# Plausibility check : an habitable exomoon

Is this moon plausible

1. this moon is a little bit smaller than our moon

2. it has thick atmosphere. so much so that floating algae thrive in the wind.

3. the moon is not too close to its planet nor it's too far away. so the moon its not tidally locked

4. its land is very mountainous and tectonically active. so that the sea in this planet resemble a connected mega lakes.

5. it orbit its planet in 4 decades. so the moon have a years long seasons. The moon life has adapted to this.

6. it rotate around a gas giant larger than Jupiter.

7. the planet plants have a blue leaves.

• Here is a useful link that explains that the smallest mass that can retain an atmosphere is 2.7% the mass of Earth or 0.16x10^24. Our moon's mass is 0.07x10^24, so anything smaller can't hold an atmosphere, either. And when it comes to tectonics, please consider this WB.SE question. Finally, please note that I'm not a fan of "realistic" because we know so little about "reality." It's your universe - keep the moon.
– JBH
Feb 24, 2022 at 6:45
• @faddllz Have it made of depleted uranium or osmium or something equally dense (need to do the calculations for that), it'll then have sufficient gravity to hold on to an atmosphere. Feb 24, 2022 at 6:46
• @EveninginGethsemane A modified form of your comment might make for a good question. Depleted uranium doesn't occur naturally, but osmium does. Could enough osmium be added to a moon to give it sufficient gravity for an atmosphere and still permit plant growth?
– JBH
Feb 24, 2022 at 6:49
• "It orbit[s] its planet in 4 decades": Is that 40 years, or is that 40 days? The word "decade" can mean either 10 years or 10 days. Or any group of ten somethings, really. Feb 24, 2022 at 9:57
• Basic orbital mechanics: all objects in orbit about a common mass will sweep equal area in equal time. That is close objects move fast, far objects slow. So an orbit of 40 years implies far away. Feb 25, 2022 at 0:31

1 is not compatible with 2, last part of 5 and 7.

We know that our moon has no atmosphere, so an even smaller moon will likely have no capacity of retaining an atmosphere for the time necessary for life to form.

3, 5 and 6 are also conflicting: orbiting a gas giant in 4 decades is very likely to lead to tidal locking. Again, our moon orbit a rocky planet in something short of 3 decades, and it is locked.

If instead by decade you mean 10 years, it would be difficult for a planet to have a Hill sphere that extended. If it had it, the distance from the central star would be so large that there would be not enough heat available to sustain life or liquids.

from the above it follows that also 4 is unlikely: with no atmosphere is very difficult for liquids to be persistent.

• so, what would be an improvement to this ? Feb 24, 2022 at 6:39
• A decade can mean a period of ten days, true, but it more usual meaning is a period of ten years... Feb 24, 2022 at 9:57

Is this moon plausible

1. this moon is a little bit smaller than our moon

2. it has thick atmosphere. so much so that floating algae thrive in the wind.

3. the moon is not too close to its planet nor it's too far away. so the moon its not tidally locked

1. its land is very mountainous and tectonically active. so that the sea in this planet resemble a connected mega lakes.

2. it orbit its planet in 4 decades. so the moon have a years long seasons. The moon life has adapted to this.

3. it rotate around a gas giant larger than Jupiter.

4. the planet plants have a blue leaves.

No, for several reasons.

It depends on many complicated factors. Parts of what you request will be a lot more plausible than others, and some parts may be totally inconsistent with other parts.

Part One: Moon Size

this moon is a little bit smaller than our moon

You failed to define "smaller". I assume that you mean the dimensions, the radius, diameter, and volume of the moon. And it is certainly physically possible for an exomoon of an exoplanet in another star system to be a little smaller than Earth's Moon.

But Earth's Moon doesn't have a significent atmosphere or water.

So you have to decided whether your moon has an atmosphere naturally, produced naturally and held in by the gravity of the moon, or artificially, created by an advanced civilization which also built a roof all over the moon's surface to keep the atmosphere in, like a gigantic moonbase all over the moon's surface.

Obviously, the smaller a world is, the less big a project would be to give it a roof to retain an artifical atmosphere.

The important quality that determines how long a planet can keep its atmosphere naturally is its escape velocity, which is determined by its mass and its radius.

There is a discussion of the way the escape velocity determines how long a world can retain its atmosphere in Stephen H. Dole, Habitable Planets for Man, 1964, pages 33-39.

