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Backstory

So, basically, for now let's handwave the organisms on the planets,because I cannot go to the absurd trouble of specifying and inventing the biology of each organism on the planet, because, I have a life (Okay, may be that's a lie) and also, I can't turn this question into a bum-numbingly boring textwall, because I really do have a sincere question.

Okay, so for now, let's pretend the creatures on this planet are just the same as those on Earth. Humans, cattle, pets etc, are just the same, cause I haven't yet thought up the biological details of the creatures on the planet, and I can't go to the trouble of inventing new terms and units etc etc.

So, in my story, there is a planet called Dovim, and it's inhabited by intelligent creatures called Dovimians. For all purposes for now$^1$, Dovim has the same characteristics as Earth (Mass, radius, gravity, rotational speed etc.)

Dovim orbits a very dim red dwarf, named Beta, at a great distance, such that the sun appears dim and the sky is a dark-red. In fact, the average noon sky on Dovim is only 50% as bright as the brightness of the sky during twilight on Earth. Due to the relative dimness of the sky, the Dovimians are afraid of bright light sources. In fact, they go mad if they are exposed to bright light for more than 10 minutes. But aside from that, the average Dovimian's anatomy is the same as that of an average human on Earth, and possess a similar level of development (technology, intelligence, logic etc).

Alr, back to the point.

In the story, the main character, a journalist, breaks into an archaelogical institute at night and steals classified documents in the bunkers of the institute. The journalist discovers a chilling truth.

According to the documents, some secret archaelogists unearthed a series of ancient civilisations on different parts of Dovim, aging from 50,000-5000 years ago. It's determined by records that every 5000 years or so, the civilisations went extinct due to unknown causes, and that all major hubs of the civilisations were totalled and gutted by fire.

However, after visiting one of the archaelogical sites, soil and other samples from the site contain an unusual amount of helium-ions (Alpha particles) and other radioisotopes in them. The journalist decides to bring them to the astronomical observatory in his town, and asks them to sample it. And also, the journalist gives the stolen documents from the institute, for hopes it might assist in the research.

Meanwhile 5 days after the incident, the journalist glimpses a unusually bright spot in the sky, and rushes to the observatory, and the results he finds are horrifying.

Apparently the astronomers after obtaining some additional information from a Cult, after calculations and simulations have discovered that every 5000 years or so, a radioactive body composed of depleted uranium, the size or Mars, comes within a astoundingly close distance of Dovim, causing the surface to be bathed in intense radiation and heat.

The astronomers also discover something horrifying, that the closest approach of the celestial body will be in a few days.

And meanwhile, the glowing spot in the sky grows larger and larger, until at last, just a 1 day before doomsday, the glowing spot has attained sufficient angular diameter in the sky so that it is noticeable by many Dovimians, and soon enough, civilians of the city start freaking out.

It isn't long after which the night side of Dovim is exposed to intense irradiation of both alpha and gamma rays, causing half of the planet to black out and lose communications.

On the night before doomsday, the journalist and the observatory staff are ambushed by a member of the aforementioned cult, but the protagonists succeed in binding the attacker inside a closet. Meanwhile, the photographers are at their cameras ready to capture the "Doomsday planet", and counting down. Meanwhile, most of the staff has been evacuated into airtight bunkers deep inside the ground, with shelter and important scientific documents, except for the journalist, the observatory's director, the photographers and an obstinate psychologist who refuses to go down into the bunkers.

At the end, the remaining staff hear earsplitting shrieks from the horizon, which suggests that the Doomsday Planet is very close to appearing on the horizon, and people in cities over the horizon have indeed gone insane from the bright light. Indeed, they see a white glow on the horizon, and soon, a giant bright disc appears on the horizon. The remaining staff goes horribly mad within mere minutes. The journalist feels a searing heat and a crackling sound, as the intense heat emitted by the Doomsday planet causes the observatory to burn down.

Back to the question

For convenience of question, let us call the Doomsday-Planet, "Gamma".

Gamma is around the size of Mars, and is composed entirely of Uranium-238. Yes, depleted uranium, not fissile uranium.

