Warming a world by nuking the oceans

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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.

Answer 6

Expanding on @RottweilerOnMarket-day's answer, I've generalized their calculations into formulae.

For a given planet radius $R$, altitude above the surface $H$, and approx. kilotonage of "nuclear" blasts $k$,...

• ...the fraction of sky occupied by the planet's disk at altitude $H$ is given by the angular diameter: $D = -\frac{{\arcsin}(-R/(H+R))}{\pi}$,
• ...the wattage required to maintain an Earthlike atmosphere is about: $W=1.74*10^{17}*\frac{4R\pi^{2}}{5.101*10^{14}}$,
• ...the kilotonage of the blasts in joules: $K=k*4.184*10^{12}$,

We can find the frequency of blasts required to maintain the atmosphere via: $E_{Hz}=\frac{W}{K*D}$

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For a Mars-sized world with radius $3400km$ and 10 Mt explosions at an altitude of $1000km$ we get $E_{Hz}\approx 42Hz$