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Vimala is a Luna-mass moon, orbiting a large gas giant in a yellow star system. Though it is two AU from its star, (and therefore outside the habitable zone) tidal heating helps it to support liquid water in the form of a global ocean about 12 kilometers deep. The moon is tidally locked to its parent planet and orbits it every 37 hours. The atmosphere is 99% oxygen, and 1% CO2, with a pressure of 0.75 bars.

Due to the lack of landmasses to shape its weather, and its lack of rotation, what would cloud formations on this world look like when seen from space?

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    $\begingroup$ Thanks to cconsta1 for the edit $\endgroup$
    – user98816
    Apr 8, 2023 at 20:20
  • $\begingroup$ On April 10, I added to my answer, suggesting several more or less plausible ways for a Luna-mass world to have a dense atmosphere. $\endgroup$ Apr 11, 2023 at 4:29
  • $\begingroup$ how do you have tidal heating on a tidally locked moon? $\endgroup$
    – ths
    Apr 11, 2023 at 14:36

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It doesn't lack rotation: it rotates every 37 hours. A precise answer would require computational simulation, but you could probably justify 4-cell atmospheric circulation, on the basis that it isn't rotating slow enough for Venus-like atmospheric superrotation, or 2-cell circulation with super rotation on the basis that the world is too small to support multiple cells per hemisphere.

In the 2-cell case, you could expect regular chevron-patterned clouds like on Venus. In the 4-cell case, you could expect a basic tripled chevron pattern interrupted in each hemisphere by seasonal cyclonic storms.

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Here is a frame challenge: Could a Luna-mass moon have an atmospheric pressure of 0.75 bars? If it is possible, what unusual conditions might be necessary for a Luna-mass moon to have an atmospheric pressure of 0.75 bars.

Stephen H. Dole discussed the factors necessary for a planet to retain an atmosphere on pages 33 to 39 of Habitable Planets For Man (1964).

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

A rule of thumb for how long a world can retain a gas in its atmosphere is discussed on pages 34 to 36. According to that rule of thumb, the length of time for atmospheric retention of a gas depends on the ratio of the world's escape velocity divided by the root-mean-square velocity of that gas in the escape layer of the planet's exopshere.

Table 5 on page 35 lists value of the ratio from one to six, with times for the world to lose enough of a gas to have only 1/e, or 0.368, of the original amount left. Note that the comparatively minor variation from one to six in the ratio corresponds to a variation from zero time to infinite time in the length of time for a gas to be reduced to 0.368 of the original amount.

I note that on Earth the atmospheric temperature in the exosphere is several times as high as the atmospheric temperature at the surface. In Dole's time it was uncertain what the cause of the high exosphere temperature was, though it is possible that today the cause of exosphere temperatures is known well enough to predict the exosphere temperatures of worlds from various factors.

So if a planet has low enough escape velocity that it is constantly losing atoms of a gas from its exosphere, it will have to produce new molecules of that gas as fast as they are lost in order to maintain the same pressure of that gas. And obviously the faster a gas is lost, the less likely it will be for the planet to be able to replace that gas fast enough.

On page 54 Dole calculated the minimum mass necessary for planet to retain an oxygen atmosphere for geologic eras of time. Assuming that a planet could be warm enough at the surface for humans while having a maximum exosphere temperature as low as 1,000 degrees Kelvin (and thus a root-mean-square velocity of oxygen in the exosphere of 1.25 kilometers per second) Dole calculated that a planet would need an escape velocity of 6.25 kilometers per second to be able to retain 0.368 of the original amount of oxygen for as long as about 100 million years.

Using his formula for the relationship between planetary mass and other factors (which should be out of date by now) Dole calculated a world with an escape velocity of 6.25 kilometers per second (0.5587 that of Earth) would have 0.195 Earth mass, 0.63 Earth radius, and a surface gravity of 0.49 g. Note that each of those factors has a different ratio to the value for Earth and thus that they don't change at the same rate.

Here is a link to a 2013 study about the habitability of exomoons, which should be of interest to those writing stories set on exomoons.

https://www.google.com/search?q=exomoon+habitability+constrained+by+illumination+and+tidal+heating+pdf&oq=Exomoon+habitability+c&aqs=chrome.1.69i57j35i39.9327j0j7&sourceid=chrome&ie=UTF-8

Note that most modern habitability discussions are about habitability for liquid water using life in general, and not about habitability for humans (or lifeforms with the same requirements) in particular.

A paragraph on pages 3 to 4 discusses the mass range of habitable worlds.

