# What conditions to make this habitable moon plausible?

I'm trying to figure out how to make this gas giant moon habitable.

Here are the factors involved:

Moon is sub-temperate, mountainous with a nitrogen-oxygen atmosphere, with the planet being mainly made up of coastal forests, vast highlands, and massive mountain ranges. Hydrosphere is both active and stormy, with there being snowy winters and short warmer summers.

Moon is NOT tidally locked.

The gas giant needs to be ringed.

The system is a trinary star system with two red dwarfs and a G-class star (exactly like ours). The two red dwarfs orbit the yellow star.

The Gas giant and moon should be in the Goldilocks Zone, but the gas giant has extensive moon system similar to our gas giants.

The Gas giant does not have any moons similar to Jupiter's Io.

The Gas giant has a 23 degree tilt.

What conditions are needed to make this moon possible?

• How are the stars arranged? Jul 5, 2020 at 23:57
• Basically the two red dwarfs orbit the yellow sun. Probably should add that in huh? Jul 5, 2020 at 23:59
• Well the little ones could orbit the big one, or the big one could orbit the tight binary of the two little ones. Or one red could be far out and the other close in. If you have some preferred arrangement that makes a difference for the planets. Jul 6, 2020 at 1:25
• somehow it's doubtful a moon like yours would be able to avoid being tidally locked. It's old enough to have developed evolved life (forests). See this question: worldbuilding.stackexchange.com/questions/39952/… Jul 7, 2020 at 9:57
• HOW do the two red dwarfs orbit the G star? One could be orbiting it closely while the other may be at the outskirts of the system. Anyway since the planet has to be in the goldilocks of G then its distance from it will be approximately 1AU. At that distance the luminance of the red dwafs will be negligible. See en.wikipedia.org/wiki/Habitability_of_red_dwarf_systems Jul 8, 2020 at 16:28

• atmosphere retention

You will undoubtedly have to tweak the parameters of your planet in order to get the desired weather patterns. However, these two factors seem most important with respect to habitability.

Before getting into the weeds, here’s a list of definitions for variables I’ll use:

• $$R_m$$, the moon’s radius
• $$M_m$$, the moon’s mass
• $$L_{s}$$, the combined average luminosity of the three-sun system
• $$D$$, the distance of the planet-moon system from the three-sun system
• $$G\approx 6.7\cdot 10^{-11} \space\text{Nm}^2/\text{kg}^2$$, the gravitational constant
• $$k\approx 1.4\cdot 10^{-23}\space \text{J}/\text{K}$$, the Boltzmann constant

Alright, let’s go! (Note: I’m bound to have made some computational error somewhere below. Hopefully it doesn’t affect my estimates too much, and they’re still within the right order of magnitude. Bonus points if you find a mistake!)

Atmosphere retention

No matter how massive or cold your planet is, it will always continuously lose some of its atmosphere (as long as this atmosphere is gaseous). This is because not all of the atmospheric gas molecules have the same speed - their speeds are random, following the Maxwell-Boltzmann Distribution. At all times, some of the molecules will be moving fast enough to escape. The question is - how long do you want your atmosphere to last?

The escape velocity for your moon is approximately equal to $$v_{\text{esc}} = \sqrt{\frac{2GM_m}{R_m}}$$ and the root-mean-square velocity of gas molecules in a gas of temperature $$T$$ is equal to $$v_{\text{rms}} = \sqrt{\frac{3kT}{2m}}$$ where $$m$$ is the mass of the gas molecule in question. You certainly don’t want $$v_{\text{rms}}>v_{\text{esc}}$$, or your whole atmosphere will be gone in an instant. So, at the very least, you need

$$\sqrt{\frac{3kT}{2m}} \lt \sqrt{\frac{2GM_m}{R_m}}$$

or, for a molecule of diatomic oxygen,

$$\frac{M_m}{R_m T} \approx 2.92\cdot 10^{12}\frac{\text{kg}}{\text{m}\cdot\text{K}}$$

For a moon the size of Deimos (which is almost certainly much smaller than yours) and with an average surface temperature equal to Earth’s, the LHS of this inequality is approximately $$8.3\cdot 10^{8}$$. That’s well below this rudimentary upper limit - so far, so good.

Let’s get a little more nitpicky. Remember what I said before about how some of your planet’s atmosphere will always be escaping?

