On Fri, Oct 23, 2015 at 07:50:27PM +1100, Rob O'Connor wrote:
> Tim Little wrote:
> > Mean surface absolute temperatures go roughly with the fourth root of
> > irradiance...
>
> Hello, stranger! Welcome back.
>
> Yes, Stefan-Boltzmann is a very useful starting point.
> Albedo and greenhouse effect will modify things a bit.

Yes, especially if you're talkign about converting a water/rock/forest
surface with some greenhouse gases into snow and ice.  In the medium
term that albedo may "trap" a world into remaining a snowball even
after the irradiance is restoyred.

Over the *long* run volcanic activity would likely push CO2 into the
atmosphere, and without oceans or life it wouldn't be sequestered.
Likewise white snow and ice may get somewhat covered by dust and rock
over time without much precipitation from the extremely dry, cold air
to replenish it.

So eventually the iceball may warm back up again, and possibly even
overshoot into a hothouse depending on many factors.

> Luminosity varies with (star radius)^2 and (Temperature)^4, right?.

Yes, and irradiance inverse proportional to the sqqare of orbital
radius.  The net effect being irradiance proportional to

  (star's angular diameter)^2 (star temperature)^4.

Reasonably habitable planets have a pretty narrow temperature range.
Among such worlds, a hotter primary would appear much smaller in the
sky, and a cooler primary would have to appear quite a bit larger to
maintain a similar planetary temperature.

- Tim