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The Wikipedia article Clearing the Neighborhood lists three numeric parameters that can be calculated for bodies orbiting the Sun as a way to indicate orbital dominance: Stern and Levinson's $\Lambda$, Margot's $\Pi$, and Soter's $\mu$. It seems reasonable to apply these criteria to orbits of moons about their primaries, but I have not seen it done. Has anyone looked to see if any of these criteria divide the moons of (at least) Saturn or Jupiter into clearcut dynamically-based primary and secondary categories? If so, what are the primary moons? (OK, I think I know the answer for Jupiter, but Saturn might be more interesting.) And might there be more than two natural categories? I can easily imagine a clear quantitative distinction between Saturn's larger moons, the little ones, and the ring particles.

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    $\begingroup$ Related discussion: astronomy.stackexchange.com/questions/28484/… $\endgroup$ Commented May 31, 2023 at 3:11
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    $\begingroup$ I looked for a duplicate before posting this question, but now I see this: astronomy.stackexchange.com/questions/40615/…. I would still like to see a quantitative response rather than the more qualitative discussion at that question, but maybe this one still should be closed as a duplicate. What do others think? $\endgroup$ Commented May 31, 2023 at 4:16
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    $\begingroup$ @Mark Foskey. At the present time moons can be classified a few ways.0. For example planetary mass and smaller than planetary mass moons. One main classification is between regular moons, which probably formed in a disc of gas and dust around the planet, and irregular moons, which probably formed elsewhere and were captured by the planet. Irregular moons are classified as those with prograde and those with retrograde orbits. So you may have suggest a new potential classification of moons. $\endgroup$ Commented Jun 1, 2023 at 1:57
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    $\begingroup$ @M. A. Golding Yes, that was kind of my thought. With Jupiter, the difference between the Galilean moons and all the rest is so great that there may not be much more to say, but I'd like to see the $\Lambda$ parameters of Saturn's moons. OTOH, they don't seem utterly trivial to calculate since you actually have to estimate properties of typical other orbits (if I understand correctly) to estimate $\Lambda$ for an object. So this question may go unanswered. $\endgroup$ Commented Jun 1, 2023 at 5:11

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Identifying moons that clear their orbits empirically is made difficult by the fact that the primary beats them to the punch by clearing a larger neighborhood. Even where the primary does not clear all of its orbital neighborhood at any time, it does clear the local portion of its neighborhood at any given time, and this locally cleared zone includes the region where the moons generally orbit.

Even so, we have evidence that Saturn's moon Mimas is actively clearing its zone around the ringed planet beyond Saturn's own clearance of the neighborhood. Baillié et al. [1] develop a model of satellite-ring interactions indicating that Mimas has cleared a resonant orbit within Saturn's rings, thereby forming the Cassini Division. Although this clearing of the CassininDivision appears to be temporary because of changes in the orbit of Mimas itself, it is possible only for objects that actively clear their own orbital neighborhoods.

Reference

Kevin Baillié, Benoît Noyelles, Valéry Lainey, Sébastien Charnoz, Gabriel Tobie (2019). "Formation of the Cassini Division – I. Shaping the rings by Mimas inward migration". Monthly Notices of the Royal Astronomical Society, 486, 2, 2933–2946. https://doi.org/10.1093/mnras/stz548

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  • $\begingroup$ I don't understand - we don't say that the sun beats the planets to the punch by clearing their orbits first. I'm really asking about the quantitative parameters relative to orbits about the primary. $\endgroup$ Commented Jun 4, 2023 at 12:26

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