How unlikely is the formation of an earth size planet made of Uranium?

[Researcher X]

And if we increased the size of our imaginary planet, how massive and large could it get before it undergoes fusion?

Also, I'm pretty sure you could never actually get a Uranium planet, but is there enough to have Uranium asteroids in a star system, or at least asteroids that are radioactive enough for radiation to be a significant factor in terms of a planetary collision?

 

[DaveC426913]

Uranium is far too close in density and reactivity to several of the other actinide elements to be found separate. It is very difficult to separate it out from other ores for this reason, let alone find it that way naturally.

Also, it's not found in pure form but rather oxidised.

Also, uranium doesn't undergo fusion; certainly not spontaneously. Are you perhaps thinking of fission? It undergoes fission all the time. That's what makes it radioactive. I think what you want to know is: will it undergo a neutron cascade, resulting in an explosion.



You would be hard-pressed to find a more implausible plot hook for a story.

 

[DecayProduct]

A quantity of pure uranium that large would almost certainly be a manufactured product (in a sci fi story), rather than naturally occurring. It only takes a very small amount (<100 kg) before it reaches critical mass.

 

[Researcher X]

It only takes a very small amount (<100 kg) before it reaches critical mass.

It wouldn't explode though. IIRC, Uranium doesn't explode unless two portions to create the critical mass are introduced to each other at high speed and also under pressure, as in the very first Atomic weapon. If it's slower than it will just emit enormous amounts of radiation.

 

[DecayProduct]

It wouldn't explode though. IIRC, Uranium doesn't explode unless two portions to create the critical mass are introduced to each other at high speed and also under pressure, as in the very first Atomic weapon. If it's slower than it will just emit enormous amounts of radiation.

But as you pile on more and more uranium creating this planet-sized ball, it seems to me that one of two things is going to happen. Either it will keep pushing itself apart by the enormous radiation and heating of the material around it, or if you get it big enough, the weight of the outside pressing in will be enough to keep it together long enough to drive it supercritical.

At any rate, such a thing would not exist as a natural occurrence. Perhaps some technologically advanced society could build something to that size by reducing the density to keep it subcritical. Or even have some manner of control over the weak nuclear interaction that cause the uranium to be unstable to begin with. I am assuming this from some sci-fi story point of view. In reality, it just wouldn't exist.

 

[Guesser7]

This is not only impossible, it is silly. A planet of pure Uranium! Considering every element has the unwavering desire to transform itself into Iron this is in the realms of fiction. If my memory serves me right our star is a 2nd generation star which in its current phase is 5 billion years and the amount of Uranium must be say of the average platetary mass of 5E+24 tonnes and the estimate from the deposits of Uranium is only c 20,000 tonnes, if my maths are correct that is 2E-21. In shorthand since the balanced atom is Iron we would just never get to a pure state of anything except good old Iron, and if we have an oxygen atmosphere we would have a planet with a surface of rust!

Guesser7

 

[Rymer]

Using which isodope. Hollywood will love it.

 

[Salish99]

It would also likely "fiss" not "fuse".

 

[dylan123]

very

 

[qraal]

Hi All

A planet made of uranium can't be Earth-sized, but it can be Earth-mass. Uranium is too dense and would compress under gravity too much to get close to Earth-sized.

But what would it do? Well such a big mass of uranium in its normal Earth abundance would be 99.3% U-238 and 0.7% U-235. That's not enough to undergo runaway fission en masse because the neutrons produced by the normal decay of U-238 are too high energy to cause multiple release of neutrons during natural fission. With the right mix of other elements it might operate as a breeder reactor, but that's a different question.

However one thing that does happen is radioactive decay. Normally the two don't make a lot of heat, but with so much uranium acting as thermal cladding the heat will have a hard time escaping. The tiny amounts of Uranium, Thorium and radioactive Potassium inside Earth are enough to melt its core remember, so a whole planet would be mostly molten inside from the radioactivity generated heat.

 

[DaveC426913]

Well let's for the moment grant the OP's fantastical premise...

