How to get a habitable moon without too long day-night cycle?

It appears that there are gas giants in habitable zones of stars, and likely some of them should have moons that are big enough to have an Earth-like world, so that part should be plausible enough.

But tidal locking or too strong tidal forces seem to be a problem for having a stable habitable moon. Tidal locking basically means that same side of the moon will be facing the gas giant, in other words day will be as long as one round around the gas giant, and the gas giant will always be visible in roughly same direction in the sky. The latter doesn't really matter, but the former would probably be a problem if the day-night cycle was more than a few Earth days.

All large moons in the solar system are AFAIK tidally locked, but it will take some time before it happens. When you take formula for the timescale and insert formula for a into it, you get

$$t_{lock} = 3 G^2 T^4 r \mu / (8 \pi^4 m_s) \cdot 10^{10} years$$

or

$$T = \sqrt[4]{8\pi^4 m_s t_{lock} / (3G^2R\mu \cdot10^{10} years)} $$

Where G is the gravitational constant, t_lock the required time in years, m_s mass of the moons in kilograms, R radius of the moon in metres and µ the rigidity of the moon.

ie. mass of the planet does not affect the time it will take, unless I brainfarted something.

https://en.wikipedia.org/wiki/Tidal_locking#Timescale https://en.wikipedia.org/wiki/Orbital_period#Small_body_orbiting_a_central_body

Let's say we want at least two billion years before the moon is tidally locked. Also, assume the mass of the moon to be half of that of Earth and radius about 4800km. When you insert the values, you get required orbital period of 22.2 million seconds or 257 days, which is clearly far too much for the moon's orbit to stay stable in the habitable zone. Though this is curiously more than Venus' orbital period around the Sun, so either the formula isn't all that accurate or I bungled it up...

Anyways, Io's orbital period around Jupiter is only 1.77 days, so the moon could just orbit it tidally locked and still have a relatively short day. But wouldn't a close orbit like this cause uncomfortably strong tidal effects on the moon?

Alternatively, could spin-orbit resonance allow moving the moon further away from the gas giant, without increasing length of day-night cycle, and with the added bonus of not having the gas giant in the same direction? For example, Mercury is locked in 3:2 spin-orbit resonance, meaning it spins three times for every trip around the sun. Apparently higher order resonances like 5:2 are also possible.

https://en.wikipedia.org/wiki/Mercury_(planet)#Spin%E2%80%93orbit_resonance

EDIT: According to this, having an atmosphere could help a planet avoid being tidally locked. It doesn't consider moons, but I'd imagine that the same would apply to moons if they orbit further away from the gas giant, like at a 50 day orbital period? Even if it requires a bit thicker atmosphere than on Earth, like a few bars, that shouldn't be an issue.

https://physicsworld.com/a/exoplanets-could-avoid-tidal-locking-if-they-have-atmospheres/

posted almost 5 years ago

Joku_242‭

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