If the Earth were adrift in space, what would happen to its atmosphere?

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If Earth were to drift away from the Sun, its atmosphere would rapidly cool due to the loss of solar heat. The core and magma would provide some residual warmth, but greenhouse gases would only delay the cooling process. The equilibrium temperature would likely drop significantly, leading to the liquefaction and freezing of oxygen and nitrogen within a few hundred to thousand years. The atmosphere would eventually become inhospitable, with temperatures plummeting dramatically. Overall, the planet would transition into a frigid state, drastically altering its environmental conditions.
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If the Earth were slung out of its orbit, away from the Sun's light and warmth, what would happen to its atmosphere? How quickly would it cool? The core and magma would provide some warmth to the surface, but even with our greenhouse gases holding in heat, I assume that everything would turn chilly very quickly. Anyone have any idea what the equilibrium temperature would be? How quickly would it be cold enough to liquify and freeze oxygen and nitrogen? A hundred or thousand years after its escape from our solar system, what would its atmosphere, if any, be like?
 
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Well, how much colder does it get at night? A good guess would be twice that per day.
 
See this post for simulations.
 
// Fixing post give me a second
 
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