Gamma also revolves around Beta in an extremely eccentric orbit. At aphelion, it is around 140 billion km away from Dovim. And because of its large orbit, it takes 5,000 years to complete revolution around Beta, which is the reason why the extinctions occur in 5000-year cycles.

Using calculations, I have already found out that Gamma is around 5x as massive as Mars, by dividing the density of Mars and the density of Uranium, of which Gamma is made up of.

I know that depleted uranium is fissionable, but not fissile, because it cannot be split by thermal neutrons, and also, it cannot sustain a chain reaction for long.

However, I do know that uranium-238 releases 0.1 W/tonne, during radioactive decay. This is a puny amount. However, since the mass of Gamma is around $3.2×10^{24}$ kg, I have calculated the total amount of power released by radioactive decay to be around $3.2×10^{20}$ $W$. Not so puny.

During final day (Doomsday), Gamma is a "bright hot disc" in the sky. I have used certain calculators to determine the distance it is at.

In the story, the angular diameter of Gamma during "Doomsday" is around $10°$, which implies that at closest approach, Gamma is merely 20,000 km from Dovim.

My concern was initially about the fact that Gamma might get torn apart by Dovim, if it crosses the Roche limit, however, after calculating the Roche limit to be around 10,000 km across, I hardly think it would be a concern at all.

My main concern now is however, about the stability of "Gamma" itself.

I know Uranium-238 releases alpha rays and a minute fraction of gamma rays. However considering the large mass of Gamma, the $γ$ and $α$ emissions will be tremendous.

I have heard that gamma rays can heat up (albeit inefficiently, as gamma rays penetrate deep) the matter through which it passes, and the same is true for alpha rays, I suppose. Considering the massive output of the two types of radiation, I am mainly concerned whether the planet will remain stable or blow apart because the heat generated exceeded its gravitational binding energy.

So my main question here is:-

Will a Mars-sized planet made up of DEPLETED uranium be stable or explode due to the intense heat generated?

Bonus question (Not necessary to answer):- How hot will the surface of the uranium planet be?

$_{Footnotes}$

1. I have not yet decided on the mass of Dovim. Dovim might be a gas giant, a Super-Earth, or even a dwarf planet in my story. But for now, for simplicity's sake, let's assume that Dovim's mass is the same as the mass of Earth for now

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    $\begingroup$ Are you at all concerned with the gravitational effects on tides/tectonics .... leads to another question. $\endgroup$ Dec 23, 2023 at 9:44
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    $\begingroup$ While the reasons have changed, the overall plot here is almost exactly Asimov's famous short story Nightfall. $\endgroup$ Dec 23, 2023 at 14:17
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    $\begingroup$ The metallic planet might have been of 100% uranium 238 four billion years ago, but by now it is made of 50% uranium 238 and 50% lead 206. Although we all believee that lead is heavy, it is much lighter than uranium; over billions of years the molten lead will have migrated outwards, so that by now the uranium is nicely enclosed in a self-made lead shield thousands of kilometers thick... $\endgroup$
    – AlexP
    Dec 23, 2023 at 14:23
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    $\begingroup$ Quick note: You mention “alpha and gamma rays.” While gamma are indeed rays, alpha are not rays but particles. And they are far from dangerous, as a sheet of paper is able to stop them. Also, planets don’t just appear in the sky like that, not so quickly. If the deadly planet were to move so swiftly in Dovim’s sky, I’d be more scared of tidal forces than anything else. And there’s no way Gamma would be able to still orbit its sun, as it would be moving too fast. And 50% of Earth’s daytime sky brightness is even brighter than a cloudy day, by the way… Anyway full of scientific mistakes here. $\endgroup$ Dec 23, 2023 at 17:44
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    $\begingroup$ Wait, if the star is so dim and the Earth-like planet so far away, then how is the planet no completely frozen over? Out Earth was a "snowball" several times in the past due to slight variation of conditions, but you planet has that magnified by orders of magnitude! $\endgroup$
    – vsz
    Dec 23, 2023 at 21:38

1 Answer 1

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With a surface area of 144 million square kilometres and an energy output of 3.2 x 10^20 watts, this is over two megawatts of power per square metre.

