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An Earth mass terran planet is orbiting a sun-like star at 2AU. I understand the limit for CO2 greenhouse effects is 1.67AU for whatever reason (giving a conventional habitable zone limit), but perhaps other gases like methane or even hydrogen could continue from that point.

At 1AU, using the formula T=(F/σ)1/4 and plugging in an absorption of 240W m^2, you get: 255.068627752. Earth's equilibrium temperature is considered to be 255K or -18.15 celsius, but the Earth's actual average surface temperature is 16 degrees celsius or so (and rising because of global warming). Earth's atmosphere and greenhouse effect has to add 34 or more degrees celsius.

At 2AU, you should recieve 1/4 the solar flux right? So 60W m^2. Plugging that into the equation gives you 180.360756351K or -92.78924364899999 degrees celsius. Let's say -93 degrees celsius. To reach 16 degrees celsius at twice the distance from the sun, the Earth would need to add 109 degrees, so it needs a greenhouse effect just over three times as strong as what it currently has.

I assume however, that the contributions of greenhouse gases are highly non-linear and you can't just triple the CO2 concentration to get triple the effect. Triple the CO2 and it makes up 0.12% of the atmosphere. I assume this wouldn't kill us, but it's clearly not enough.

If you actually calculate the amount of extra CO2 and/or other greenhouse gases you need, like methane (which is a stronger greenhouse gas to be fair), does the end result become ridiculously toxic to humans?

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  • $\begingroup$ Ozone is a greenhouse gas, too, so perhaps a thick layer of ozone in addition to higher methane and CO2 concentrations that aren't quite enough to kill humans and maybe we're getting close? $\endgroup$
    – TheRaptorsClaw
    Commented Jan 30, 2020 at 2:36
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    $\begingroup$ Ozone is 1000 times as strong as CO2 in causing global warming. However, ozone is short-lived, and decays in the atmosphere much more quickly than CO2. Over a 20-year span, the global warming potential of ozone is much less, roughly 65 times CO2. Alternatively, nitrous oxide (300x CO2), but this does destroy ozone, so maybe not at the same time. (tried to edit to stay in one comment but couldn't) $\endgroup$
    – TheRaptorsClaw
    Commented Jan 30, 2020 at 2:42
  • $\begingroup$ What about excess methane gas? Methane is also short-lived compared to CO2, but perhaps some process on the planet's surface steadily produces steadily high quantities of methane? $\endgroup$
    – arpanet101
    Commented Jan 30, 2020 at 4:44
  • $\begingroup$ CO2 gets less effective as a greenhouse gas the further you get from a star because its Rayleigh scattering effects begin to outweigh its greenhouse effects - effectively bouncing more light into space than trapping it as the atmosphere gets colder. Imo you can't just add more air the further you get from a star, because it begins to behave differently at a distance. Would such an answer as a frame-challenge be helpful or not? $\endgroup$
    – Zxyrra
    Commented Jan 30, 2020 at 5:31
  • $\begingroup$ Even WATER VAPOR is a better greenhouse gas than CO2. Just allow a 2-3x thicker atmosphere, with corresponding greater amounts of greenhouse gases between the surface and the sky. $\endgroup$
    – user79911
    Commented Oct 28, 2020 at 16:22

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FWIW CF4 & SF6 are very powerful greenhouse gasses. If you want a large greenhouse effect & breathable atmosphere you could reduce the amount of CO2 required IF you have the industry on the planet needed to make the CF4 or SF6.

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