How quickly could a rogue Earth return to habitability after a deep freeze?

Question

Background
A large star makes a relatively close approach to a solar system like our own and the orbits of many of the planets are badly perturbed. A planet similar to Earth is in the wrong place at the wrong time and receives a particularly strong gravitational pull from the passing star that flings the planet out into interstellar space. Millions of years pass and by a strange coincidence this rogue planet blunders into another very similar solar system and is captured into an orbit that approximates to that from where it came from (strange but true for the purposes of this question).

Human explorers arrive in this new solar system shortly after the rogue Earth arrives. This rogue Earth is now starting to thaw but has not yet reached a stable thermal equilibrium as the process will take some time.

Question
How long after the capture of the rogue Earth before the human explorers can safely land on the planet, establish a base making use of local resources and how long before they can go outside without protective clothing?

Assume Current technology level plus what might reasonably be foreseen within the next few hundred years (quite a lot of scope).

Answer 1

Amount of water on Earth is estimated at 1.386 billion km³ - let's get rid of the decimals and take it at 1 billion km³. Means 10⁹⁺⁹⁼¹⁸kg of water.

Let's take the average initial temperature at -200C, to account for some heating done by the planet's core and energy gained by various tidal sloshing happening during planet's braking and getting into the parking spot at destination.

Now, the specific heat capacity of water and ice are, respectively 4.187 kJ/kgK and 2.108 kJ/kgK with the heat of fusion for ice (which, in reverse, is how much heat you need to make a kg of ice to melt) is 333kJ/kg - yeap, no mistake there, those weak hydrogen bond forces that keep the water as a crystal surely pack a punch.

So, to melt that ice to 20C, you need:

• heat the ice to 0C - takes 200*2.1*10¹⁸kJ = 4.2e+20kJ
• melt the ice to water at 0C - takes 333*10¹⁸kJ = 3.3e+20kJ
• heat the water to 20C - takes a puny 20*4.187*10¹⁸ kJ or about 8.3e+18 kJ. We're gonna neglect this.

Grand total, with a single decimal 7.5e+20 kJ.

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Total solar irradiance upon Earth - 1.365 kilo⁠watts/sqm. Allowing some loss for reflection/scattering in the atmosphere, we get 1kW/sqm.

At a planet radius of 6300km (a wee smaller than the Earth), we get the planet's cross-section on the solar flux of 1.25e8 sqkm = 1.25e14sqm.

Let's assume the planet is painted as black as the space where it came from (boy, surely lotsa smoke there from those burning stars) and happily absorbs all the solar radiation (minus atmospheric losses).

With the above we get 1.25e14 kJ every second. To get to the total energy required to melt that cold ice and make luke warm water, is gonna take 7.5e20/1.25e14 = 6000000 seconds.

Which is to say, the planet cannot thaw in less than 70 Earth-days.

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Now, the things are a bit more complicated:

• the atmosphere won't kick in until the gases evaporate. Which may be a blessing and a curse, 'cause of course the planet is going to receive more energy without an atmosphere (10%-20% more), but is going to lose part of the energy by radiation at night
• there's no way all that ice is going to absorb all the energy, 'cause albedo
• there will be some ice that won't melt, around the planet's poles
• there's not only the water, but at least some 20 or so meters of soil would need to thaw as well
• once the equatorial areas are ice free, the energy is going to be absorbed faster and the atmosphere will distribute the heat towards the poles, accelerating the process...
• ... but with the water getting into the atmosphere, the clouds are gonna reflect more.

Let's say the thawing of the top soil amount for another 25% and, as we ignored over 0C temperature anyway, let's say the ice albedo allows only 5% of the energy to contribute to heating.

In this case we have 70d*1.25/0.05 = 1750 Earth-days = 5 Earth-years to be considered as the new "lower limit, can't heat it faster".

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One on top of the other, feeling of guts, I'd say one should expect a no-longer-deep-space-frigid planet no sooner than somewhere in the 100-1000 Earth years as order of magnitude.

Answer 2

It may be a while before the planet becomes habitable

Snowball Earth hypothesis posits that in the past there were periods when Earth was frozen all over. This is scientifically plausible. However, it is not clear how the Earth can recover from such overwhelming ice age. Even if it is staying in a comfortable orbit and receiving plenty of sunshine, ice and snow will reflect most of that sunshine back to space, and planet would remain frozen.

Current explanation for the eventual thawing is that greenhouse gases accumulate in planetary atmosphere over millions of years, eventually causing climate equilibrium to shift and glaciers to melt.

In the case of an Earth-like rogue planet it is unlikely that its atmosphere would contain an abundance of greenhouse gases. Technically it might contain a plenty of methane, for example, but then it won't be exactly Earth-like. So your humans may have to accept that the new planet would stay frozen for millennia. Another interesting opportunity is to induce global warming, so the process can be shortened to mere centuries.

But there are good news. After the planet is ejected from its original system, its atmosphere would be frozen and remain intact for many million years. This means that oxygen and ozone, if they were originally present, would be restored once the planet gets close to a star. You humans can land on this planet, and potentially breathe the air without masks - they only would have to dress warmly.

Answer 3

Explorers equipped to travel between stars ought to have no problem landing safely on a surface at just a few Kelvins -- the hazards will be the same as they'd been landing on Kuiper belt type ice-ball objects that have never been warm.

Internal heat from the planet's core means that as long as it hasn't been wandering for hundreds of millions of years, the crust shouldn't be more than a few degrees cooler than usual by the time you're down a couple kilometers -- so it's only the top layers and oceans we have to worry about (the frozen-out atmosphere will sublimate in a matter of years once it's getting sunlight at habitable-zone rates). It will likely take centuries, at least, and possibly as much as hundreds of centuries, for the "dead zone" between the surface and the core-heated deeper crust to thaw, however. Ground water will be frozen long after the oceans have recovered (at least thermodynamically).