However, temperature is a fourth-power property calculated by the Stefan-Bolzman law. Plugging in the surface area and power, we get a surface temperature of 2,502K, or 2,229°C.

Considering the properties of Uranium, we have a melting point of 1405.3 K ​(1132.2 °C) and a boiling point of 4404 K ​(4131 °C).

So, we can see that Gamma would be a sphere of liquid uranium... glowing yellow-white with a colour-temperature of around 2500K, similar to that of a M-class star.

enter image description here (From https://github.com/godotengine/godot/issues/29122)

With a liquid surface and all this thermal energy, I would expect that Gamma would be trailing a tail of Uranium vapour from the higher-energy Uranium atoms that have escaped from its gravity. It would not be completely stable, though its rate of evaporation would be quite low.

As pointed out by ihaveideas, I got the calculations for radiated energy in my previous version of my answer wrong...

Gamma's radius is 3389.5km, so diameter is 6679. At a distance of 20,000km, this is 2.95 diameters. Using the inverse square law, the power per square metre at that distance would be 1/2.95^2, 1/8.7, or 0.11. So, this would be 255,304 watts per square metre (rather more than the 0.003w/m^2 I originally came up with)

Earth receives about 1370w/m^2 from the sun. The energy recieved from Gamma by Dovim is 186 times as great, and Dovim already has a much lower power per square metre from its sun than Earth, probably on the order of 1/75th... so about 18.3w/m^2.

Multiplying watts per square metre received at Dovim's surface by the number of square metres and plugging the area and watts into the Stephan-Boltzman law calculator, this would raise the temperature at Dovim's surface to as much as 1183°C... with prolonged exposure. Given that this is a relatively brief close-approach, I would expect less effect, but still enough to significantly raise temperatures and cause fires as the OP said.

Given that Dovim's normal surface temperature would be much lower, that I calculated to be on the order of -135°C using the same online calculator, this would be a near extinction-level event. It would be a near extinction-level event even for Earth. It would quite likely be a civilisation-destroying event.

It should be possible to retreat deep underground and wait for Gamma to pass, or rely upon being on the other side of Dovim at the point of closest approach to Gamma, which would make it plausible that some records from previous encounters between Dovim and Gamma were preserved.

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    $\begingroup$ Uranium is also an excellent gamma shield, the amount of gamma radiation would only be coming from very near the surface of Gamma. Then earth's atmosphere would further be a strong shield as gamma radiation for inhabitants living neat the earth surface. I was doing the same calc's myself while your answer was posted. Conveniently, we came up with the same conclusions. $\endgroup$ Dec 23, 2023 at 6:24
  • $\begingroup$ You did make a mistake though. Because the angle of incidence changes over a sphere, the effective radiation/absorption area is equivalent to the cross sectional area of a sphere, so the cross-planet radiation effects are even smaller. $\endgroup$ Dec 23, 2023 at 6:32
  • $\begingroup$ @GaryWalker I expect you're right... but it's the order of magnitude that counts. $\endgroup$
    – Monty Wild
    Dec 23, 2023 at 6:38
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    $\begingroup$ @MontyWild, unfortunately your calculations ignore the size of Gamma. Seen from Dovim, it would have an angular size of some 16 degrees, and would appear more than 30 times bigger in the sky that the Sun or the Moon. 20,000 km is also almost exactly 6 Martian radii, so at his distance the Gamma's radiation will be 1/36th as much as on its surface, i.e. some 60 kW/m2. That's still some 60 times more potent that Sun at zenith; for an Earth analogue, think being strapped to a focal point of a concentrated solar power plant. $\endgroup$
    – ihaveideas
    Dec 23, 2023 at 14:49
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    $\begingroup$ @ihaveideas You're right... I forgot that it was proportional. I did the math, but it didn't feel quite right. Thanks. $\endgroup$
    – Monty Wild
    Dec 24, 2023 at 0:49

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