Radioactivity-Warmed "Rogue" Planet

[yotta]

Main Question or Discussion Point

How much radioactive warming would occur in the astronomical body specified below?

I want to write a story about a very advanced civilization, not yet of Dyson Sphere capability, able to artificially create large planets up to Saturn's mass, of any composition. They decide to create one not orbiting any star, a "rogue" planet, using the radioactivity of one of the very long half-life isotopes to provide warmth for at least 10^21 years.

Composition:100% germanium-76, decay: β-β-, T1/2 ≈ 1.8×10^21y, decay energy = 2.039 MeV, incl. antineutrinos. Statistics relative to Earth: density ≈ 5.5 g/cm3, or ≈ 1.0⨁, radius ≈ 2.0⨁, mass ≈ 8.0⨁, gravity ≈ 2.0⨁. (This ignores gravitational compression, reducing the size and increasing the gravity somewhat.)

For a ballpark estimate, if all of the energy of radioactive decay occurring at the moment of T=0 arrived at the surface instantaneously, how close would the energy flux be to 20mW/m2? Of course, this first-approximation model ignores the heat absorbed by the planet, and the time for it to arrive at the surface. These can be dealt with later.

If it's too hot,* then they'd use <100% radioactive material. *I'm not sure exactly what "too hot" is; I'll want to see what I'm dealing with first to make that determination. Likewise for "too cold." Perhaps, a really thick layer of aerogel, say one kilometer, might be able to prevent any more than one mW/m2 of energy escaping, or even less.

2x Earth atmospheric pressure is desirable to fully protect the surface, which would be the mass of one atmosphere above any given area. It would be 100% helium-3, because all other gases would freeze, and this very light gas would be easily retained by 2x Earth gravity, in the absence of any star. (O2 is provided in underground rooms for breathing.)

The ability to create this planet is, of course, highly speculative, and is not what my question is about, which is the quantity of heat generated by radioactive decay within this body in our known universe. If the heat generated is truly insufficient, then other somewhat "faster" decay isotopes could be used.

The purpose of the planet is to be a great repository of knowledge, to be to "all races in physical reality" what the Library at Alexandria was on Earth. Movies, music, and news videos are of particular interest to alien races, as they are informative of a civilization, but need for someone to explain them, in order to be entirely so. And, individuals from each species to observe in person. Hidden video cameras might be placed in civilizations not having video media.

 

[member 656954]

or a ballpark estimate, if all of the energy of radioactive decay occurring at the moment of T=0 arrived at the surface instantaneously, how close would the energy flux be to 20mW/m2?

Does it really matter? Just describe the situation and move on with the plot. Very few readers will care to see calculations on radioactive isotopes and heat transmissions curves, and even fewer will try and calculate an actual planetary mass that might generate sufficient heat. And for reference to a rogue planet kind of like the situation you are describing, read L.E. Modesitt's The Eternity Artefact. It's loaded with handwavium and unobtanium to describe the rogue planet, but gripping nonetheless.

 

[Vanadium 50]

While I agree with Tghu, your planet is only putting out 500W of power.

Essentially, you want something that puts out a lot of power, and never has to be refueled. And for a very, very, very long times - a billion times longer than the age of the universe. You need magic to make this work - if you want the power to match the solar constant on the earth, and can convert the entire mass of the planet to energy, you still get only 0.01% of the energy you need.

A billion times longer than the age of the universe is very long indeed.

 

[yotta]

Does it really matter? Just describe the situation and move on with the plot. Very few readers will care to see calculations on radioactive isotopes and heat transmissions curves, and even fewer will try and calculate an actual planetary mass that might generate sufficient heat. And for reference to a rogue planet kind of like the situation you are describing, read L.E. Modesitt's The Eternity Artefact. It's loaded with handwavium and unobtanium to describe the rogue planet, but gripping nonetheless.

I had already sort of thought of this, that a detailed explanation of the engineering aspects of creating the planet would severely bog down the story. I was going to put it in an appendix, so that people who are interested could see that the planet could, in fact, exist in our known universe, with the hard part being its creation in the first place. I'll probably get the book. Will respond to the other post tomorrow.

 

[yotta]

While I agree with Tghu, your planet is only putting out 500W of power.

