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Assuming the Moon in question is tidally locked to its parent, then on the facing-side of the moon a significant portion of the day time would be spent in eclipse behind the gas giant, essentially making more than 50% of its day-night cycle dark (and therefore cooling down).

Wouldn't this create a negative feedback loop in its average temperature, since more time is spent cooling down than is spent heating up?

I had this thought earlier and was trying to come up with a reason why it wouldn't happen, but couldn't think of anything. Am I missing something, or shouldn't a habitable moon have the facing-side of its surface permanently encased in ice?

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    $\begingroup$ I'm having a hard time figuring out how this is supposed to result in a feedback loop. (I suspect you actually mean a positive feedback loop that will diverge to infinity, rather than a negative feedback loop that will converge to some stable value.) Shade from the planet might decrease the moon's temperature compared to if it was just orbiting the star on its own, but it should be stable at that new temperature. $\endgroup$
    – Cadence
    May 21, 2023 at 0:37
  • $\begingroup$ Also, you should look through the description of the {hard-science} and {science-based} tags, and pick one that describes this question; they shouldn't be used together. $\endgroup$
    – Cadence
    May 21, 2023 at 0:41
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    $\begingroup$ Callisto is fully eclipsed by Jupiter on every orbit. Its orbit is 16.7 days and it is eclipsed for about 4.6 hours every orbit. That's not so bad ~1% of the time. Io on the other hand orbits every 1.8 days and is fully eclipsed for about 2.3 hours every orbit, still only about 5% of the time. The north pole of earth is fully eclipsed (by the earth) for about 11 weeks of the year. (~20% of the time) And that's not a "runaway" cooling effect. I mean, it's cold, but its average temperature has changed by only 2 degrees or so over the last 100 years (but it's actually getting warmer!) $\endgroup$
    – Wyck
    May 21, 2023 at 0:45
  • $\begingroup$ @Foosic17 See my answer from 05-22-2023. $\endgroup$ May 22, 2023 at 18:31

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Radiation is an inefficient means of losing heat, and the colder the moon gets, the more inefficient. Consequently, it will stabilize at the point at which the decreased radiation counterbalances the increased period of darkness.

(After all, it will never get even to absolute zero.)

Calculating it would depend on the radiation received, the specific heat and insulating properties of the atmosphere, and the percentage of time in the dark.

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    $\begingroup$ Heat redistribution is a thing. If the moon is "habitable" it may have an atmosphere, meaning there is significant heat redistribution in the atmosphere (wind). If it is habitable it also likely has surface water and oceans, and the water of the oceans and storms may redistribute considerable heat. It may very well dictate the direction of the prevailing winds though as colder air rushes away from the eclipsed side at low altitude and warmer winds rush toward the eclipsed side at higher altitudes. Similarly for ocean currents. $\endgroup$
    – Wyck
    May 21, 2023 at 0:57
  • $\begingroup$ @Wyck. The usual definition of "habitable" is having liquid water on the surface. Liquid surface water requires atmospheric pressure sufficient to keep all the water from boiling off. So a habitable moon, and especially a human habitable moon if that is what a writer wants, will have to have an atmosphere, resulting in some heat distribution between light and dark part so the world. And see my answer. $\endgroup$ May 22, 2023 at 18:30
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No problem. Over time the moon will come to equilibrium. The only question is if this final state habitable or not. "Too cold" problem is easily solved by making the star warmer.

"Feedback loop" - where is feedback here? The moon gets less energy than it could without massive planet, as long as it is enough to keep it warm it is warm.

"More than 50% of the time" - why? The moon can't be too close to the planet due to Roche limit (https://en.wikipedia.org/wiki/Roche_limit). For Earth-Moon system Roche limit is 18237 km and from this distance Earth occupies ~40 degrees of the sky. So, if the Moon was as close as possible to Earth, Earth would block a point on Moon surface from the Sun at most slightly more than 10% of the time.

All the surface of your moon would get direct sun light at some point during orbital period. Shadow's effect would be relatively small and depending on atmosphere of your moon it doesn't have to be below water freezing point.

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  • $\begingroup$ Half the time, it would be in the dark merely from facing away from the sun. Plus the time eclipsed means more than 50% $\endgroup$
    – Mary
    May 21, 2023 at 13:09
  • $\begingroup$ See my answer from 05-22-2023. $\endgroup$ May 22, 2023 at 18:25
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The eclipses of the moon by the giant planet should not have a major effect on the moon's climate. The body of my answer has five parts.

Part One: the Habitable Edge.

Apparently gas giant planets have an "habitable edge", and a moon orbiting closer to the planet than the habitable edge would have so much tidal heating from the planet that - combined with other sources of heat - the moon would overheat. A lot of liquid water would become water vapor, which is a greenhouse gas, and that would make the moon hooter and hotter and increase evaporation of liquid water, until all the water on the moon becomes vapor in the atmosphere.

Since by definition a habitable world is one with liquid surface water, an otherwise suitable moon that suffers such a runaway greenhouse effect will become uninhabitable.

I have read that the habitable edge of a gas giant planet would be at a distance of about 5 radii of the planet. So the shadow of the gas giant planet would be about two planetary radii, or one diameter, wide, where it falls on a moon's orbit at a distance of 5 radii from the center of the planet.

