Some planet temperature questions

[ajtribick]

I'm currently using the formula

Tplanet = Tstar * [ (1-A)/4 ]^0.25 * SQRT ( Rstar / a )

Tplanet = planet temperature
Tstar = star temperature
A = planet albedo
Rstar = star radius
a = orbit semimajor axis

As far as I know this handles the fact that M-class stars produce more infrared for the same amount of visible light than G-class stars do.

How would this be modified for multiple star systems?

Also, what kind of values for Tplanet allow the planet to have liquid water (Earth being around 260K)?

[granthutchison]

Take a look at this thread, where we discussed this problem before:
http://shatters.net/forum/viewtopic.php?t=3325

The Evil Doctor's equation is different from your own, but the same principle applies: raise to the fourth power, add fluxes, take the fourth root.

As for the temperature compatible with liquid water, it depends on the greenhouse effect of your planet's atmosphere, which is what drags Earth's real average temperature above the sub-zero values calculated from the modified black-body equation. If your imagined planet is Earthlike, then you should try to match the value your equation calculates for the real Earth. But you could go for a colder calculated temperature if you had more greenhouse gases in the atmosphere of your imagined planet.

Grant

[ajtribick]

Thanks for the raise ^4 information.

As far as I know there comes a point where carbon dioxide clouds start to form and this is usually taken as the outer region of the habitable zone, likewise if the planet is too far in it won't be able to support liquid water.

What temperature values would these limits correspond to?

[granthutchison]

Kasting et al's classic Icarus paper gave the limits for the Sun's "habitable" (=liquid water) zone as 0.95AU to 1.37AU, with the inner limit determined by the onset of moist greenhouse at 1.1 times the Earth's level of insolation, and the outer limit at 0.53 times Earth insolation, at which point CO2 clouds begin to offset the required CO2 greenhouse.
You should be able to work backwards to the corresponding temperatures.

Grant

[granthutchison]

Oh, one more thing that may or may not be of use, depending on what you're doing with these data. If you want a shirt-sleeves outdoor habitat for humans, you're constrained to very much lower levels of CO2. With the toxic cut-off at about 10mbar, you can only cope with an insolation around 0.85 of Earth's before the temperature drops below freezing - equivalent to around 1.08AU from the Sun.
Humans can cope with higher levels of CO2 (50-100mbar) for short periods, but at the expense of huge hyperventilation and feeling absolutely dreadful.
150mbar renders you unconscious after a few breaths, and anything more than 200mbar sends you into immediate convulsions.

Grant