Suppose that a wandering frozen planet is captured by a star and this planet could develop an human breathable atmosphere. How much time could the process take?

EDIT: the planet is earth-sized with frozen oxygen and nitrogen, no moon or rings

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    $\begingroup$ Can we have a little more information? If the planet is a 200km ball with frozen oxygen and nitrogen it'll take a few weeks for that to melt and then you're good. But if youre needing a natural terraforming process that could take millenia. What's the size? What's the core made of? What things are in the crust? etc. $\endgroup$ – Ash Sep 16 '20 at 8:19
  • $\begingroup$ I have added info, it is an earth sized planet, thank you so much! :D $\endgroup$ – Alessar Sep 16 '20 at 8:21
  • $\begingroup$ "Captured" interstellar wanderers are most likely to wind up in a comet-like highly elliptical orbits, suffering long extremes of cold punctuated by rare searing heat, instead of stable, mostly-round, bucolic planet-like orbits. $\endgroup$ – user535733 Sep 16 '20 at 15:21

If the planet has frozen that much, the core is frozen, in which case the magnetic field is basically gone, and all atmosphere is gone. That means that the planet will not stay habitable forever. (But after warming up it will last a few thousand years)

You need to melt about 2000 trillion tones of oxygen, nitrogen, and other trace gases. Lets assume for sake of simplicity they're all frozen on the top layer of the planet

Frozen oxygen and nitrogen exist below -220C, so lets assume your entire planet is -240C. You'll get a breathable atmosphere at about -180C. I'm also assuming the planet is rotating at a decent rate and isn't stuck one side facing the sun, as that has its own problems.

The specific heat capacity of air is about 1000 J/kg/K.

This needs 120420 Etta-Joules of energy to heat up

The sun gives 430 Etta-Joules per hour.

That's 280 hours before the atmosphere has theoretically entirely returned. That's just under 2 weeks. I'd round this up a bit though for safety, as heat will be sucked into the frozen ground and frozen ocean, and there'll be no greenhouse effect for a while.

As the thing warms up there will be unstable ground, you probably want to keep your distance.

Youll get cycles of flooding; Creeks and rivers will thaw before the big lakes they flow into melt. And those lakes will thaw before the ocean does.

This could be a nasty place to visit even though the air would be breathable, I'd suggest waiting 6 months before stepping foot on the world if it can be avoided.

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    $\begingroup$ Thank you so much Ash, this is amazing :) $\endgroup$ – Alessar Sep 16 '20 at 8:59
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    $\begingroup$ You forgot to mention that the now available oxygen will desperately bind with any atom, going out of the atmosphere $\endgroup$ – L.Dutch - Reinstate Monica Sep 16 '20 at 9:14
  • $\begingroup$ Like an oxydizing environment? So for example lots of rust? $\endgroup$ – Alessar Sep 16 '20 at 9:18
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    $\begingroup$ @Alessar, oceans of rust - like it was on pre-oxygen Earth $\endgroup$ – ksbes Sep 16 '20 at 10:47
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    $\begingroup$ I think it's reasonable to assume that all the good things to bind to wouldve been oxidized before the planet froze. Sure some iron meteors mightve impacted but all the oxygen wont disappear. $\endgroup$ – Ash Sep 16 '20 at 11:46

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