A minimum mass of an exomoon is required to drive a magnetic shield on a billion-year timescale (Ms ≳ 0.1M⊕, Tachinami et al. 2011); to sustain a substantial, long-lived atmosphere (Ms ≳ 0.12M⊕, Williams et al. 1997; Kaltenegger 2000); and to drive tectonic activity (Ms ≳ 0.23M⊕, 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 (Kivelson et al. 1996; Gurnett et al. 1996), suggesting that satellite masses > 0.25M⊕ 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 our limit in either direction. An upper mass limit is given by the fact that increasing mass leads to high pressures in the moon’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 2M⊕ (Gaidos et al. 2010; Noack & Breuer 2011; Stamenković 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 sources say that the lower mass to retain a substantial and long lived atmosphere is about 0.12 Earth mass, while other factors may raise the minimum mass for habitability to 0.25 Earth mass.

The mass of Luna, the Moon, is about 0.0123 that of Earth.

https://en.wikipedia.org/wiki/Moon

That is 0.063 of Dole's lower limit of 0.195 Earth mass, and 0.1025 of 0.12 Earth mass, and 0.0492 of 0.25 Earth mass.

So finding a way for a Luna-mass moon to have sufficient escape velocity to retain an atmosphere is a problem.

Fortunately I have ideas for ways that a Luna mass moon might be able to retain an atmosphere. And tomorrow I will add them to my answer.

Added April 10 ,2023.

Part two: Science Fiction Hardness.

A science fiction writer should decide what score he wants the story he is working on to have on the Sliding Scale of Science Fiction Hardness.

https://tvtropes.org/pmwiki/pmwiki.php/SlidingScale/MohsScaleOfScienceFictionHardness

A writer who is okay with having a very low score doesn't have to pay any attention to the problem with a Luna-mass moon having a dense atmosphere and doesn't have to read any farther here. A writer who wants their story to have a high score will have to find a solution to the problem of a Luna-mass moon having a dense atmosphere.

Since the question asks for advice on what type of weather patterns their fictional moon would have, presumably they care about whether some readers will think it is impossible for their moon to have a dense atmosphere.

Part Three: Water Worlds.

Research a few years ago suggests a new lower limit on the mass of a planet which can have an atmosphere dense enough to have liquid water on the surface and thus potentially be habitable.

According to this article:

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

Worlds covered in water like the moon in the question can potentially have thick enough atmospheres for liquid surface water. The article puts the lower mass at about0.0268 Earth mass, significantly lower than 0.25 Earth mass, or 0.195 Earth mass, or 0.12 Earth mass.

The research paper is:

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

Luna mass is still too small to retain an atmosphere according to that research. 0.0123 Earth mass is only 0.4589 of this new lower mass limit.

Part Four: Changing the Density.

Technically all lower mass limits are invalid. To retain a dense atmosphere, a planet needs to have a high enough escape velocity. A lower mass world with a higher average density might have as high an escape velocity as a higher mass world with a lower average density.

So if the study selected 0.0268 Earth mass as the lowest mass with a high enough escape velocity, we can guess what escape velocity was considered necessary.

Earth has an average density of 5.5134 grams per cubic centimeter, Mercury 5.427 grams per cubic centimeter (0.98 Earth's), and Mars 3.9335 grams per cubic centimeter (0.7134 Earth's).

So a world with 1.00 of Earth's density and 0.0268 Earth's mass would have to have 0.0268 of Earth's volume.

According to this online cube root calculator,

https://www.calculatorsoup.com/calculators/algebra/cuberoots.php

a world with 0.0268 of Earth's volume would have 0.299 of Earth's mean radius. Earth's mean radius is 6,371.0 kilometers, giving that world a radius of 1,904.9 kilometers.

According to this online escape velocity calculator:

https://www.omnicalculator.com/physics/escape-velocity

Such a world would have an escape velocity of 3.3499 kilometers per second.

A word with 0.0268 the mass of Earth and a Martian density of 3.9335 grams per cubic centimeter (0.7134 Earth's) should have about 0.0375 the volume of Earth. Thus it should have a radius of 2,132.37 kilometers, 0.3347 that of Earth. That gives it an escape velocity of only 3.165 kilometers per second.

With such low escape velocities those worlds would be losing water vapor from their atmospheres rapidly, but the study assumes those water worlds would have extremely deep world wide oceans, probably hundreds of kilometers instead of tens of kilometers. For example, if such a world lost water at rate that lowered the ocean surface by a kilometer every hundred million years, it might not dry up for tens of billions of years. Anyway the study considered that keeping atmosphere nd water for one billion years was long enough for its purposes. And of course more massive - though still small - water worlds would have higher escape velocities to help retain water longer.

