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Wrathful aliens are teaching the humans a lesson by relocating their world from a cosy 1 AU to around 4 AU away from the central Sun-like star. The planet is Mars-sized and covered in a salt-water ocean averaging at 6 km in depth with very little land. The atmosphere is Earth's in both composition and pressure at sea level, but the scale height is greater due to the lower, Mars-like gravity.
If no human intervention takes place, the oceans and atmosphere would condense and freeze, turning the world into something resembling Enceladus.
The humans hastily cobble together a plan: use a magical device capable of remotely spawning thermonuclear-like explosions at any location to constantly explode the depths of the ocean everywhere around the planet. The heat released into the oceans eventually finds its way to the atmosphere, warming it as well. (The magical device doesn't produce any nuclear fallout.)

Is this a viable method to save the planet (meaning, keep the oceans liquid and the air unsolidified)? If so: if the limit of explosive force delivered by the magical device is 10 megatons, and assuming we intelligently distribute the explosions to areas of ocean that need them most, how frequently do we need to detonate? Once a second? A hundred times a second? A thousand?

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    $\begingroup$ Your question begs how the planet was habitable in the first place. Mars's lack of habitability today is not because of its distance, but its size. Even at 1 AU it's unlikely it would've been able to preserve an atmosphere because it needs a large enough core to form a protective magnetic field. If you placed Earth at the Mars distance from the Sun, it would definitely be much colder on average, but it would still most likely be habitable, especially at the equator. $\endgroup$ – stix Feb 22 at 22:52
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    $\begingroup$ @stix Yeah. I left out and altered a lot of details to keep the question simple. The planet isn't natural, it was built. $\endgroup$ – BMF Feb 22 at 22:55
  • $\begingroup$ @Tantalus'touch. No, no reason. That's an option too if you wish to explore it. essentially the nuke device has to be used in some way to make the planet viable. $\endgroup$ – BMF Feb 22 at 23:31
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    $\begingroup$ @stix: Obviously, humans settled this Mars-sized world in the first billion years or so of its existence, when it had a good deal more water & presumably air. en.wikipedia.org/wiki/Noachian $\endgroup$ – jamesqf Feb 23 at 4:10
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    $\begingroup$ If your Planet can autoMAgically detonate the needed 20 * 10 Megaton nuke equivalent per second, projected at an arbitrary point in the sky, for an unlimited duration, I can see why the Aliens tried to exterminate them. Your people are DANGEROUS! $\endgroup$ – PcMan Feb 23 at 9:09
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Slight frame-challenge.

I'd suggest detonating them in the highest level of the reaches of the atmosphere, Just outside the limits of the exosphere. (About 1000 Km up)

The detonations should happen on the side of the planet facing the sun (such as it is, far away).

Maths: Each 10 Mt explosion consists of $4.6*10^{16}$ joules, 35% of which would be thermal and light, and much of which would be directed away from the planet. At the limits of the exosphere, approx 46% would go planet-wards. That's $7.4*10^{15}$ joules per explosion.

The Earth needs (by pre-industrial standards) $1.74*10^{17}$ Watts of energy delivered incident on the upper atmosphere. (That's joules, per second).

That's about 23 or 24 detonations per second delivered above the "midday" point as the sun apparently moves. Fits with the UK frame rate for old terrestrial TV as it turns out, you'd not notice much flicker probably. Half sized ones, at twice the rate to make sure might be better.

Say take it down to 21 or 22 per second (*2?) to compensate for residual solar radiation at 1/16 the normal rate (inverse square law).

You can vary it a bit to make seasons.

Easy.

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    $\begingroup$ Man, I wonder what that would look like. There would be a slight parallax between the faint sun and the explosions. Shadows might have a slight 24Hz flicker to them. Cool! $\endgroup$ – BMF Feb 23 at 0:29
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    $\begingroup$ Er, I rather meant 7-8 per second. Forgot that 54% of the energy that doesn't reach the planet regardless. $\endgroup$ – BMF Feb 23 at 4:04
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    $\begingroup$ I'd also be very worried about the distribution of energy per photon - whether there's the right amount of visible light to see by, enough UV for photosynthesis, low enough levels of higher-energy photons, etc. Weather patterns would also be dramatically affected, and I don't know what this would do to the ozone layer. EMP would also be a concern. $\endgroup$ – user2357112 supports Monica Feb 23 at 12:23
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    $\begingroup$ If the device can produce explosions that are in motion, that could also help with parallax, and additionally help adjust the artificial light's spectrum by red- or purpleshifting it as needed. $\endgroup$ – Egor Hans Feb 23 at 14:18
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    $\begingroup$ @EgorHans: The parallax comes from the fact that people are spread out spatially across the surface of the planet, not from the motion of the sun and the explosions. Adding velocity to the explosions won't help with that. $\endgroup$ – user2357112 supports Monica Feb 23 at 16:04
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The earth every hour receives 430 quintillion Joules of energy, where 1 qunitillion = 10^18. The energy from a 1 Megaton nuclear bomb is 4.18*10^15 joules. Thus, a nuke of 10 MegaTon TNT equivalent releases 1000th the part of hourly radiation of sun.

