Meleti and Maci - Whistler's Worldbuilding

In my story, my planet, Meleti, has two moons: Maci, the larger and outer, and Monte, the smaller and inner. They orbit in a 3:10 resonance, and both are tidally locked to their parent planet, which I thought would orbit every 17-ish hours. However, while running the calculations in a spreadsheet by Artifexian, I realized that the inner moon would slow the rotation of the planet down enough that they have become tidally locked with each other.

What a discovery!

Now, my planet rotates once every 50-ish hours. And the tides would be ~80 meters different due to both of the moons and its star's tidal effects. This could create an idea where Monte, Maci, and the star (Letuaf), are all battling for control of the water (it's a water-world). This would create huge intertidal zones, prevalent with wildlife.

This would also affect locals' circadian rhythms; the life there would have probably 30 hours' wake time and 20 hours' sleep. If an earthling somehow ended up on Meleti, they would have to get used to sleeping once in the day and once at night—a midday nap, if you will.

And think of the cultural implications!

On the side facing the moon, cultures would probably see it as an all-seeing eye, watching over their every decision. Solar eclipses would be special occasions for them, as it ends up revealing what its true eye looks like.

On the side opposite the moon, there would only be one thing in the sky, and if they ever decided to set sail to the other side, they would find something never seen before. And on a planet which is about 99.9% water, that would be seen as a good omen, that land is on the way.

What tech level are your inhabitants? Are they natives, or immigrants?

Natives. There's a few volcanic islands scattered about, so the only sapient species are so far clustered on one of the larger archipelagos. There are some air currents, and they know how to sail, so they have somewhat spread throughout. However, due to the amount of water, they are unlikely to be able to access many natural resources and are thus stuck in a stone age.

The biggest "issue" I have with waterworlds in general and I'm not being mean here is geology. If the planet has sufficient volcanism to produce peaks capable of exceeding an excessively high sea level and build them up enough to not all be worn away to atolls or guyots, it would've had enough activity over geologic time to produce at least micro-continents. We're talking Madagascar, Papua New Guinea, Japanese archipelago, Sicily, New Zealand, maybe Greenland type islands and micro-continents.

Sufficient volcanism to produce volcanic islands thousands of meters above the sea floor and potentially thousands of meters high above sea level would also prove to have enough internal heat to drive plate tectonics and thus lead to further creation of land. It would also produce "sunken continents" (several exist on Earth) owing to flood basalts, erosion and tectonic action.

Edited by MajorTom on Aug 5th 2020 at 6:55:07 AM

Actually, that would work. It would actually make more evolutionary sense for a sapient species to develop on a large landmass, then spread out to further lands. So yes, there may actually be more natural resources. Still so much open ocean though.

Side-note: I just realized that my moons were too dense, then scaled them back somewhat. Meleti is still tide-locked to its inner moon, but it would take longer to do so.

Just out of curiosity, what spectral class is the star that you described? Because based on what you said about the star also having a significant hold on tides as the moons, my rough estimates place it at either late K (K5-K9) or M (red dwarfs).

This is important because greater tidal interactions that close to the star will cause the 50-hour resonance between your planet and moon to decay, leading to a Tidally Locked Planet and your moon suffering one of two fates: collision with the planet or being flung out of orbit.

M1.5V. Very early red dwarf. Were the moons not there, the planet would have become tidally locked within 13 Ma.

Alright, so in order for a two-way tidal lock to happen around an M 1.5V star, your planet and moon would need to be orbiting very close, and I mean so close that, at minimum, would put the orbital resonance at around 11 hours, give or take. This depends on the masses of your planet and moon of course, but this is important because closer in to the star, your planet's hill sphere (basically its region of gravitational influence) becomes smaller. Unfortunately, having a 50-hour resonance becomes an issue because your moon would need to be farther from the planet to work, thus putting it closer to the hill sphere boundary and becoming more susceptible to being perturbed by the star. This leads to orbital decay like I mentioned earlier.

Also, having a second moon in there makes things even worse, because it makes the orbits of both your moons really unstable.