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

Note that table 5 on page 35 shows that if the velocities of atmospheric gas remains the same, increasing the escape velocity by 3 times, from twice the gas velocity to 6 times the gas velocity, is sufficient to change atmospheric retention time from zero to infinite.

There are other factors which can increase the rate at which a world loses its atmosphere, but nothing can slow atmospheric loss below the rate dictated by its escape velocity and exosphere temperatures. Only a constant replenishment of gases into the atmosphere can keep atmospheric density the same if the world is losing atmosphere rapidly. And of course all sources of atmosphere are finite and limited.

A new theory suggests that some types of worlds could be habitable at much lower masses than previously believed. These worlds could retain atmospheres for long periods of time, thus permitting water to be liquid on their surfaces, even with masses down to 0.027 that of Earth.

https://earthsky.org/space/small-rocky-exoplanets-can-still-be-habitable/

Hiwever, that study only concerted low mass waterworlds, worlds entirely covered with water, and with atmospheres of water vapor. Obviously such worlds would have a lot of liquid water to replace water vapor lost into space.

https://iopscience.iop.org/article/10.3847/1538-4357/ab2bf2

Since your moon has a lot of land surface, it cannot be a waterworld and so this lower mass limit does not apply.

In "Exomoon habitability constrained by illumination and tidal heating" Rene Heller and Roy Barnes discuss factors affecting the habitability of exomoons.

https://faculty.washington.edu/rkb9/publications/hb13.pdf

On page 20 they discuss the mass range for habitable worlds, both moons and planets:

A minimum mass of an exomoon is required to drive a magnetic shield on a billion-year timescale (MsT0.1M4; Tachinami et al., 2011); to sustain a substantial, long-lived atmosphere (MsT0.12M4; Williams et al., 1997; Kaltenegger, 2000); and to drive tectonic activity (MsT0.23M4; Williams et al., 1997), which is necessary to maintain plate tectonics and to support the carbon-silicate cycle. Weak internal dynamos have been detected in Mercury and Ganymede (Gurnett et al., 1996; Kivelson et al., 1996), suggesting that satellite masses > 0.25M4 will be adequate for considerations of exomoon habitability. This lower limit, however, is not a fixed number. Further sources of energy—such as radiogenic and tidal heating, and the effect of a moon’s composition and structure—can alter the limit in either direction. An upper mass limit is given by the fact that increasing mass leads to high pressures in the planet’s interior, which will increase the mantle viscosity and depress heat transfer throughout the mantle as well as in the core. Above a critical mass, the dynamo is strongly suppressed and becomes too weak to generate a magnetic field or sustain plate tectonics. This maximum mass can be placed around 2M4 (Gaidos et al., 2010; Noack and Breuer, 2011; Stamenkovic´ et al., 2011). Summing up these conditions, we expect approximately Earth-mass moons to be habitable, and these objects could be detectable with the newly started Hunt for Exomoons with Kepler (HEK) project (Kipping et al., 2012).

Their source for 0.1 Earth mass being the minimum mass for a world to have a magnetosphere is:

Tachinami, C., Senshu, H., and Ida, S. (2011) Thermal evolution and lifetime of intrinsic magnetic fields of super-Earths in habitable zones. Astrophys J 726, doi:10.1088/0004-637X/726/ 2/70.

Their sourcse for 0.12 Earth mass being the minimum mass for a world to have a long-lived atmosphere are:

Williams, D.M., Kasting, J.F., and Wade, R.A. (1997) Habitable moons around extrasolar giant planets. Nature 385:234–236.

and:

Kaltenegger, L. (2000) What does it take for a moon to support life? In Proceedings of the Fourth International Conference on Exploration and Utilisation of the Moon: ICEUM 4, ESA SP-462, edited by B.H. Foing and M. Perry, European Space Agency, ESTEC, Noordwijk, the Netherlands, pp 199–201.

Their source for 0.23 Earth mass being the minimum mass necessary for plate tectonics and the carbon-silicate cycle is:

Williams, D.M., Kasting, J.F., and Wade, R.A. (1997) Habitable moons around extrasolar giant planets. Nature 385:234–236

Since you want your moon to have a natural atmosphere and plate tectonics 0.12 Earth mass and 0.23 Earth mass are the lower limits according to those studies.