A planet made of uranium can't be Earth-sized, but it can be Earth-mass. Uranium is too dense and would compress under gravity too much to get close to Earth-sized.

What are you saying? If more and more uranium were heaped on the planet, its radius would not increase? I think I'd need to see some numbers to back that up.

But what would it do? Well such a big mass of uranium in its normal Earth abundance would be 99.3% U-238 and 0.7% U-235. That's not enough to undergo runaway fission en masse because the neutrons produced by the normal decay of U-238 are too high energy to cause multiple release of neutrons during natural fission.

Again, I don't follow. You're saying a giant ball of purified uranium would generate neutrons with too much energy to start a cascade?

 

[qraal]

Well let's for the moment grant the OP's fantastical premise...

What are you saying? If more and more uranium were heaped on the planet, its radius would not increase? I think I'd need to see some numbers to back that up.

Yep. According to my planetology texts the maximum radius of cold body of given atomic number and mass number is 119,000*(Z^0.5/A) km which means for Uranium with Z = 92 and A = 238, the maximum radius is 4,796 km.

Again, I don't follow. You're saying a giant ball of purified uranium would generate neutrons with too much energy to start a cascade?

No. The ball size doesn't really matter. Plain U-238 produces neutrons at too high an energy to trigger runaway fission of U-238 i.e. a chain reaction. Thermal neutrons are needed - or something mixed into slow the fast ones down.

 

[Researcher X]

Interesting. What is the maximum radius for a planet with a composition and density similar to Earth?

 

[Chronos]

How would such a planet shed its non-uranium outer shell? Earth has a core comprised largely of heavy [like uranium] elements but has not shed its less dense shell.

 

[qraal]

How would such a planet shed its non-uranium outer shell? Earth has a core comprised largely of heavy [like uranium] elements but has not shed its less dense shell.

I'm not saying such a planet can form, or how it could, just what it's limits are.

 

[qraal]

Interesting. What is the maximum radius for a planet with a composition and density similar to Earth?

Well it won't have a similar density will it? Planets compress and compact as they get heavier because their constituent atoms get squeezed ever harder by their own self gravity. Eventually the maximum radius is reached, beyond which the planet's radius gets smaller with increasing mass because the core is now degenerate matter.

Earth's uncompressed density is actually just 4.08 compared with its average density of 5.5148, so it's already somewhat compacted. To get a rough estimate of its maximum radius we have to make a few guesstimates about its composition - it's ~83.8% silicates and about 16.2% iron/nickel, by volume. By mass it's more like 67%:33%. If we approximate all the silicates by SiO₂ and the core as just Fe-56, then we can roughly work out the relative numbers of the component atoms. So we'll assume the silicon has a Z = 14 and A = 28, the oxygen has a Z = 8, A = 16 and the iron Z = 26, A = 56. This ignores the lesser isotopes, but including them won't change much. We've also ignored a few other elements, but they're all close to Silicon or oxygen anyway.

So SiO₂ has Z = (14 + 8 x 2)/3 = 10, and A = (28 + 16 x 2)/3 = 20 and there's M*(0.67/20) kilomoles of SiO₂ and M*(0.33/56) kilomoles of Fe. In otherwords by number it's 85% SiO₂ and 15% iron. Plug in the numbers and the maximum radius is 16,500 km or ~2.6 Earth radii. A pure SiO₂ planet would max at ~3 Earth radii, more or less.

These are rough figures. More elaborate modelling using more detailed physics gives similar results.

 

[Rymer]

For similar density a 2.6 increase in radial size means a 2.6^3 increase in mass. But the size would reduce the surface gravity by 2.6^2 -- implying a maximum earth-like surface gravity of 2.6.

Is that what your estimator shows?

(Well, what do you know the scifi books are wrong!)

I don't believe its that simple.

 

[qraal]

For similar density a 2.6 increase in radial size means a 2.6^3 increase in mass. But the size would reduce the surface gravity by 2.6^2 -- implying a maximum earth-like surface gravity of 2.6.

Is that what your estimator shows?

(Well, what do you know the scifi books are wrong!)

I don't believe its that simple.