There are estimated around 14000 nukes in the world. If you burst all of them simultaneously, you will only produce around 15 hours of extra sunlight effect. Of course, the Sunlight is countered by various ions etc in upper mesosphere and thermosphere as well, so you could probably add a couple of hours of extra sunlight to that.

But that still won't be enough in the long term to deter aliens. The heat so generated would dissipate away in the atmosphere anyway.

Next, total volume of all oceans is 1.3 sextillion liters. It takes 4200 joules to raise temperature by 1 degree of 1 liter water. You can do the maths, but all your nuclear weapons blowing simultaneously would not even raise the temperature of seas by 1 degree.

Thus I don't think nukes will help you to keep things warm.

Rather, you can

  1. look into pulling stray asteroid matters of small enough size into the earth's atmosphere. that way, the asteroid constantly burns in the atmosphere, keeping the temperatures high, and the ill effects (ash/gas) etc are not enough to trigger a global cooling on its own.

  2. You find a way to increase the amount of green house gas in atmosphere. This keeps earth warmer for longer due to trapping of solar energy. But you've to be careful not to cause more cloudy conditions, as those can trigger cooling of surface. CO2 is thus a natural option, but you can look into increased methane or ozone production as well.

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    $\begingroup$ @mu, I feel like you didn’t read the question, since the OP specifically said that there is no fallout and he also said that he had a magical device. -1 $\endgroup$ – fartgeek Feb 22 at 23:14
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    $\begingroup$ "Rather, you can look into pulling stray asteroid matters of small enough size..." In my story, this was the original plan. The planetary system they inhabited had no asteroids, so they were to use this magical device to pull material from beneath the planet's crust through millions of small wormholes and let it all rain down from space into the atmosphere. This i know would've warmed the atmosphere significantly. However, for plot reasons, this plan failed and they had to instead fall back on releasing energy into the oceans. $\endgroup$ – BMF Feb 22 at 23:15
  • $\begingroup$ In the end, the energy release isn't quite enough, the planet's mean temperature isn't quite there, and the planet remains a frozen hellhole as millions of inhabitants die. $\endgroup$ – BMF Feb 22 at 23:15
  • $\begingroup$ So, great answer! But for story purposes I need to use the magical nuke device. (Also, as stated in the question [and again by @fartgeek], the nuke device doesn't release any fallout or nuclear particulate. Just thermal, light energy, and the associated blast wave.) $\endgroup$ – BMF Feb 22 at 23:15
  • $\begingroup$ @fartgeek you are right, I had skipped over that line on fallout. Have edited to remove that. $\endgroup$ – mu 無 Feb 22 at 23:27
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These hypothetical people might be better off using their magical device to create volcanic eruptions. When a volcano goes off, it releases a significant amount of greenhouse gases as well as ash and lava, so the heating would be more of a cumulative process. You wouldn't just be relying on the heat from the explosions, but using the resulting gases to help the atmosphere hold in more heat. Agitating the planet's mantle artificially would also boost activity at deep-ocean vents, keeping the ocean floor a viable biome.

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  • $\begingroup$ I might be wrong about this, but at 4 AU the planet would be receiving something like 9x less solar energy. The sheer quantity of greenhouse gases needed to make up for that loss might make for a totally toxic atmosphere. The humans have this magical device, but they don't have the technology or industry to build artificial habitation. Could you maybe explore the feasibility of this super-volcanism? $\endgroup$ – BMF Feb 22 at 23:01
  • $\begingroup$ @BMF that sounds like detail that should have been in the question, but now shouldn't be added because it is too late. You could perhaps create a new question about that topic. $\endgroup$ – Starfish Prime Feb 23 at 10:17
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    $\begingroup$ @StarfishPrime Which detail? The fact that the planet must be liveable after having "saved" it? I thought that was a given, given the phrasing of my question lol $\endgroup$ – BMF Feb 23 at 13:21
  • $\begingroup$ @BMF "The humans... don't have the technology or industry to build artificial habitation". That being the only detail that wasn't already present in the question. $\endgroup$ – Starfish Prime Feb 23 at 13:36
  • $\begingroup$ @StarfishPrime the planet remaining Earth-like and liveable by people was something of a prerequisite, I should still be able to clarify that in the question without invalidating answers, assuming @ Karst's intent wasn't to raise the temperature and then deal with that little nagging side effect of all life on the planet dying. $\endgroup$ – BMF Feb 23 at 13:44
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Use the nukes to thicken the atmosphere by selective rock shattering.