The Earth has a mean radius of 6.371.0 kilometers and one Earth mass. It has a surface gravity of 1 g, an escape velocity of 11.186 kilometers per seocnd, and an overall density of 5.512 grams per cubic centimeter (g/cm3).

You want your moon to be a little bit smaller than the Moon of Earth.

The Moon has a mean radius of 1,737.4 kilometers, a mass of 0.123 Earth mass, a surface gravity of 0.1654 g, an escape velocity of 2.38 kilometers per second (0.2127 of Earth's), and an overall density of 3.344 g/cm3.

Since the mean radius of the Moon is about 0.2727044 that of the Earth, the Moon has about 0.202803 the volume of Earth.

For you Moon-sized world to retain a long-lived atmosphere it would need at least 0.12 the mass of Earth. That gives it a density at least 5.9170722 times that of Earth, & so 32.26736 g/cm3.

For your Moon-sized world to have plate tectonics, it would need at least 0.23 the mass of Earth. That would give it a density at least 11.3441055 times that of Earth, and so at least 62.534577 g/cm3.

The most dense common element in the universe is Iron, with 7.874 g/cm3. The very rare element Irridium, has a density of 22.56 g/cm3. The equally rare - and very toxic - element Osmium is the densest naturally occurring element, with a density of 22.59 g/cm3.

Matter in the core of a planet will be compressed to higher densities than it would have on the surface. But of course a small world the size of Earth's Moon would not have enough mass to compress its matter much.

You might be able to give your world a little less mass if it is dense enough to have a high enough surface gravity.

The temperatures in Earth's exosphere are 1000 K to 2000 K. Accordig to Dole on page 54, if a planet with Earth like surface temperatures had a maximum exosphere tmperature of 1000 it would have a root-mean-square velocity of Oxygen in the exosphere of 1.25 km/s, and would need and escepe velocity 5 times that, 6.25 km/s, to retain a lot of atmosphere for about 100 million years. Andif the world had an escape velocity 6 times 1.25 km/s, or 7.5 km/s, i t could retainits atmosphere infintely long. But if your world has exosphere temperatures up to 2000 K, it would need an escape velocity a few km/s higher. Let's say maybe 9.5 km/s.

So your world might need sufficient mass within the volume of Earth's Moon to have an escape velocity of 6.25 to 9.5 km/s.

Using this escape velocity calculator http://calctool.org/CALC/phys/astronomy/escape_velocity, I find that a world with the radius of the Moon and 0.085 the mass of Earth would have an escape velocity of 6.24590 km/s. It would have 4.1912 times the density of Earth, or about 23.110604 g/cm3.

A world with the radius of the Moon and 0.197 the mass of Earth would have an escape velocity of 9.50864 km/s. It would have a density 9.7138 times Earth's, or 53.562225 g/cm3.

So using an escape velocity lower than Earth's, but high enough to retain an atmosphere for some time, can reduce the density problem a little.

I note that if a small world is dense enough to have a high enough escape velocity, it might be too dense to have the desired plate tectonics. Rene and Heller suggest that the maximum mass of a habitable world might be about 2 times the mass of Earth the paragraph quoted above:

. Above a critical mass, the dynamo is strongly suppressed and becomes too weak to generate a magnetic field or sustain plate tectonics. This maximum mass can be placed around 2M4 (Gaidos et al., 2010; Noack and Breuer, 2011; Stamenkovic´ et al., 2011).

And obviously extreme densities in a world would also increase the pressure and thus the viscosity and thus decrease circulation.

So if you want your moon to naturally have a dense atmosphere and have palet tectonics, it should have at least 0.25 times the mass of Earth and thus atleast twice the massof Mars, which is 0.107 times the mass of Earth.

Otherwise you should probably make your moon, smaller than the Moon, artificially habitable due to a vaste terraforming project by some advanced group of beings. And quite probably you would have to give your small moon a roof, of matter or of force fields, to keep the atmosphere in.

Part Two: Thick Atmosphere

it has thick atmosphere. so much so that floating algae thrive in the wind.

I have already discussed what may be necessary for your moon to be able to retain a thick enough atmosphere for long periods of time. Of course no world can retain an atmosphere unless it has an atmosphere, produced naturally or artificially.

What thickness of atmosphere is needed for algae to float in the wind?