Hi Rymer

The maximum mass of a maximum radius planet goes up - except for helium - according to M_m = M_o*(Z⁷/A⁴)^0.5. For hydrogen the maximum mass is 2.69E+27 kg and that's the value of M_o. As you can see the mass goes up pretty rapidly with atomic number. Thus so does the average density and surface gravity.

 

[Widdekind]

Yep. According to my planetology texts the maximum radius of cold body of given atomic number and mass number is 119,000*(Z^0.5/A) km which means for Uranium with Z = 92 and A = 238, the maximum radius is 4,796 km.

Would you please cite such sources ??

If you would take the time to do so I would really appreciate it, thanks!

 

[Widdekind]

Well it won't have a similar density will it? Planets compress and compact as they get heavier because their constituent atoms get squeezed ever harder by their own self gravity. Eventually the maximum radius is reached, beyond which the planet's radius gets smaller with increasing mass because the core is now degenerate matter.

Earth's uncompressed density is actually just 4.08 compared with its average density of 5.5148, so it's already somewhat compacted. To get a rough estimate of its maximum radius we have to make a few guesstimates about its composition - it's ~83.8% silicates and about 16.2% iron/nickel, by volume. By mass it's more like 67%:33%. If we approximate all the silicates by SiO₂ and the core as just Fe-56, then we can roughly work out the relative numbers of the component atoms. So we'll assume the silicon has a Z = 14 and A = 28, the oxygen has a Z = 8, A = 16 and the iron Z = 26, A = 56. This ignores the lesser isotopes, but including them won't change much. We've also ignored a few other elements, but they're all close to Silicon or oxygen anyway.

So SiO₂ has Z = (14 + 8 x 2)/3 = 10, and A = (28 + 16 x 2)/3 = 20 and there's M*(0.67/20) kilomoles of SiO₂ and M*(0.33/56) kilomoles of Fe. In otherwords by number it's 85% SiO₂ and 15% iron. Plug in the numbers and the maximum radius is 16,500 km or ~2.6 Earth radii. A pure SiO₂ planet would max at ~3 Earth radii, more or less.

These are rough figures. More elaborate modelling using more detailed physics gives similar results.

That's really interesting. It may be, that most Exo-Planets are younger than the Earth*. And, it's certainly well-known, that Star Metallicity strongly correlates w/ the probability of Planetary Systems existing; and that Star Metallicities have gradually increased across the ages, through Enrichment. Thus, Exo-Planets are possibly becoming more & more probable, and are becoming composed of more & more enriched constituents.

* https://www.physicsforums.com/showpost.php?p=2199428&postcount=22​

Thus, according to your quoted equations, the Maximum Masses of rocky Exo-Planets may be increasing, even as their Maximum Radii are decreasing, b/c of their increasing Metallicities / Enriched Compositions.

 

[Rymer]

So what is the surface gravity of your maximum sized earth-like planet?

 

[Researcher X]

So what is the surface gravity of your maximum sized earth-like planet?

Painful, I'll bet.

 

[qraal]

Would you please cite such sources ??

If you would take the time to do so I would really appreciate it, thanks!

"Planetary Science: The Science of Planets Around Stars", George H. A. Cole & Michael M. Woolfson, IoP Publishing, 2002. Section P.4 page 310 specifically.

If you do a "Google" search a number of papers come up which discuss the mass-radius relation for planets. There's been quite a lot of work on the topic in recent years because radii & masses from transiting exoplanets give vital clues on composition.

You can look at that exact page - but not the ones just after it - on Google Books...

http://books.google.com.au/books?id...6zWDA&sa=X&oi=book_result&ct=result&resnum=4"

...so it's right there. I think the book might even be downloadable from different places on the web, but I've no idea of the quality or legality of those versions. I have a hard-copy I bought for $AU 125 - including postage - a few years ago.

 

[qraal]

So what is the surface gravity of your maximum sized earth-like planet?

Damned heavy. The mass at maximum radius, M_R, is 2.69E+27 kg * (Z⁷/A⁴)^0.5 so you can work it out yourself.