Edited by DivineFlame100 on Aug 5th 2020 at 10:21:44 AM

The planet is about 1.5x as heavy as Earth, and only 1.2x as big. Its inner moon (the one it is locked with) is 0.0075 Earth masses and orbits 95Mm away, and the outer is 0.02 Earth masses and orbits 209Mm out. I have a file of them for GravitySimulator, and both moons seem to be stable.

Also, self-correction: the planet and moon rotate/orbit every 60.5 hours, for a total of 30 even days in a year.

Edited by TheWhistleTropes on Aug 5th 2020 at 1:33:26 PM

Have you run the simulations over billions of years of in-simulation time to see if the orbits are stable in the long run? Because even if the orbits look fine initially, they shift overtime due to gravitational influences from the star and other neighboring planets. And considering it took life (at least on Earth) around 4 billion years to evolve into a complex ecosystem we see today, depending on the time period, your inhabitants may not get to see your moons if their orbits have already decayed.

Edited by DivineFlame100 on Aug 5th 2020 at 10:46:31 AM

You know, I was hoping that you'd start a thread about this world. When I first saw Meleti described, I was wondering how that planet would work under real world physics.

• 60.5 hours is a pretty close orbit, indeed. At that point I wonder how close the moon is to the planet's Roche lobe. I presume your gravity simulator did cover this aspect? I did see that some real world hypothetical exomoons in M dwarf systems have life expectancies of over 14 billion years.
• Do note that the existence of an atmosphere can impede the onset of tidal locking. An ocean too might have an inhibiting or accessory effect, but I don't have any studies about this at hand.
• Regarding Major Tom's point: AFAIK, it's an unsettled question whether oceans+high heat flow are enough to start plate tectonics. The big sticking point is that even on Earth it's very difficult to start subduction zones out of nowhere (instead of propagating them from pre-existent subduction zones) and much easier to shut one of them down for good. Without them you pretty much can only have stagnant lid tectonics. Having said that even a stagnant lid isn't necessarily even - you could have broad upwarps that may emerge from the ocean.
• I am willing to bet that if the moons are close enough to overpower the star's tidal effects, your planet (and/or the moons) will undergo a lot of tidal heating and be very volcanically active. Enough to influence the climate, perhaps.
• Speaking of climate, I kind of worry about the climatic stability of a waterworld. An ocean planet has by default strong water vapour greenhouse and ice-albedo feedbacks, but without large landmasses the carbonate-silicate feedback will be weak. That means that even slight variations in the star's luminosity (or if it's large enough to matter, volcanic heating and degassing) might tip the planet into a Venus-like supergreenhouse or a Snowball Planet climate.
• A little detail, but the climate of a world with a day over twice as long as Earth's is likely to feature a very different atmospheric circulation. In particular, the much weaker Coriolis force makes a difference.
• How did Meleti manage to hold on its water in the early lifespan of the star? M dwarfs in their early life (which even for low mass M dwarfs like TRAPPIST-1 is not more than 1-2 billion years so it should be over by now) are much brighter and emanate lots of ionizing radiation that will boil off all oceans and convert them to oxygen (and hydrogen which escapes). I could imagine that the migration of an icy body from farther out - perhaps with life, Europa-style - and its subsequent collision with Meleti restored its water budget.

Edited by SeptimusHeap on Aug 6th 2020 at 1:44:21 AM

Is 95 million miles that close enough to touch the Roche Limit? I may have gotten my own calculations wrong.

Anyway WhistleTropes, from what I already see, M-type stars already present enough problems for Earth-type planets that it becomes very risky to pull off without some clever hand-waving. I honestly see your configuration working much better around early K stars (K3-K0) and G stars like our Sun.

Edited by DivineFlame100 on Aug 6th 2020 at 5:21:41 AM

Calculating the Roche limit is not trivial, I think there are exoplanet simulators that might be able to do it.

I don't think habitable worlds or Earth-type planets around M-dwarfs are impossible or even implausible. They are just not going to be exactly identical to Earth, is all. And, with all due practicality, there are more M dwarfs than F or K class stars and if memory serves Earth sized planets are more common around the former too.