Triton, the largest moon of Neptune, has a very thin atmosphere about 1/70,000 th the density of Earth's atmosphere, despite having a mass of only 0.00359 Earth mass, and an escape velocity of only 1.455 km/s. That is due to the extremely cold temperatures in its exosphere. I fyou want your floating bacteria to use liquid methane or something instead of water, I suppose that your world could be as small and as cold as Triton.

Streaks on Triton's surface left by geyser plumes suggest that the troposphere is driven by seasonal winds capable of moving material of over a micrometre in size.[45]

I am not sure how that material on Triton compares to the size and mass of your floating algae.

Mars has a mass of 0.107 Earth mass, and escape velocity of 5.027 km/s, and a thin atmosphere, much denser than Triton's but only up to about 0.006 tht of Earth.

The atmosphere of Mars consists of about 96% carbon dioxide, 1.93% argon and 1.89% nitrogen along with traces of oxygen and water.[1][165] The atmosphere is quite dusty, containing particulates about 1.5 µm in diameter which give the Martian sky a tawny color when seen from the surface.[166] It may take on a pink hue due to iron oxide particles suspended in it.[18]

https://en.wikipedia.org/wiki/Mars#Atmosphere

Mars has the largest dust storms in the Solar System, reaching speeds of over 160 km/h (100 mph). These can vary from a storm over a small area, to gigantic storms that cover the entire planet. They tend to occur when Mars is closest to the Sun, and have been shown to increase the global temperature.[183]

https://en.wikipedia.org/wiki/Mars#Climate

Titan, the largest moon of Saturn, has only 0.0225 the mass of Earth and an escape velocity of only 2.639 km/s, only 1.1 times that of the Moon. But - helped no doubt by its very low temperatures and gas velocities - it has a titanic atmosphere compared to those of Triton and Mars, or even Earth.

If your algae could use liquid methane or some other ultra cold fluid instead of water, they could float in the atmosphere of a world as small as Titan.

Observations from the Voyager space probes have shown that Titan's atmosphere is denser than Earth's, with a surface pressure about 1.45 atm. It is also about 1.19 times as massive as Earth's overall,[44] or about 7.3 times more massive on a per surface area basis.

https://en.wikipedia.org/wiki/Titan_(moon)#Atmosphere

I haven't read anythng about the winds or wind-born objects on Titan.

On Earth the winds are strong enough to carry many seeds and spores of various organisms.

Angel hair or siliceous cotton is a sticky, fibrous substance reported in connection with UFO sightings, or manifestations of the Virgin Mary.1 It has been described as being like a cobweb or a jelly.35

It is named for its similarity to fine hair, or spider webs, and in some cases the substance has been found to be the web threads of migrating spiders. Reports of angel hair say that it disintegrates or evaporates within a short time of forming.37

https://en.wikipedia.org/wiki/Angel_hair_(folklore)

Some types of spiders are known to migrate through the air, sometimes in large numbers, on cobweb gliders.2 Many cases of angel hair were found to be these spider threads and, in one occasion, small spiders have been found on the material.8 Linyphiidae spiders frequently cause showers of gossamer threads in England and the Northern hemisphere.[14] Australia and New Zealand have frequent cases, caused by several native species of spiders and by some introduced species of Linyphiidae.[14]

https://en.wikipedia.org/wiki/Angel_hair_(folklore)#Published_explanations

So you find out how the weights of those spiders compare to the weights of algae.

And of course those spiders don't spend all their lives in the air,a s a presumabe you want your alaae to. Perhaps the algae will have sacs containing lighter than air gas, to make their overall bodies lighter than air so they can float.

One way a very small world could have folating alagae would be a world covered with ice kilometers deep, with a global ocean of liquid water below the ice. Thre are a number of such worlds in our solar system,a nd others are suspected to have subsurface oceans.

The smallest such world in our solar system with a known global subsurface ocean is Enceladus, a moon of Saturn, which has a mean radius of 252.1 kilometers, about 0.1451 that of the Moon, and thus about 0.0027 the volume of the Moon. If life can exist in the subsurface oceans of such small worlds, there could be algae floating in the subsurface ocean of your moon, and people might encounter it and other life forms exploring that ocean in submarines.

Part Three: Not Tidally Locked

the moon is not too close to its planet nor it's too far away. so the moon its not tidally locked

The moon could have three conditions with respect to being tidally locked.

