# 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?

• Not clear why you need a resonance. E.g. Venus has a very long day, but AFAIK is not locked to anything. Would it not be sufficient to have a late impact in planet formation that cancelled most of the angular momentum? Mar 28, 2017 at 3:38
• @SherwoodBotsford Good point. I could have an arbitrary distance from the star with arbitrary day/night periods. I was overthinking. Make that an answer and I'll accept it (since it answers what I want rather than what I asked for) Mar 28, 2017 at 3:48
• Just don't give it a moon of significant mass. Something the size of our Moon would probably have enough tidal pull to break a resonance that slow and increase the planet's rotation. Mar 28, 2017 at 3:59
• … with tons of volcanic activity it could be pretty far. Add wind for constant temperature around planet and you have a nice piece of rock for life. Other requirements are … too specific. Mar 28, 2017 at 12:48
• @MolbOrg I'm not sure you have understood the question - it simply says "How far from a star can a planet in 3:2 resonance be while remaining habitable?" This has an answer; if I were to remove the mention of resonance there would be nothing left to answer. Sherwood Botsford did not point out that my requirements don't make sense; he simply pointed out that if what I want is for the planet to have a very long day, I don't need an orbital resonance to get it. That doesn't mean there is a conflict between my wishes and real life; that just means there is a simpler way to achieve my wishes. Mar 30, 2017 at 15:49