Subduction zones can form "out of nowhere" just as you can have rift zones, graben and transform faults emerge. It's all motion and density. If the planet has sufficient heat to generate mantle convection, eventually the crust will start moving and because crust is more rigid than asthenosphere or mantle eventually it'll fracture or buckle beginning your first faults and rifts. If you have two parts of a planet converging you'll get either a suture zone where the two plates basically "weld" together (there are numerous of those on Earth) or eventually the stress will cause the crust to buckle and one side (typically but not always the denser one) will sink into the mantle to melt and disintegrate, hence a subduction zone. It's easier to propagate a subduction zone from existing ones than form new ones but it's not impossible for new ones to emerge.

This can happen even in the ocean, it's why back-arc basins and various island formations (for example the Marianas) exist.

If the planet Meleti has plate tectonics, regardless of whether or not micro-continents or true continents ever emerge it'll have at least one or more examples of those island arcs and basins caused by subduction zones.

Edited by MajorTom on Aug 6th 2020 at 5:54:05 AM

Nah, from what I can see the scientific consensus is pretty much that creating subduction zones and thus plate tectonics in an environment where there weren't any before ("stagnant lid") is hard. See how Mercury, Mars and Venus both lack evidence of ongoing plate tectonics. There certainly is some process that can do this - Earth after all has many subduction zones - but generating the kind of force needed to buckle a "stagnant lid" is not easy w/o already existing trenches. An open access source that discusses subduction initiation in the planetary context.

One could say that since Earth has them it's likely that Meleti could also have such. Or Meleti might end up like Io - no plate tectonics, strong tidal heating from the 4-body interaction and lots of volcanoes that form islands (given that unlike Io Meleti has oceans). It's not clear why Io has no plate tectonics but this paper suggests it might be a matter of lava composition which "hardens" the crust to the point that it can't easily buckle.

Tidal heating? Wow! Just imagine a volcanic planet with a volcanic moon or two to boot!

That would actually be bad news for your planet. A planet with Io-levels of tidal heating will render it an uninhabitable volcanic wasteland. And since your planet is 1.5 times the mass of Earth, unlike Io, it'll be massive enough to retain an atmosphere. All those volcanoes will trigger a runaway greenhouse effect, turning it into, well, Venus.

OK... maybe keeping it with one moon would be better off for the planet as a whole.

However, the inner moon's tidal force on the planet only 6 times that of our Moon's. The star's is about 12, and the outer moon's is 13 times greater.

Actually, "Super-Ios" - planets where much of the heat flux comes from volcanism - are potentially habitable. The trick is that the combined energy from the star and volcanism should not heat the planet to the point of boiling. In this case it means moving Meleti a bit farther out from its star.

I don't think that calculating the exact heat flow is trivial. Putting aside for a moment that leftover heat from Meleti's birth and from radioactive components also counts, it'd be a complicated function of the planet's geological and orbital properties. I'd say that you can get away with handwaving this bit.

It is also kind of on the outer edge of its habitable zone, maybe a little beyond. Using a habitable zone calculator the outer edge was at 0.246 AU. My planet orbits at 0.28.

So... within 1,000 years, the second moon gets thrown into a high-inclination, high-eccentricity orbit.

With 3,300 years, the inner moon collided with the outer moon.

So there's that.

You've got a three-body problem. In classical physics, such systems are fundamentally unstable.

Four body problem, actually (this planet has two moons). But yes, moons around a planet in the habitable zone of a M-dwarf are a tightrope walk.

That said, some three body systems are stable for more than the age of the universe. See some of the citations linked above. I am not sure how such a system can be made stable, the key point is that it must be located about halfway to the planetary Hill radius. Also, perhaps the resonance between Maci and Monte is destabilizing?

Figure 4 here has some discussion of parameters of orbital stability in the 3-body case.

Edited by SeptimusHeap on Aug 6th 2020 at 3:21:30 AM

Admittedly, it was. Maci does get plenty of tides from the star, so its orbit varies like the Moon's. It's just in the right zone where it is unpredictable enough to be good, but not too unpredictable to be torn away from its parent.