1. Tidally locked with respect to the star, but not to the planet.

2. Tidally locked with respect to the planet, but not to the star

3. Not tidally locked to either the planet or the star.

A fourth category would be tidally locked to both, but that seems utterly impossible to me.

A planet orbiting a dim star would be deep within its gravity well, and would likely be tidally locked to the star, which might make it uninhabitable. One reason why scientists are interested in the potential habitability of exomoons is because the forces that create tidal locking for a moon to its planet would be stronger than the forces to tidally lock a moon to its star. Thus any planet sized and otentially habitable exomoon in the habitable zone of a star, even a very dim (and very common) red dwarf star would tidally locked to the planet and not to the star, & thus would have alternating day and night instead of eternal day on one side and external night on the other.

So condition 1, being locked to the star and not to the planet, seems to be impossible. That leaves only the possibile conditions that the moon would be tidally locked to the planet, or that it would not be tidally locked at all.

Many of the moons of the giant planets in our solar system are tidally locked to their planets. For example, in the satellite systemof Saturn, all the moons out to Titan are tidally locked to Saturn. Iapetus, orbiting beyond Titan is also tidally locked to Saturn.

But Hyperion, orbiting between the orbits of Titan and Iapetus, is not tidally locked to Saturn. Hyperion is classified as a regular moon, and all of the moons in the solar system which have ever been suggested as potential abodes of life are classified as regular satellites, except for Triton, an irregular moon, believed to be a captured dwarf planet. So your habitable moon would have to be a regular moon, or else a rare and unusual irregular moon, that like Triton is at least as large as the smallest regular moons.

The Voyager 2 images and subsequent ground-based photometry indicated that Hyperion's rotation is chaotic, that is, its axis of rotation wobbles so much that its orientation in space is unpredictable. Its Lyapunov time is around 30 days.[21][22][23] Hyperion, together with Pluto's moons Nix and Hydra,[24][25] is among only a few moons in the Solar System known to rotate chaotically, although it is expected to be common in binary asteroids.[26] It is also the only regular planetary natural satellite in the Solar System known not to be tidally locked.

Hyperion is unique among the large moons in that it is very irregularly shaped, has a fairly eccentric orbit, and is near a much larger moon, Titan. These factors combine to restrict the set of conditions under which a stable rotation is possible. The 3:4 orbital resonance between Titan and Hyperion may also make a chaotic rotation more likely. The fact that its rotation is not locked probably accounts for the relative uniformity of Hyperion's surface, in contrast to many of Saturn's other moons, which have contrasting trailing and leading hemispheres.[27]

So your moon could be close enough to your planet to be a regular moon, and close enough to be tidally locked to the planet, without being tidally locked, if some factor prevented it from becoming tidally locked to the planet.

With life on your moon, it would have to be large enough to be a spheroid or ellipsoid, gravitationally rounded, but it wouldn't have to be a perfect sphere. So it wouldn't have as irregular a shape as Hyperion. But it might have the other factor of orbiting close to the orbit of an other large moon, and thus having strong tidal forces from that Moon.

Anyway, I gues that is all for today. I will continue later, and I hope with shorter coverage of each point.

Continued on 02-25-2022

As it happens, Hyperion has a mass of about 5.6199 times 10 to the 18th poer kilograms, while Titan has a mass of about 1.3452 times 10 to the 23rd power kilograms, which shold be about 20,000 times the mass of Hyperion.

If your moon is massive enough to be habitable and the other moon which keeps it from being tidally locked has to be about 20,000 times as massive, that other moon would be as massive as a gas giant planet itself and thus your moon would be orbiting a double gas giant planet.

But fortunately scientists don't seem to think that the other moon needs to be so much more massive. According to "Exomoon Habitability constrained by Illumination and tidal heating" Heller and Barnes, 2013, page 20:

https://faculty.washington.edu/rkb9/publications/hb13.pdf

Since the satellite’s rotation period also depends on its orbital eccentricity around the planet and since the gravitational drag of further moons or a close host star could pump the satellite’s eccentricity (Cassidy et al., 2009; Porter and Grundy, 2011), exomoons might rotate even faster than their orbital period.

Considering how massive an exomoon would have to be to be considered potentially habitable, the odds that another moon orbiting the same planet would be many times more massive still would seem to be extremely low, so if the other moon has to be many times as massive as the habitable, there would be no point in discussing such rare situations where a habitable moon rotates faster than its orbital period.

