What's the longest plausible orbital period for a habitable planet with a 3:2 spin-orbit resonance?
I want a planet with a 3:2 spin orbit resonance (which would experience 1/3 of a year of nighttime followed by 1/3 year daylight), but I want
- relatively long periods of dark and night
- liquid water possible
(As with tidally locked planets, I'm assuming a sufficiently thick atmosphere and oceanic circulation could distribute temperature enough to avoid the dark side freezing completely and the hot side completely baking.)
I thus need a planet which is
- as far away from its star as possible (to make the orbital period longer)
- far enough from its star for the hot side to not be destructively hot (although see the effects of thick atmosphere and clouds above)
but which is also
- close enough to the star for the 3:2 orbit resonance to have occurred
- close enough for liquid water (again, see the effects of thick atmosphere)
I was thinking that a cooler star than the sun (maybe K class) would allow the planet to get closer and locked into resonance without being too hot, but a star that is too cool (e.g. a red dwarf) would require the planet to orbit very close and give a very short orbital period.
What kind of star and what distance of planet would be suitable, and what would the orbital period be?