A moon orbiting at a distance of 5 planetary radii would have an orbit with a total length of 2 pi r, where r is 5 planetary radii. So the planetary orbit would 31.4159 planetary radii long. Thus the side of the moon facing the planet would spend half the orbit, or 15.70795 planetary radii, in sunlight, minus 2 planetary radii, or a total of 13.70795 planetary radii in Sunlight.

Part Two: Light Reflected from the Planet.

When the moon was between the star and the planet, the side of moon facing the planet would be in darkness, except for light reflected from the planet. Of course the moon would cast a shadow upon the planet, and the shadowed part of the planet wouldn't reflect light back on the moon. But the total side of the planet facing the star should be many times as large as the shadow cast by the moon, so that would make just a tiny reduction in the reflected sunlight received by the moon which would help heat up the moon.

Part Three: Move the Planet and Moon a Little Closer to the Star.

So the shadow of the planet upon the moon would have only a minor effect on the total amount of sunlight which the moon received. That can be compensated by moving the planet and the moon a little closer to their star so that the light of the star is a little more intense at that closer distance.

Part Four: Make the Moon orbit beyond the Habitable Edge.

And that is in the case of a moon orbiting at a distance of 5 planetary radii, right at the habitable edge for the planet. A moon orbiting right at the habitable edge of the planet would be right on the brink of suffering a runaway greenhouse effect, and so being in the planet's shadow for a small period of time during every orbit would help to keep the moon from suffering a runaway greenhouse effect.

And of course moons orbiting farther from their planets than the habitable edge would be in the shadows of their planets for smaller percentages of their orbits and would be cooled less by those periods in shadow.

Part Five" Orbital Planes and Axial Tilts.

Now consider orbital planes. One orbital plane would be the plane the planet orbits around its star in. Another orbital plane would the plane the moon orbits its planet in.

Gravitational effects between a gas giant planet and its moon should make the moon orbit in the equatorial plane of the planet.

If a planet's axis of rotation is at a right angle, 90 degrees, to the plane it orbits in, the planet's equatorial plane will be in the plane of it's orbit around the star. In that case the planet is said to have an axial tilt of zero degrees. If a planet's axis of rotation is in the plane of its orbit around its star, it will have an axial tilt of 90 degrees and the planet's equatorial plane will be at 90 degrees to the plane of the planet's orbit.

Because the Earth's axis of rotation has an axial tilt of about 23 degrees, and because the Moon's orbit is not the plane of Earth's equator, the moon is not eclipsed by the Earth every time it is on the far side of Earth from the Sun.

The moon is on the far side of Earth about 12 or 13 times in a year, but only has an average of two lunar eclipses each year.

It would be easy to design a star system where a moon wouldn't ever be eclipsed by its planet.

Draw a circle representing the gas giant planet. Make it two planetary radii wide. Draw parallel lines from the planet two radii apart to represent the shadow of the planet in space. And then measure five planetary radii from the planet.

Put a tiny moon right above the shadow of the planet, and at a distance of 5 planetary radii from the center the planet and then measure the angle necessary which should only be about 10 degrees or something. If a moon orbits in the equatorial plane of the planet and at the habitable edge of its planet, that is the number of degrees the planet's axial tilt needs to be for the moon to never be in the shadow of the planet. The farther the moon orbits beyond the habitable edge, the lesser the axial tilt of the planet needs to be.

The four giant planets in our solar system have varying axial tilts. Jupiter 3.13 degrees, Saturn 26.73 degrees, Uranus 97.77 degrees, Neptune 28.32 degrees. So it seems fairly probable that a gas giant planet with a habitable moon will have an axial tilt high enough for the moon to never be in the the planet's shadow.

Part Six: Atmospheric Distribution of Heat.

Planets orbiting in the habitable zones of red dwarf stars would probably be tidally locked to the stars, so that one side always faced the star and the other side always faced away from the star. And it has been feared that such worlds would loose all their atmospheres which would freeze solid on the eternally dark and cold sides of the planets.

n contrast to the previously bleak picture for life, 1997 studies by Robert Haberle and Manoj Joshi of NASA's Ames Research Center in California have shown that a planet's atmosphere (assuming it included greenhouse gases CO2 and H2O) need only be 100 millibar, or 10% of Earth's atmosphere, for the star's heat to be effectively carried to the night side, a figure well within the bounds of photosynthesis.[23] Research two years later by Martin Heath of Greenwich Community College has shown that seawater, too, could effectively circulate without freezing solid if the ocean basins were deep enough to allow free flow beneath the night side's ice cap. Additionally, a 2010 study concluded that Earth-like water worlds tidally locked to their stars would still have temperatures above 240 K (−33 °C) on the night side.[24] Climate models constructed in 2013 indicate that cloud formation on tidally locked planets would minimize the temperature difference between the day and the night side, greatly improving habitability prospects for red dwarf planets.[4] Further research, including a consideration of the amount of photosynthetically active radiation, has suggested that tidally locked planets in red dwarf systems might at least be habitable for higher plants.[25]

https://en.wikipedia.org/wiki/Habitability_of_red_dwarf_systems#Tidal_effects

Sop atmospheric distribution of heat should keep the dark sides of habitable moons from becoming too cold and the light sides from becoming too hot, especially since their day and night cycles would be a lot shorter than the eternal night and eternal day of tidally locked worlds.

Conclusion:

Although the climate of another world is hard to calculate the factors mentioned above should make it reasonable for a planetary mass moon orbiting a giant planet to not have significant cooling problems resulting from eclipses by the planet.

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