And you might be able to check what:

Cassidy, T.A., Mendez, R., Arras, P., Johnson, R.E., and Skrutskie, M.F. (2009) Massive satellites of close-in gas giant exoplanets. Astrophys J 704:1341–1348.

and:

Porter, S.B. and Grundy, W.M. (2011) Post-capture evolution of potentially habitable exomoons. Astrophys J 736:L14.

have to say about the relative masses of the exomoons involved.

Impacts with other large astronomical objects can change the rotation rates of astronomical objects. Thus your moon could have had its rotation rate speeded up by by such random collisions.

The orbital period of Hyperion around Saturn is 21.276 Earth days. If Hyperion was tidally locked to Saturn its sidereal rotation period with respect to the stars would also be 21.276 days. Hyperion's synodic rotation period is given as about 13 days.

https://en.wikipedia.org/wiki/Hyperion_(moon)#cite_note-11

I think that means the synodic period of Hyperion with respect to the Sun, and not to Saturn. Thus a period of alternating light and darkness on Hyperion would be about 13 days, and thus about 0.611 as long as its orbital period.

If your exomoon had a light/dark cycle or synodic period which was longer,than its orbital, another possibility for a non tidally locked moon, the day cycle would have to be short enough for the moon to be habitable. It could not get too hot during daylight or tooc ould during dark night for life to survive. And in turn the orbital period of the moon would have be shorter than that. Thus the moon would have to orbit closer to the planet that a tidally looked moon at a distance where its day would be the maximum length.

If your exomoon has a synodic period and light/dark cycle shorter than its orbital period, it will have to orbit much closer to the planet that a tidally locked moon with a light/dark cycle of the same length.

In Habitable Planets for Man, 1964, pages 58 to 61, Stephen H. Dole discusses the range of rotation periods for planets habitable foor humans, but was unable to calculate a very firm upper limit. On page 60 he writes:

Just what extremes of rotation rate are compatable with habitabiity is difficult to say. These extremes, however, might be estimated at, say, 96 hours (4 Earth days) per revolution at the lower end of the sacle, and 2 to 3 hours per revolution at the upper end, or at angular velocities where the shape becomes unstable because of the high rotation rate. If you accept Dole's estimations that a habitable world should have a rotation period between 2 or 3 hours, and if your exommoon is tidally locked, and if you know the mass of your exoplanet, you can calculated the orbital distances at which your exomoon will have rotaton periods with in the range of 2 or 3 hours to 96 hours.

"Exomoon Habitability constrained by Illumination and tidal heating" Heller and Barnes, 2013, page 20:

https://faculty.washington.edu/rkb9/publications/hb13.pdf

Mentions the possible day lengths of tidally locked exomoons:

The synchronized rotation periods of putative Earthmass exomoons around giant planets could be in the same range as the orbital periods of the Galilean moons around Jupiter (1.7–16.7 d) and as Titan’s orbital period around Saturn (&16 d) (NASA/JPL planetary satellite ephemerides)4

So Heller and Barnes seem to consider day lengths of about 1.6 to 16.7 Earth days be reasonably suitable for habitability, at least in this paragraph.

If you decide that an exommon with a day between 1.0 and 16.7 o r17.0 Earth days could be habitable if other facters favored habitablity, and if you knew the mass of your giant planet, and if your moon was tidally locked, you could calculate the inner an douter ranges of distances that the moon would have to orbit at.

But of course you do not want your moon to be tidally locked. To be continued in another answer.

• This is a very well through answer. Very big thank you for this answer ! Feb 25, 2022 at 6:44

A continueation of my previous answer:

Part Four: Tectonically Active and Enclosed Oceans

According to current scientific theory, a world could possibly be tectonically active if it has a mass within a rather wide range.

Going back to Heller and Barnes, 2013, on page 20 they discuss the minium mass:

...; and to drive tectonic activity (MsT0.23M4; Williams et al., 1997), which is necessary to maintain plate tectonics and to support the carbon-silicate cycle...