Essentially, you want something that puts out a lot of power, and never has to be refueled. And for a very, very, very long times - a billion times longer than the age of the universe. You need magic to make this work - if you want the power to match the solar constant on the earth, and can convert the entire mass of the planet to energy, you still get only 0.01% of the energy you need.

A billion times longer than the age of the universe is very long indeed.

I see that my plan A is clearly not going to work. I've some ideas for a plan B. There's now no reason for the planet to be large, so I'm going for small and dense, say the size of the Moon, made of solid iridium, which is to me the coolest metal in the periodic table. Living spaces might be miles deep, allowing for a large population on a small planet.

There'd be a small percentage of some material that undergoes spontaneous fission, with a half-life of a few thousand years or less, to provide warmth in the beginning. Later, zero-point energy would be used to keep the planet warm underground, as well as for their everyday energy needs, which would in itself create a lot of what in other places would be waste heat, but is quite valuable there.

By the way, what would be a ballpark estimate of the lowest amount of warmth that could be prevented from leaking out the surface above, with a kilometer of aerogel, or some such very efficient insulator? Given 295 Kelvin inside, as low as 4 K outside, and 0.5 K in space, and the considerable increase in thermal conductivity of even the best insulators at very low temperatures. Could it be so incredibly efficient that even 3He would freeze out of the atmosphere? I probably won't use these minimum values, but I'd like to know what they are. Their incidental energy usage, when the resulting warmth is allowed to leave through the surface, would probably be enough to prevent 3He from freezing out, especially if the population is large, up to even more than Earth's.

 

[Vanadium 50]

There's now no reason for the planet to be large, so I'm going for small and dense, say the size of the Moon, made of solid iridium, which is to me the coolest metal in the periodic table.

So your plan is to scale down by one or two orders of magnitude when you have a problem that is many, many, many orders of magnitude.

You need magic.

 

[member 656954]

made of solid iridium

It is pretty cool, but given that iridium dust is very reactive and can be flammable, it's probably not the ideal material to make a whole moon out of

You need magic.

@Vanadium 50 is right, and I see you're now looking to utilize zero point energy (which is essentially magic!) but if this is a purpose-built habitat, why wouldn't you turn it inside out? Make it mostly hollow and put all the people on the inside. Not quite a Dyson sphere, but it makes more sense from an engineering and safety perspective, not to mention heating the place. You can use an active heat source - zero point if you like, or fusion if you want readers to instantly understand the design - but you don't need all the aerogel or to even worry about what's happening on the exterior surface.

A billion times longer than the age of the universe is very long indeed.

This pickup is the most interesting to me, @yotta. Why does your habitat need to persist for so long? I can think of a few detective-style plots that could make sense, but carrying readers across billions and billions of years is a pretty heavy load for any author.

 

[yotta]

So your plan is to scale down by one or two orders of magnitude when you have a problem that is many, many, many orders of magnitude.

You need magic.

Perhaps I gave up too soon on large planets warmed by radioactive decay. I'll do some checking of somewhat faster decaying isotopes. The question remains, with more significance for large planets, what's a ballpark estimate of the lowest amount of warmth that could be prevented from leaking out onto the surface above?

 

[yotta]

It is pretty cool, but given that iridium dust is very reactive and can be flammable, it's probably not the ideal material to make a whole moon out of

1) Iridium is nearly non-reactive in bulk quantities, as a solid rather than a powder, 2) reactivity doesn't matter, if there's nothing else for it to react to, and the material above in contact with it is non-reactive with it.

@Vanadium 50 is right, and I see you're now looking to utilize zero point energy (which is essentially magic!) but if this is a purpose-built habitat, why wouldn't you turn it inside out? Make it mostly hollow and put all the people on the inside. Not quite a Dyson sphere, but it makes more sense from an engineering and safety perspective, not to mention heating the place. You can use an active heat source - zero point if you like, or fusion if you want readers to instantly understand the design - but you don't need all the aerogel or to even worry about what's happening on the exterior surface.

1) They're living underground in my plan, right below the aerogel, 2) How do you have gravity in a hollow planet?, 3) I see what you're saying, hundreds of kilometers of rock between would well protect the living areas, so no need for an atmosphere or aerogel.

 

[yotta]

Vanadium 50 said: A billion times longer than the age of the universe is very long indeed.

This pickup is the most interesting to me, @yotta. Why does your habitat need to persist for so long? I can think of a few detective-style plots that could make sense, but carrying readers across billions and billions of years is a pretty heavy load for any author.