Assuming the atmosphere’s depth is negligibly small compared to the planet’s radius, we have that the surface area of atmosphere exposed to space is approximately $$4\pi R_m^2$$. According to the Maxwell-Boltzmann distribution, if $$T$$ is the average temperature, then the proportion that have achieved escape velocity at any given time is equal to

\begin{align}\alpha_{\text{esc}} &= 2\sqrt{2\pi}\int_{\sqrt{GM_m m/kTR_m}}^\infty v^2 e^{-v^2}dv\\ &= \frac{2\xi e^{-\xi^2}+\sqrt{\pi}\text{erfc}(\xi)}{4}\\ &\sim \frac{\xi e^{-\xi^2}}{2} \end{align} for reasonably small values of $$\xi$$, where $$\xi=\sqrt{\frac{GM_m m}{kT}}$$

As an estimate, let’s use the Moon’s mass and radius and Earth’s surface temperature (and consider diatomic oxygen molecules). This yields approximate values of $$\xi\approx 18.5$$ $$\alpha\approx 2.13\cdot 10^{-148}$$ Yowza, that’s a tiny value of $$\alpha$$! The volume of atmosphere that would escape over the course of $$t$$ seconds would be approximately equal to $$4\pi\alpha R_m^2 v_{\text{esc}} t$$ But I’m not going to proceed further with the calculations. The value of $$\alpha$$ is so microscopically tiny that it will basically overwhelm the other factors in the above expression. Looks like your planet’s atmosphere is probably safe!

If you really want to make sure your atmosphere is secure, I’d recommend the following additional precautions:

• Make your planet nice and dense. This keeps $$R_m$$ low while driving up the value of $$M_m$$, which will make $$\alpha$$ even tinier.
• Give your moon and the planet it orbits a hefty magnetic field to deflect atmosphere-destroying cosmic rays.

Now for the easy part! This won’t be nearly involved as the above.

I claim that any given point on your moon’s surface spends about $$1/4$$ of the time in the daylight and $$3/4$$ of the time in the dark, under the following assumptions:

• no tidal locking, as stated in the question
• the moon’s orbit is independent of position of the planet it orbits around the sun
• the gas giant is massive compared to the moon
• the three stars in this ternary star system are relatively close to each other and very far away from the planet and its moon

Why? Well, about $$1/2$$ of the time, the moon is on the opposite side of the planet, so it receives no light. When it is on the lit side of the planet, only $$1/2$$ of the moon’s surface is lit at any given time. Thus, for any point on the moon’s surface (poles excepted), it is lit about $$(1/2)(1/2)=1/4$$ of the time.

This means that, in order to maintain an Earth-like climate and temperature, something must compensate for this increased duration of night-time. Here are some suggestions:

• Greater amount of solar radiation. There are three stars in the system, after all.
• Increased luminosity $$L_s$$ of the stars.
• Smaller distance $$D$$ from the three stars. It wouldn’t have to be much smaller, though, since intensity at a distance $$D$$ is proportional to $$1/D^2$$.
• Lower albedo, to avoid reflecting away solar energy.
• Lots of greenhouse gases to help trap solar radiation energy.

Here are some other non-sequitur speculations about what your moon might be like:

• You mentioned that you didn’t want there to be any tidal locking, but if there’s any significant amount of liquid water on the planet’s surface, the gravitational pull of the gas giant will exert significant force upon it. At the very least, this could cause some very extreme tidal rising and falling (exacerbated by the planet’s low gravity), creating vast tidal zones on the planet’s surface.
• As mentioned above, the day-night cycle on the moon will be wacky, nothing like the regular half-day-half-night cycle of Earth. There will be a long stretch of darkness (when the moon is behind the planet), followed by a series of day-night cycles whose length depends upon the rotational velocity of the moon, and then a return to darkness. I wonder how this will affect the circadian rhythms of animals and photoperiodism of plants on the surface?
• Since the moon spends a significant amount of time on the dark side of the planet, freezing/thawing will be common. As temperatures will rise and fall rapidly as the moon moves into and out of the planet’s shadow, you can expect some crazy weather (think massive cyclones) as a result.
• So it might be better for the moon to be a bit more colder than sub-temperate then huh? Jul 6, 2020 at 2:41
• @SCPilot You could pull off temperate, I think. Maybe make the sun really hot during the daytime and the atmosphere very humid, so that it retains much of its heat during the nighttime. Jul 6, 2020 at 11:16
• Why would the moon be in the shadow of the gas giant for half of its orbit? The moon should be orbiting quite far from the gas giant to avoid tidal locking (if that is at all possible given the OP conditions). So the shadow of the planet would cover the moon only for a small portion of the orbit. Even less in case of a highly elliptic orbit. Jul 7, 2020 at 9:54
• @DuncanDrake Good point, I kind of assumed that the moon would be very small in comparison to the gas giant and that it would be rather close. Jul 7, 2020 at 11:31
• @DuncanDrake so the moon would still be able to get some sunlight from the third suns then correct? How would a highly elliptic orbit affect the planet? Jul 8, 2020 at 14:53

If you plan to write stories set on planets or moons which are more or less habitable for humans and other advanced multi celled lifeforms with biochemistry similar to that on Earth, what you need to do is find a copy of Stephen H. Dole, Habitable Planets for Man (1964, 2007).

https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf[1]

It is a well known fact that some Earth lifeforms thrive in environments where humans would instantly die if teleported into, such as miles high in the air, miles deep in the ocean, or miles underground in rock. And humans would also die swiftly if teleported to the majority of the surface of the planet Earth, such as the surface of the ocean, the surface of deserts, the surface of ice sheets, etc., despite some Earth lifeforms flourishing in those places.