Part Four: Getting a Luna-mass world with a high enough escape velocity.

The Moon, or Luna, has 0.0123 of the mass of Earth, a mean radius of 1,737.4 kilometers (0.2727 of Earth's) - and thus a volume of 0.02 that of Earth - a density of 3.334 grams per cubic centimeter (0.606 that of Earth), a surface gravity of 0.1654 g, and an escape velocity of 2.38 kilometers per second (0.2127 that of Earth).

So for a world with the mass of the Moon to have an escape velocity as high as 3.165 or more kilometers per second it would have to have a smaller radius and volume than the Moon and thus be denser than the Moon.

A world with 1.00 the average density of Earth and 0.0123 the mass of Earth would have to have a volume 0.0123 that of Earth. Thus it would have to have a radius of 1,470 kilometers, 0.2308 that of Earth.

It would have an escape velocity of 2.5823 kilometers per second.

Part Five: A Mostly Iron World.

The heaviest common element in the universe is iron, with a density of 7.874 grams per cubic centimeter, 1.428 the average density of Earth.

So a world mostly made of Iron with an average density of 1.428 that of Earth and 0.0123 the mass of Earth would have a volume of about 0.0086134 that of Earth. It would have a radius of about 1.305 kilometers, 0.2049 that of Earth.

It would have an escape velocity of 2.7406 kilometers per second.

A world almost entirely iron, with a thin film of rock and a thin ocean over it, would be rather rare, but such worlds should exist somewhere in the universe. But an escape velocity of 2.7406 kilometers per second would still be too low.

Part Six: An Iridium or Osmium World.

The densest naturally occurring element is the deadly toxic osmium, with a density of 22.59 grams per cubic centimeter, about 4.097 times the density of the Earth. The next most dense naturally occurring element is iridium, with a density of 22.56 grams per cubic centimeter, about 4.092 times the density of the Earth.

A world made of iridium with 4.092 the average density of the Earth, and 0.0123 times the mass of Earth, would have 0.0030 the volume of Earth. Thus it would have a radius of 918.69 kilometers, 0.1442 that of the Earth.

So an almost entirely iridium world with the mass of the moon would have a n escape velocity of 3.267 kilometers per second. And that is between 3.165 and 3.3499 kilometers per second, which apparently should be enough for a water world to replace its atmosphere as fast as it escapes into space for a billion years.

Of course iridium and osmium are very rare elements. So a world mostly made of iridium and/or osmium would have to be artificial, built by a highly advanced civilization which gathered iridium and/or osmium from many sources to build that world.

Part Seven: Black Hole.

Primordial black holes would hypothetically have been created during the Big Bang. And they could be much less massive than black holes created by collapsing stars. Theoretically a low mass back hole might settle into the core of a planet or moon and thus increase the mass within, the density, and the escape velocity.

Suppose that a world with 1/8 the mass of the Moon had the same average density as the Moon. Then it would have 1/8 the volume of the Moon and thus 1/2 the radius of the Moon. It that world encountered a black hole with 7/8 the mass of the Moon and that black settled into the center of the world, the world would now have the mass of the Moon, 0.0123 that of Earth, within 1/8 of the volume of the Moon.

It would have an escape velocity of 3.36 kilometers per second, enough for one of those hypothetical water worlds that manages to keep its atmosphere for a long time. And that world wouldn't have to be built by a highly advanced civilization, but could occur naturally.

Now imagine a world with the density of the Moon and 1/27 of the moon's mass and thus 1/27 of the volume of the Moon and thus 1/3 the radius of the Moon. Suppose a black hole with 26/27 of the mass of the Moon fell into the center of that world.

It would then have an escape velocity of 4.115 kilometers per second, which would somewhat better.

Picture a world with the density of the Moon and 1/64 the mass of the Moon. It have 1/64 the volume of the Moon and thus 1/4 the radius. If a black hole with 63/64 the mass of the Moon entered the center of that world, the combined world would now have an escape velocity of 4.787 kilometers per second.

And so on with different combinations of masses.

One problem would be that it is not known whether primordial black holes exist or what their mass range is.

Another problem is that I have no idea how long it would take a black hole with less than the mass of the Moon to swallow a celestial object subatomic particle by subatomic particle.

Part Eight: Generated Gravity.