The designers wanted the habitat to last such an incredibly long time. My story won't cover billions of years; in fact, the people might get bored in just a few thousand years. They can leave, can teleport even billions of light-years, but cannot return, because the planet is in a void; the nearest star is a quarter-billion light-years away, so there are no stars near enough to use as reference coordinates.

Is there a way to put quotes within quotes? At least one more layer?

 

[member 656954]

2) How do you have gravity in a hollow planet?

It's spinning, so they live 'upside down' in the interior. It's actually a concept I've just used in my novel, at a considerably smaller scale, so it was top of mind.

in fact, the people might get bored in just a few thousand years. They can leave, can teleport even billions of light-years, but cannot return, because the planet is in a void; the nearest star is a quarter-billion light-years away, so there are no stars near enough to use as reference coordinates.

That's not how it works. Unless the planet is somehow moving erratically, orbital mechanics for such an isolated object is easy to calculate - if you can figure out a teleport billions of LY, you have sufficient precision to get back to the starting point, even if it's moved in the meantime. Basically, everything at that distance is moving relative to everything else, so returning is as trivial as going.

But if you actually can't get back, then your planet will likely be denuded over a small (by galactic standards) time period. You'd need a policy of birthrate replacement to make up for the exits. And I'd assume any species that can create this planet to be long-lived and probably have either entirely artificial conception or a low birthrate, just because that's what we see with human populations, so it's a constraint you're embedding into the plot.

Is there a way to put quotes within quotes? At least one more layer?

I've seen it done, but don't know how to do it myself, there's probably a thread about it somewhere, I've just never looked

 

[Vanadium 50]

I'll do some checking of somewhat faster decaying isotopes.

This will not work. As I pointed out, even if you convert 100% of your planet's mass to energy, you are off by a factor of 10,000.

the nearest star is a quarter-billion light-years away

After 10²¹ years there likely are no stars.

 

[yotta]

yotta said:
I'll do some checking of somewhat faster decaying isotopes.

This will not work. As I pointed out, even if you convert 100% of your planet's mass to energy, you are off by a factor of 10,000.

What about osmium-186, half-life 2.0×10^15y, ~1,000,000 times faster than germanium-76? And, wouldn't thorium-232 provide way more than I'd need, with a half-life of 14 billion years? If not, I'll give up on a large planet, and go small with zero-point energy, which if not scientific here at PF, makes a great sci-fi, tech-sounding energy source. They used it in Stargate Atlantis, in ZPMs.

----------------------------------------------------------------------------------

yotta said:
the nearest star is a quarter-billion light-years away

After 10²¹ years there likely are no stars.

I wasn't entirely clear, I meant if some people wanted to leave after only a few thousand years.

 

[yotta]

It's spinning, so they live 'upside down' in the interior. It's actually a concept I've just used in my novel, at a considerably smaller scale, so it was top of mind.
That's not how it works. Unless the planet is somehow moving erratically, orbital mechanics for such an isolated object is easy to calculate - if you can figure out a teleport billions of LY, you have sufficient precision to get back to the starting point, even if it's moved in the meantime. Basically, everything at that distance is moving relative to everything else, so returning is as trivial as going.

But if you actually can't get back, then your planet will likely be denuded over a small (by galactic standards) time period. You'd need a policy of birthrate replacement to make up for the exits. And I'd assume any species that can create this planet to be long-lived and probably have either entirely artificial conception or a low birthrate, just because that's what we see with human populations, so it's a constraint you're embedding into the plot.
I've seen it done, but don't know how to do it myself, there's probably a thread about it somewhere, I've just never looked

Your plan for a hollow world sounds workable, at least in sci-fi, but it's not my preference. I like my idea of stacked living areas, even miles deep, allowing for a huge population on a small planet. Stacking would work in a hollow planet, as well, if you wanted to have them do that.

I'm using the "cannot come back" as a plot device, as the "stick." They don't know what's there in any other place they might go, because no one has ever returned to tell them what's there. For the "carrot" I'll need to find things to do for fun, and have some work time for everyone, to keep things running.

If it's to be a really serious story, I'll want to go into the dilemmas of civilizations, and ways I think would in some measure solve them, at least enough for the civilization to not just survive, but be reasonably happy, as well.

