What's the longest plausible orbital period for a habitable planet with a 3:2 spin-orbit resonance?

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?

posted over 7 years ago

Tharaib‭

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