy source.
Mike: to, to travel to the closest star once-
Saul: Right
Mike: … we need to be a type one civilization and capture all the energy available to us.
Saul: And that was a spaceship, uh, for– With a perfect fuel, a spaceship that carried three people, and that’s it.
Mike: So this is why there’s no aliens?
Saul: This might be why there’s no aliens. Everything is just so far apart that it take, would take an ungodly amount of energy to get anywhere, so, I mean, you should spend it locally, I would think.
Mike: Mm-hmm.
Mike: We really did a lot of math there.
Saul: Yeah.
Mike: That was great. I remember a scene in the movie version of “Hail Mary.”
Saul: Mm-hmm.
Mike: I think, uh, that the main character was using a calculator a bunch, and then his rock friend was doing these calculations just in his rocky head.
Mike: Yeah, and for all of, for all of how “Hail Mary” hinges upon this perfect source and is still barely possible-
Saul: Mm-hmm
Mike: I kinda wanna go through and figure out-
Saul: Oh
Mike: … the energy for some of these other big properties.
Saul: Maybe we should look at what the Death Star actually– The energy requirements of the Death Star. Yeah, mag “Star Wars.” Totally.
Mike: Great. Well, thank you for taking me through mag energy, Saul.
Saul: Absolutely, Mike. Thank you so much for being here. I’m glad we got a chance to do this.
Mike: Yeah. Yeah. We got to do the math.
Saul: Yep, and I will see you next time.
Mike: Bye-bye.
Mike: And even doing, having Ryland Grace do that math out loud for the reader, I think is really a tremendous, uh, service to readers of science fiction.
Saul: Yeah, and to be honest, I was a little surprised as I was reading through it. I was like, “Wow, this is great.” I’m, I’m enjoying the nerding out over the actual math about this.
Saul: just like the character was, Dr. Grace was.
Mike: Ooh, I feel like that’s a new episode.
Saul: Yeah, we can do mag sci-fi, a whole season of mag sci-fi. Totally.
| item | value | mag |
|---|---|---|
| seconds in a year | ~32 million s | ↑7.5 s |
| speed of light | 300,000,000 m/s | ↑8.5 m/s |
| mass converted to energy (c²) | ↑17 J/kg | |
| the Hail Mary itself | 100,000 kg | ↑5 kg |
| astrophage fuel it carries | 2,000,000 kg | ↑6.3 kg |
| energy in the fuel — the number to beat | ↑23.3 J | |
| solar collector output | 300 W/m² | ↑2.5 W/m² |
| collector area to charge that fuel in 3 years | ↑12 m² | |
| Earth’s total surface area | ↑14 m² |
| item | value | mag |
|---|---|---|
| ton of TNT | ↑9.6 J | |
| barrel of oil | ↑9.8 J | |
| Hiroshima (“Little Boy”) | ~15 kt | ↑13.8 J |
| Tsar Bomba | 50 Mt | ↑17.3 J |
| all conventional explosives ever manufactured | ↑18 J | |
| largest earthquake ever recorded (Chile, 1960) | M9.5 | ↑19.1 J |
| peak Cold War nuclear arsenal (US, 1960) | 20,491 Mt | ↑19.9 J |
| uranium, once-through reactors | ↑21.4 J | |
| the world’s forests (living wood) | ↑22.0 J | |
| all plants | ↑22.2 J | |
| the whole biosphere | ↑22.3 J | |
| all fossil fuel ever burned | ↑22.4 J | |
| all fossil fuel reserves | coal ↑22.4, oil ↑22.0, gas ↑21.9 | ↑22.6 J |
| all energy humans have ever used | ↑22.6 J | |
| uranium, breeder reactors | ↑23.2 J | |
| all fossil fuel in the ground, reserves or not | ↑23.5 J | |
| thorium, breeder reactors | ↑23.7 J | |
| geothermal heat in the crust (to 5 km) | ↑26.2 J | |
| Earth’s total internal heat | ↑31 J |
| item | value | mag |
|---|---|---|
| tidal power we generate today | ~500 MW | ↑8.7 W |
| wind power we generate today | ↑11.5 W | |
| civilization, 1890s | 1 TW | ↑12 W |
| all the tide there is | 3.7 TW | ↑12.6 W |
| civilization, since the 1970s | 10-20 TW | ↑13.3 W |
| Earth’s internal heat, replenishment rate | 47 TW | ↑13.7 W |
| wind we could recover | 80 TW | ↑13.9 W |
| all the wind there is | ↑14.4 W | |
| sunlight reaching Earth | 174 PW | ↑17.2 W |
| Kardashev Type I (a planet’s worth) | ↑16 W | |
| Kardashev Type II (a star’s worth) | ↑26 W | |
| Kardashev Type III (a galaxy’s worth) | ↑36 W |
| item | value | mag |
|---|---|---|
| geothermal, used per year | ↑18 J/yr | |
| wind, used per year | ↑19 J/yr | |
| all the tide there is, per year | ↑20.1 J/yr | |
| natural gas, used per year | ↑20.2 J/yr | |
| coal, used per year | ↑20.3 J/yr | |
| all fossil fuels, used per year | ↑20.7 J/yr | |
| all human energy use, per year | 180,000 TWh | ↑20.8 J/yr |
| all the wind there is, per year | ↑21.9 J/yr |
Where the numbers come from: