I don’t know the answer but let me write down some thoughts.
If I’m a point on the surface of a planet then I spend the day slowly getting warmer as I absorb sunlight and the night slowly getting cooler as I radiate my heat into space. If the days are longer then the temperature I reach during the day is higher, which means that when the night begins I radiate heat more rapidly into space. But conversely by the end of the night I’ve cooled down to a lower temperature so I absorb more heat from the sun at the star of the day.
In fact none of this should matter. Can’t we say that the space at that distance from the sun has a particular temperature, and both planets are in thermal equilibrium with that space, so they have the same temperature? That’s not such a convincing argument, since the space near a star is not a typical thermodynamic system.
What about atmospheres? They should help warm up the (solid) surface of the planet via the greenhouse effect. I guess the faster spinning planet has a thinner atmosphere, because of centrifugal force, so maybe it’s colder.
I think the rate of cooling depends on temperature much more than the rate of warming up, because T_sun—T_planet >> T_planet—T_space. So a faster rotating planet should be warmer.
And this explains a lot. The so called Faint Sun Paradox is then not a problem at all.
Early Earth was much warmer despite of a fainter Sun mostly thanks to its faster rotation. Partly also because of a smaller distance to the Sun back then, but mostly because of its faster rotation.
I don’t know the answer but let me write down some thoughts.
If I’m a point on the surface of a planet then I spend the day slowly getting warmer as I absorb sunlight and the night slowly getting cooler as I radiate my heat into space. If the days are longer then the temperature I reach during the day is higher, which means that when the night begins I radiate heat more rapidly into space. But conversely by the end of the night I’ve cooled down to a lower temperature so I absorb more heat from the sun at the star of the day.
In fact none of this should matter. Can’t we say that the space at that distance from the sun has a particular temperature, and both planets are in thermal equilibrium with that space, so they have the same temperature? That’s not such a convincing argument, since the space near a star is not a typical thermodynamic system.
What about atmospheres? They should help warm up the (solid) surface of the planet via the greenhouse effect. I guess the faster spinning planet has a thinner atmosphere, because of centrifugal force, so maybe it’s colder.
I think the rate of cooling depends on temperature much more than the rate of warming up, because T_sun—T_planet >> T_planet—T_space. So a faster rotating planet should be warmer.
Cool (heh). Good thinking!
Of course.
And this explains a lot. The so called Faint Sun Paradox is then not a problem at all.
Early Earth was much warmer despite of a fainter Sun mostly thanks to its faster rotation. Partly also because of a smaller distance to the Sun back then, but mostly because of its faster rotation.
It’s quite elementary if you think about it.
For now, put the atmosphere aside.
The thing is, that the radiation power is proportional to the T^4. And that the peak temperature matters a lot. Don’t you agree?