And if a world doesn't have sufficient escape velocity to retain an atmosphere, maybe generated gravity could increase the world's escape velocity.

In Jack Williamson's The Legion of Space (1934, 1947) humans have colonized the solar system, giving various planets, moons, asteroids, etc. artificial breathable atmospheres and using gravity generators to increase the surface gravity of low gravity worlds to a comfortable level.

Though Williamson didn't mention it, gravity generators would be necessary to also increase the escape velocity of small solar system worlds to enable them to retain their new atmospheres.

Of course most physicists believe that generated gravity is almost certainly impossible. So a writer who wants a high score in the scale of science fiction hardness may find that using gravity generators to explaining how a lunar mass world could retain an atmosphere is almost as bad as not trying to explain it at all.

Part Nine: A "titanic" World.

Titan, the largest moon of Saturn, has a mass of 1.829 the mass of the Moon, and an escape velocity of only 2.641 kilometers per second, 1.11 that of the Moon.

But Titan has a dense atmosphere, with a surface pressure of 1.5 bars, 1.48 the surface pressure on Earth.

No doubt the cold at Titan's distance from the Sun contributes to retaining a dense atmosphere. Titan has a surface temperature of about 94 degrees K, or -172 degrees C, or - 290.47 F. The exosphere temperature is probably much higher than that, but still much lower than Earth's exosphere temperatures.

Of course Titan is far too cold for liquid surface water.

But I suppose that a Lunar-mass moon with its surface temperature mostly due to tidal heating, could conceivably have a surface temperature warm enough for liquid water while still having an exosphere temperature as cold as Titan's, thus enabling it to retain a sufficiently dense atmosphere.

But I certainly couldn't calculate whether such a situation would be possible.

Part Ten: A Roof.

One way a world with the mass of the Moon could retain an atmosphere would be if he had a roof to hold it in; if it was a shellworld. Shellworlds are hypothetical megastructures in space surrounded by shells.

One type of shell world would be:

An inflated canopy holding high pressure air around an otherwise airless world to create a breathable atmosphere.4 The pressure of the contained air supports the weight of the shell.

https://en.wikipedia.org/wiki/Shellworld

So you could make your moon a world that was terraformed by an advanced civilization sometime in the past, giving it a breathable oxygen rich atmosphere and putting a shell around the moon to hold the atmosphere in.

And some science fiction writers might consider that to be the best method for a Luna-mass moon to have a breathable atmosphere.

And those are all the suggestions I could think of for a Luna-mass moon to have a breathable atmosphere.

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

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In addition to Logan's answer, which I upvoted:

  1. You still have stellar heating, even though it's small. Stellar heating will create some interesting effects as it moves across the moon every 18.5 hours.

  2. It's very unlikely (OK, unbelievable) that tidal heating would be perfectly uniform. Especially when "tidal heating" refers to keeping the core of the moon hot, not the surface. This means that heat will be (OK, can be) radiative and volcanic. Radiative meaning the core is hot so the mantle is warm. However, it's hotter where the mantle is thinner. Volcanism creates local hot spots. And wherever you have differences in temperature you have high and low pressure zones.

Short answer

Since we have one and only one example to work with (Earth), I can't say that your moon will look substantially different from Earth. Clouds are formed when there's sufficient water vapor and a temperature differential in the atmosphere. You don't mention the mass of the moon or the thickness of the atmosphere — but the right combination of tidal heating, stellar radiation, mass and atmosphere will result in 24/7 (proverbially) rain. The right combination will result in no clouds at all. If you create a mix that permits clouds, I don't see why they wouldn't look a lot like what you'd see on Earth from space.

And there's a point to be made here. It's often easier to ask us, "Given my star, parent planet specs, and following basic moon specs, what must I do to the moon to achieve (on average) the following well-defined atmospheric phenomena?" than it is, "here's the specs for my moon, what's the climate like?" Climate is whomping complex, which is why it's often easier to work backwards.

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  • $\begingroup$ Earth is the only present example of a world with an oxygen rich atmosphere. But planetary scientists now have some knowledge of the climate and weather on various worlds with atmospheres, including Venus, Mars, Jupiter, Saturn, Uranus, Neptune, Titan, Triton, and Pluto. $\endgroup$ Apr 11, 2023 at 4:27
  • $\begingroup$ @M.A.Golding You're not wrong, but the OP stated the moon had an oxygenated atmosphere over an ocean. None of the examples you state have that, and it's not surprising that none of them look like the one planet we're familiar with that does. $\endgroup$
    – JBH
    Apr 11, 2023 at 13:55

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