So most scientific discussions about the habitability of other worlds discuss their habitability for life forms similar to any type of life on Earth in general, not for large land swelling oxygen breathing animals like humans in particular. Thus most scientific discussions list as habitable many possible worlds which would be instantly fatal to unprotected humans teleported there.

That is why Habitable Planets for Man is especially useful for science fiction writers.

Dole describes the range of star types suitable for having habitable planets in orbit around them. Since it takes billions of years for a planet to become habitable for humans, the star has to stay on the main sequence for billions of years. Fortunately type G and type M stars will stay on the main sequence long enough. There is considerable scientific uncertainty whether class M red dwarf stars can have habitable planets, so you will probably want to have your gas giant and habitable moon orbit the type G star.

Here is a link to the Wikipedia article on multiple star systems.

https://en.wikipedia.org/wiki/Star_system#:~:text=Multiple%2Dstar%20systems%20are%20called,or%20septenary%20with%20seven%20stars.[2]

And note specially the hierarchical structure of multiple star systems which are old enough to have habitable planets.

https://en.wikipedia.org/wiki/Star_system#Hierarchical_systems[3]

So your triple star system is likely to consist of a pair of stars and a single star, and the distance between the pair of stars and the single star is likely to be several times the distances between the stars in the pair - possibly tens, hundreds, or even thousands of times as far.

Your giant planet and habitable moon could orbit in an S-type orbit around one of the stars, or in a circumbinary or P-type orbit around two of the stars. But because of the hierarchical structure of multiple star systems, it seems highly unlikely that a planet orbiting around all three stars could orbit close enough to any of the stars to have habitable temperatures.

https://en.wikipedia.org/wiki/Habitability_of_binary_star_systems[4]

Examples of exoplanets in S-Type orbits, and others in P-type orbits have been discovered.

If your giant planet and habitable moon orbit around one star in an S-type orbit it is more likely to be class G star than a class M star, although a moon tidally locked to its planet instead of to its star would avoid some of the problems with having a habitable planet of a class M red dwarf. You say that you don't want to have your moon tidally locked to its planet, which will be a problem.

If your giant planet and habitable moon orbit around two stars in a circumbinary or P-Type orbit, they are more likely to be the class G star and one class M red dwarf instead of two class M red dwarfs.

Because of the hierarchical structure of a triple star system, only the one star or two stars that the planet and habitable moon orbit should be close enough to have visible discs in the sky of the moon. The other two stars or one star should appear as two points or one point of light in the sky of the moon, although probably extremely bright.

Science fiction writers and scientists have considered the possibility of life on planet sized exomoons orbiting giant exoplanets.

https://en.wikipedia.org/wiki/Habitability_of_natural_satellites#:~:text=The%20habitability%20of%20natural%20satellites,have%20environments%20hospitable%20to%20life.&text=Tidal%20forces%20are%20likely%20to,potential%20habitability%20of%20natural%20satellites.[5]

Heller, René; Rory Barnes (2012). "Exomoon habitability constrained by illumination and tidal heating" Astrobiology. 13 (1): 18–46 is an important scientific discussion of the habitability of exomoons worthy of study.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549631/[6]

Another important article is:

Heller, René (September 2013). "Magnetic shielding of exomoons beyond the circumplanetary habitable edge". The Astrophysical Journal Letters. 776 (2): L33.

https://arxiv.org/abs/1309.0811[7]

You might also want to check my answers to questions like:

https://worldbuilding.stackexchange.com/questions/175614/temperatures-on-an-earth-with-a-week-long-rotational-period/175719#175719[8]

https://worldbuilding.stackexchange.com/questions/174597/is-there-a-plausible-way-to-have-a-gas-giant-with-two-or-more-earth-to-mars-size/174624#174624[9]

https://worldbuilding.stackexchange.com/questions/174401/what-types-of-flora-would-flourish-on-a-tidally-locked-moon/174453#174453[10]

Since I quote from some of the sources I mentioned above.

• I keep seeing people saying that a lot of moons of gas giants are going to be tidal locked. Jul 6, 2020 at 19:51