Could Earth theoretically have another moon, beside the existing one, that would have a stable orbit? If it is possible, could Newtonian physics describe where it would be (i.e its position relative to Earth and the Moon)?
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5$\begingroup$ Howdy, welcome to the site. The answer depends on how big the second moon is for sure; if the moon is allowed to be small enough not to have hydrostatic equilibrium I think there are very large ranges of orbit it could stably take. If it's large enough to make itself a sphere, I'd expect interactions between it and Luna to put them into resonance. If it were as large as Luna (or larger!) I'd imagine things would end up more like the Pluto system. But since this is off-the-hip guessing, sticking with a comment and not an answer. $\endgroup$– Erin AnneOct 14, 2022 at 22:47
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1$\begingroup$ What do you consider to be a moon (e.g. how large of a body and/or how large visibly to a human viewing it without aid from the Earth's surface)? For how long must the orbit be stable (e.g. thousands, millions, or billions of years)? Are you asking: A) "If an additional moon could magically appear orbiting Earth, could it be in a "stable" orbit?"; or are you asking "Could an additional moon have developed over billions of years in addition to the existing Earth-Moon system?"; or are you asking "Could the Earth have in the past, or now/future, capture an additional moon?"; etc. $\endgroup$– MakyenOct 15, 2022 at 19:56
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$\begingroup$ @Makyen To clarify, my question is if it would be possible to have another moon orbiting earth stably all while taking Lunas gravitational influence in consideration. What would a system of these three bodies look like/behave? Would the second moon given "appropriate" mass, speed and distance have a stable orbit in such a system or would a collision (for example) be inevitable? Concerning the shape, I am thinking of a sphere and not a non uniform asteroid kind of looking shape. $\endgroup$– HaleOct 15, 2022 at 21:39
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1$\begingroup$ @Mayken Please excuse my short of knowledge and unclear desription as I am not an expert on this topic. My definition of moon is based on Luna. I assume that this second moon has similar characteristics to Luna in terms of appearance and possibly structure. A bit like a copy of Luna but with variable mass, speed and distance from earth and luna. I think I am perhaps describing a planetary-mass moon (based on my understanding of the article linked above). $\endgroup$– HaleOct 16, 2022 at 10:19
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1$\begingroup$ In the sky! Hyuk, hyuk, hyuk. $\endgroup$– Jacob KrallOct 16, 2022 at 14:37
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1 Answer
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Certainly the Earth could have ended up with additional moons, and Newtonian physics can say some things about the kinds of orbits they might have, but there is a range of possibilities.
First of all, stable orbits in multi-object systems tend to be fairly circular, just because objects in highly elliptical orbits will cross the orbits of other bodies and eventually collide, or be flung out of the system, or end up in a non-interfering orbit. (But, for instance, comets have highly elliptical orbits around the sun that can last for many centuries. The thing is, they tend to get perturbed into different orbits on longer time scales.)
Another general pattern, within the category of circular-ish orbits, is the phenomenon of resonance. Sometimes moons will end up in stable patterns where, for instance, the inner moon orbits twice every time the outer one orbits once. Around Jupiter, for every four orbits of Io, Europa orbits twice, and Ganymede once. So we might see that pattern. (But there is no guarantee. The different planets don't have resonances with each other, for instance, and those orbits operate under the same rules. But Pluto, no longer a planet, does have a 3:2 resonance with Neptune.)
Also, objects in circular orbits with very different radii don't effect each other as much as they would if the orbits were similar. And the moon's orbit allows a lot of room. If you can picture a vinyl LP with the earth filling up the hole in the center, then the edge of the record is about the moon's orbit. So a much closer moon is plausible.
But these are all just general thoughts. It turns out there is a recent study on this: "Moon-packing around an Earth-mass Planet" by Satyal, Quarles, and Rosario-Franco. The authors find that the earth could, in principle, have more than ten moons the size of the asteroid Ceres, six the size of Pluto (smaller than our moon), and four the size of the moon. The article linked didn't say anything about the kinds of possible orbits, but I am confident they would be approximately circular and not too close together.
