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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?

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    $\begingroup$ 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? $\endgroup$ – Sherwood Botsford Mar 28 '17 at 3:38
  • $\begingroup$ @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) $\endgroup$ – Tharaib Mar 28 '17 at 3:48
  • $\begingroup$ 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. $\endgroup$ – Salda007 Mar 28 '17 at 3:59
  • $\begingroup$ … 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. $\endgroup$ – Jan Ivan Mar 28 '17 at 12:48
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    $\begingroup$ @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. $\endgroup$ – Tharaib Mar 30 '17 at 15:49
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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?

You could also have fun with a Roche World like setup (Novel by same name by Robert Forward)

You have a pair of planet in mutual orbit. If it were earth and twin at Luna's distance you'd have a period, I think of about 2+ weeks (about 1/sqrt(2))

The two don't have to fully locked. You could have one of them appear in the planet's rotating system of reference to take months or years to pass thorugh the sky.

I don't know how stable the climate would be. In another question I posited that if you lenghtened Earth's day to even 100 hours large parts of the planet would be un-inhabitable. Anything borderline desert right now. Places that are cold air traps in irregular terrain.

A slower rotation means smaller coriolis forces. This I think would make for larger storm systems with slower movements. That hurricane sits on top of you for 2 weeks raining 3 feet of rain a day...

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