And a maximum mass:

...An upper mass limit is given by the fact that increasing mass leads to high pressures in the planet’s interior, which will increase the mantle viscosity and depress heat transfer throughout the mantle as well as in the core. Above a critical mass, the dynamo is strongly suppressed and becomes too weak to generate a magnetic field or sustain plate tectonics. This maximum mass can be placed around 2M4 (Gaidos et al., 2010; Noack and Breuer, 2011; Stamenkovic´ et al., 2011).

https://faculty.washington.edu/rkb9/publications/hb13.pdf

So according to those calculations, any world with a mass between 0.23 and about 2.0 the mass of Earth would have a possiility of having and nternal dynamo to drive plaete tectonics.

It is believed that have large liquid regions in the core and rapidly rotating can increase the probability that a planet will have an internal dynamo. That is one reason for you to desire to make your moon's rotation period shorter instead of longer.

Venus has a sidereal rotation period of 243.0226 Earth days and a mass of 0.815 Earth.

Like that of Earth, the Venusian core is most likely at least partially liquid because the two planets have been cooling at about the same rate,[107] although a completely solid core cannot be ruled out.[108] The slightly smaller size of Venus means pressures are 24% lower in its deep interior than Earth's.[109]

The principal difference between the two planets is the lack of evidence for plate tectonics on Venus, possibly because its crust is too strong to subduct without water to make it less viscous. This results in reduced heat loss from the planet, preventing it from cooling and providing a likely explanation for its lack of an internally generated magnetic field.[111] Instead, Venus may lose its internal heat in periodic major resurfacing events.[83]

The lack of an intrinsic magnetic field at Venus was surprising, given that it is similar to Earth in size and was expected also to contain a dynamo at its core. A dynamo requires three things: a conducting liquid, rotation, and convection. The core is thought to be electrically conductive and, although its rotation is often thought to be too slow, simulations show it is adequate to produce a dynamo.[114][115] This implies that the dynamo is missing because of a lack of convection in Venus's core. On Earth, convection occurs in the liquid outer layer of the core because the bottom of the liquid layer is much higher in temperature than the top. On Venus, a global resurfacing event may have shut down plate tectonics and led to a reduced heat flux through the crust. This insulating effect would cause the mantle temperature to increase, thereby reducing the heat flux out of the core. As a result, no internal geodynamo is available to drive a magnetic field. Instead, the heat from the core is reheating the crust.[116]

https://en.wikipedia.org/wiki/Venus#Magnetic_field_and_core

So even a planet or moon of the right size might lack an internal dynamo and plate tectonics, due to variousfactors not yet well understood. Thus a science fiction writer who wants plate tectonics on their planet will have to just hope that future discoveries won't show that some aspects of their planet are incompativle with plate tectonics.

so that the sea in this planet resemble a connected mega lakes.

having any connection to the plate tectonics.

How common it would be for your moon's oceans to all be surrouned by land would depend on how much water you moon has compared to Earth. If it has too like surface water, life might not flourish there. Whether the oceans are all surrouned by land at any one time will depend on how the plate tectonics move the continents around the globe and if they make the continents round, or long and thin.

And though it takes tens or hundreds of millions of years for a major reconfiguration of continents, flucuations in the percentage of water tied up in glaciers can raise and lower the sea level over thosuands of years, which can make the difference between separate oceans surrounded by world wide land mass and one world wide ocean surrounding the separate continents.

So it is perfectly possible for your moon to have separate oceans surrounded by one world-wide land mass, though that would change gradually over tens and hundreds of millions of years, and might also change much more rapidly over thousands and tens of thousands of years.

Part Five: Length of Orbit

it orbit its planet in 4 decades. so the moon have a years long seasons. The moon life has adapted to this.

The length of seasons depends on the length of the planet's orbit around the star. If the planet has any axial tilt, at some times one hemisphere will be tilted toward the star and receive more starlight and be hotter, and the other hemisphere will be titled away from the star and will receive less radiation and be cooler. And half a planetary orbit later, the seasons in the two hemispheres will be reversed.

If the planet has no axial tilt, seasons will be caused by the eccentricity of the planet's elliptical orbit. There will be summer allover the planet when the planet is closest to the star and winter everywhere on the planet when the planet is farthest from the star. Winter will last longer than summmer, since the planet will be travellig flower when farther from the star.

Your large exomoon will almost certainly share the planet's axisl tilt and will almost certainly orbit the planet in the equatoral plane of the planet. Thus it will share the seasons of the planet, and the length of the planetary year will determine the length of the moon's seasons.

