As part of the backstory of my setting, a wormhole base on the Moon catastrophically failed around 500 years ago. The energy released was enough to melt a huge portion (edit: approximately size of Mare Imbrium, 700-800 miles across) of the Moon's crust and create a new lunar mare. My question is (to which I've only gotten snarky replies on Quora), how long could such a lunar scar be visibly molten? As in, glowing red visibly from earth when in the shadowed part of the Moon?
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2$\begingroup$ Nice question! Can you tell us (approximately) how big and how deep you envisage the catastrophe to have affected the Moon? "Huge portion" could be half the Moon! I'm asking for this clarification simply because the more energy is in the original wound, the longer any molten stone (magma) will glow; and the converse is similarly true. $\endgroup$– elemtilasCommented Apr 26 at 0:26
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$\begingroup$ Have you looked at how long basaltic magma examples stay red glowing on earth? Going by those I would expect less then 48 hours. because there is the how long will it be red hot, how visible is red hot from Earth? $\endgroup$– Gault DrakkorCommented Apr 26 at 0:27
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2$\begingroup$ @GaultDrakkor : that's initially what I thought but it is not just a flow, but a vast sea of molten crust. Idk enough about the geology of the moon. Could the sudden pressure difference from the liquidized crust start short-lived volcanic or other geothermal processes that keep it going longer? How fast would it cool with less in the way of conductive medium due to the lack of atmosphere and flowing water etc... All the energy would dissipate through radiation. Would it form a skin that would keep the layer beneath the surface molten for longer, occasionally cracking to show red fracture? Idk $\endgroup$– Chromatic RealmsCommented Apr 26 at 1:46
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$\begingroup$ @elemtilas : about the size of Mare Imbrium, 700-800ish miles across $\endgroup$– Chromatic RealmsCommented Apr 26 at 1:51
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1$\begingroup$ Thank you for editing that into your question! $\endgroup$– elemtilasCommented Apr 26 at 4:22
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1 Answer
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Sounds like a good candidate for a Fermi estimate / dimensional analysis!
Conceptually, we'll simplify to a ball of molten rock hooked up to a "perfect" heatsink (aka, ignoring the size of the moon and any heat radiated into space).
For a quick "back-of-the-envelope" sketch, we'll need to estimate how much energy there is in the molten rock and how fast that energy will dissipate.
Let's make a few "guesses" for the numbers and see what pops out:
- The specific heat capacity of rock is
~800 J/(kg*K) - The thermal conductivity of rock is
~10 W/m^2 - The density of rock is
~3 g/cm^3 - The radius of the mare is
300 miles
To get the energy of the mare, we'll do volume*density*temperature*specific heat capacity. That's approximately (300mi)^3*(1500K)*(800 J/(kg*K)) = 10^26 Joules (~1 billion times the yield of the most powerful nuclear weapon ever detonated).
Divide that by heatsink area*thermal conductivity (300mi)^2*(10 W/m^2) and we end up with something on the order of a million years to dissipate that much energy. So I'd say a still visible glowing scar only half a century later is plenty reasonable.
Note that this is a very fast and loose calculation, literally just googling various constants and smashing them together until the units cancel, but it's enough to make the concept palatable (to me at least).
Link to the math, if you want to play around with the numbers yourself a bit. Even dropping the molten volume by quite a bit keeps the number of years reasonable and brings the total energy involved down to more...modern...numbers.
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1$\begingroup$ Unfortunately, what counts is not the time needed for all the rock to cool down, but rather the time needed for the topmost layer of the rock to cool down. For example, the interior of the Earth is still molten, four and a half billion years after it was formed; but the thin crust is cold, and as a result Earth does not glow at all. $\endgroup$– AlexPCommented Apr 26 at 20:55
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$\begingroup$ Very true, like I said this is a pretty fast and loose calculation. Part of my simplification was to disregard any radiative cooling (since it will have a negligible effect compared to the "heatsink" of the moon), which means in my simple model the hottest portion will actually be at the surface of the moon. A better model would account for that, but then you're talking about heat gradients and black bodies etc. Since the simplified model spit out numbers MUCH larger than needed, I wouldn't worry too much about it myself, but you are welcome to do those calculations! $\endgroup$– Kyle GCommented Apr 26 at 21:11
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1$\begingroup$ On the contrary, I would expect that the topmost layer at the surface will freeze quite fast, exactly because radiative cooling. Yes, below it the rock may remain molten for a long time, but the question is about the surface layer. $\endgroup$– AlexPCommented Apr 26 at 21:16
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$\begingroup$ Even adding a term for the radiant emissivity (assuming the mare/rock interface is about the same area as the mare/moon interface) doesn't really move the needle on the orders of magnitude involved here. Is this calculation exact? No. Is it enough to completely suspend any disbelief in a rather cool plotpoint? I think so but YMMV. $\endgroup$– Kyle GCommented Apr 26 at 21:48
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$\begingroup$ @KyleG thank you for being the first person to try and give an actual time estimate! :) I appreciate it! I think the radiation cooling would play a large role irl and my gut tells me it probably wouldn't be visible for long, since the heat gradient even in the "vacuum" of space is pretty extreme toward heat rapidly leaving warm bodies, but you're exactly right the purpose of this isn't to make this happen irl, it's to make it sound plausible. I WANT the Moon to have a glowing scar. If people read it and go "is that possible? Actually it might be, hmmmmm..." That's good enough for me :) $\endgroup$ Commented Apr 27 at 16:08