I'll just give up on quotes within quotes, unless I find out how to do them.

 

[Vanadium 50]

What about...

Let me say this again. Even if you covert all the matter in your planet into energy, it's not enough. By about a afctor of 10,000, so it's not even close.

 

[yotta]

Let me say this again. Even if you covert all the matter in your planet into energy, it's not enough. By about a afctor of 10,000, so it's not even close.

OK, the final verdict is in, a large planet warmed by radioactivity is just not going to work. A close second would be engineered planets orbiting the lowest mass red dwarf star, which would last 12 trillion years, and would be based solidly on science, once they're created.

A small planet warmed by zero-point energy would work in a sci-fi universe, but not in the universe we know. Even if it is hand-wavium, at least there's precedent in other sci-fi stories.

 

[member 656954]

A small planet warmed by zero-point energy would work in a sci-fi universe, but not in the universe we know.

I like that you've iterated to a conclusion, @yotta, but you've mentioned teleportation, so this is not 'the universe we know' regardless. BTW, as you've noted orbiting a red dwarf, why don't you just send the planet off into the void along with its companion star. That's more ambitious engineering than a lone planet (or my 'inside out' planet).

 

[Vanadium 50]

A close second

You have just shaved eight orders of magnitude off your requirement. That's the ratio between the size of a person and the distance to the moon. Not very close.

I think you need to seriously think about your story and what the requirements for the setting really are.

 

[yotta]

You have just shaved eight orders of magnitude off your requirement. That's the ratio between the size of a person and the distance to the moon. Not very close.

I think you need to seriously think about your story and what the requirements for the setting really are.

I see I wasn't entirely clear, and hadn't thought about my meaning being misread. Rereading my post, I can see it. I didn't mean a close second in magnitude, I meant a close second in choice.

Thorium-232 might have been a somewhat close third choice, but it's nearly three orders of magnitude lower than a red dwarf star in longevity, which would defeat the purpose of a planet being habitable longer than any star can burn. And, as you've said, it wouldn't work, anyway.

 

[yotta]

I like that you've iterated to a conclusion, @yotta, but you've mentioned teleportation, so this is not 'the universe we know' regardless. BTW, as you've noted orbiting a red dwarf, why don't you just send the planet off into the void along with its companion star. That's more ambitious engineering than a lone planet (or my 'inside out' planet).

There's one possibility about that, sending the whole star system into the void, which is particularly interesting to me. The sky would look totally black, and they probably wouldn't have thought to build telescopes to find something they had no idea was even there. They'd think their star system was the entirety of the universe.

There might exist star systems that form naturally in an otherwise empty void, so far away from any other stars that the inhabitants there might think their star system was the entirety of the universe. I might be better off to write about a naturally formed planet, if it's reasonable scientifically for it to have so formed, than go through the trouble of having it be artificially created.

If I go the small rogue planet route, that would require artificial creation. I'm not committed either way yet, and will want to continue considering, until I either have enough possibilities I like, or feel like I've run out of new possibilities, or they're harder to find.

 

[member 656954]

The sky would look totally black, and they probably wouldn't have thought to build telescopes to find something they had no idea was even there. They'd think their star system was the entirety of the universe.

Perhaps if the planet is populated by people who have either reverted from some previous high-tech society, or are still pre-Enlightenment. Because it is hard to imagine a telescope never having been invented (they are useful for looking at things other than stars, after all), and one never having been pointed away from the sun. Given the lack of other near-by light sources, they'd see something of the universe, for sure.

I'm not committed either way yet

I've found it helps to get back to the basics of what your story is intended to convey when I'm stuck with such a fundamental dilemma as this is. From your posts, it seems you have an idea, which is the lone planet, and want to wrap that into a story structure. Typically that is difficult to extend into a novel, because it's essentially a single narrative device and you get tied up in knots either having to explain everything or having to constrain everything. Stories that explore some essence of humanity allow you to introduce an idea without having to make it the sole motivating purpose, and that's usually way easier to write because the narrative arc can move with the characters, rather than the characters having to move to the narrative arc.

 

[essenmein]

As to the original question, if its still helpful, you could use Earth as a starting point, half the heat comes from radiogenic sources.

https://physicsworld.com/a/radioactive-decay-accounts-for-half-of-Earth's-heat/

 

[Vanadium 50]

It won't last for 10²¹ years.