For the moon to have 4 astronomical seasons which are the same length and each exactly 1 Earth year long, the planet will have to have an orbital period 4 Earth years long. For the moon to have seasons 1.5 Earth years long, the planet will have to have an orbital period 6 Earth years long. For the planet to have seasons 2 Earth years long, the planet will have to have an orbital period 8 Earth years long, and so on.

If the planet has taken billions of years to naturally develop a breathable oxygen atmosphere, the star in the system should be no more massive than a class F2V star or a class F0V star.

A spectral class F2V star has about 1.46 times the mass of the Sun and about 5.13 times the luminosity of the Sun. A spectral class F0V star has about 1.61 times the mass of the Sun and about 7.24 times the luminosity of the Sun.

https://en.wikipedia.org/wiki/F-type_main-sequence_star

If you increased the luminosity of the Sun 4 times, the EED (Earth Equivalent Distance) where a planet would receive as much radiation as Earth gets from the Sun would be 2 times the distance of Earth from the Sun, and thus 2 AU. That is beause illumination received decreases with the square of the distance.

So the EED of a F2V star would be about 2.2659 AU, and the EED of a F0V star would be about 2.6907 AU.

A planet orbiting at the MED (Mars Equivalent Distance) would receive as much radiation as Mars gets from the Sun, and so might be warm enough to be habitable. Mars orbits the Sun at 1.523 AU, so the MED of a F2V star should be about 3.4509 AU and the MED of an F0V star should be about 4.0979 AU.

According to this orbital period calculator:

http://www.calctool.org/CALC/phys/astronomy/planet_orbit

A planet in the EED of a F2V star would have an orbital period of 2.82235 Earth years and one in the MEd would have a period of 5.30454 Earth years. A planet in the EED of an F0V star would have a period of 3.47785 Earth years, and a planet in the MED would have a period of 6.53664 Earth years.

So a year of about 6.53 Earth years and seasons 1.6325 Earth years long are about the longest you can hope for on a naturally habitable moon orbiting a single star.

What if you put the planet and the moon in orbit around two F0V class stars? With twice the luminosity of two such stars, the EED and the MED will be 1.414 times as far, at 3.8046 and 5.7944 AU. With twice the stellar mass of 1 F0V star, the orital period at 3.8046 AU will be 4.13486 Earth years, and at 5.7944 AU will be 5.7944 Earth years.

Suppose that your planet and moon orbit a quadruple F0V star, with two close pairs closely orbiting Earth. With 4 times the luminosity the ED and MED will betwice as far, at 4.5318 and 5.3814 AU. The orbital periods would be 3.80092 and 4.91842 Earth years.

So adding the mass and luminosity of increasing numbers of separate stars to the system will start decreasing the length of the years instead of increasing them.

Oee way to get around that for a habitable exomoon would be to make it and planet orbit beyond the habitable zone of the star, and so receive receive insuffient stellar radiation to be habitable. The moon could compensate for the missing heat from the star by orbiting close to the planet and receiving a lot of tidal heating as a result.

So maybe that process might increase the posisble lenght of years 10 or 20 times, ant least until the light from the star(s) becomes insufficient for plants to survive.

And if the exomoon is not naturally habitable, but orbits a star too young to have naturally habitable worlds, itmight have been terraformed to b ehabitable by an advance civilization.

A spectral class A0V star would have 2.18 times the mass of the Sun and 38.02 times the luminosity.

https://en.wikipedia.org/wiki/A-type_main-sequence_star

The square root of 38.02 is 6.1660, so the EED of an A0V star is at 6.1660 AU, and the MED is at 9.390 AU. The orbital periods would be 10.3531 and 19.4848 Earth years.

A B5V star has a mass of 4.70 Suns and an luminosity of 589 Suns.

https://en.wikipedia.org/wiki/B-type_main-sequence_star

The square root of 589 is 24.2693 , so the EED would be 24.2693 AU and the MED would be 36.962 AU, giving years of 55.1395 and 103.623 Earth years.

I could go on, but more massive and luminous stars emit larger and larger amounts of ultra violent ultraviolet light, and some astrobiologists fear that spectral class F stars, let alone A & B stars, might emit too much of it to be habitable.

And I will continue later.

• this is impressive, thank you so much for this. Feb 26, 2022 at 7:33