All the other answers so far have good maths re energy and warming and such, and I'm not going to repeat good work, but there is one more possibility - greenhouse effects and geological carbon sinks.

Detonate your nukes at the bottom of the sea, such that it fractures rock. You haven't specified the lithosphere of the planet, lets say there's a layer that's rich in limestone (which is often under oceans - it's old shells and sediment under pressure).

When this is shattered and heated - carbon dioxide is released. This will build a greenhouse effect, heating the planet.

Humans will detect the air as bad at about 2000ppm - 5000ppm, that's an order of magnitude more than Earths CO2 levels in the 20th century, so you can increase the insulation by a factor of ~10 before the air even starts to seem stale. That's 10-fold increase in insulation, enough to make up for the decrease in incoming energy.

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    $\begingroup$ This shares the same problem as the other 2 answers positing a greenhouse effect as a possible solution. At 4 AU we'll be receiving something like 9x less solar flux. Can we actually have a non-toxic atmosphere at that point? $\endgroup$ – BMF Feb 23 at 3:29
  • $\begingroup$ @BMF Totally. 1900 CO2 levels were 300PPM. Humans notice the air is stuffy at about 4000ppm. That's a 13 fold increase in insulation over Earth before we even notice the air is stale. $\endgroup$ – Ash Feb 23 at 3:33
  • $\begingroup$ Sounds like you hope to saturate the ocean with CO2 first and rely on it off-gassing the excess to the atmosphere... that's going to be bad news for a whole host of oceanic ecosystems. You'd be better off blasting surface deposits, but only after you've vapourised any ice caps because a) ice has a great albedo for reflecting heat and b) water vapour is an excellent greenhouse gas all by itself. $\endgroup$ – Starfish Prime Feb 23 at 10:19
  • $\begingroup$ Problem with this calculation: only about 9%-26% of the Earth's greenhouse effect is due to CO2 so increasing CO2 concentrations tenfold will not improve insulation by anywhere near tenfold. Meanwhile, moving from 1 AU to 4 AU will divide your insolation by a factor of 16, so this scenario gets much much colder. $\endgroup$ – Geoffrey Brent Feb 23 at 10:37
  • $\begingroup$ @StarfishPrime Evaporating water isn't going to help you here. Yes, it's an important greenhouse gas, but if you add more of it, the extra is just going to fall out of the sky again within a few days. $\endgroup$ – Geoffrey Brent Feb 23 at 10:40
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The magical device doesn't produce any nuclear fallout

I think you're missing something very important with this. You want the fallout, because what you want to do is

Strengthen the greenhouse effect using water vapour

Water vapour is a major player in the greenhouse effect. We focus on CO2 because that's human-created, but CO2 doesn't directly cause all of its effects itself. It also has has a role in how much water vapour stays in the atmosphere, which causes a further impact on the global climate.

Intuitively, we do know that days are warmer when there is cloud cover. Of course we experience more direct heating from direct sunlight, but cloud cover maintains the temperature when the sun is not at its peak by acting as an insulating layer to prevent convection from dissipating that heat, keeping a warmer layer of air closer to the ground. This effect is experienced locally, of course, but modelling suggests that increased humidity will increase global temperatures. This is still a matter of discussion and significant research, but is well supported by the science to date.

So the focus of your nukes should not be specifically to warm the oceans. Instead, it should be to disperse as much water vapour into the air as possible. You don't need to actually boil the water, you just need to maximise the aerosol effect.

Note that this is a different scenario to nuclear winter or volcanic winter, where soot particles in the atmosphere prevent heat from reaching the Earth. Water vapour passes substantial amounts of heat and light, so whilst clouds and smoke are superficially similar, their effects are different.

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  • $\begingroup$ So, the explosions should be used to eject water vapor, a better greenhouse player than CO2, into the air. Sorry if I'm missing something obvious, but how does keeping the nuclear fallout play a role in that? $\endgroup$ – BMF Feb 23 at 20:04
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    $\begingroup$ @BMF Fallout is whatever gets thrown into the air from the explosion. $\endgroup$ – Graham Feb 23 at 20:40
  • $\begingroup$ oh, right, okay. I only ever hear "fallout" in conjunction with "nuclear", so that's where my confusion was. The only type of fallout that I wouldn't like is the nuclear transuranic type. $\endgroup$ – BMF Feb 23 at 22:05
  • $\begingroup$ @BMF TBH that probably isn't your biggest concern if the planet is about to freeze to death. A slightly increased risk of cancer is only a problem if you can live long enough for the risk to manifest itself. $\endgroup$ – Graham Feb 23 at 22:37

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