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The reason quadruple eclipses can never happen on Jupiter is because of the 1:2:4 orbital resonance between Io, Europa, and Ganymede. As far as I know this isn't a problem for Saturn's moons.

From Wikipedia's Solar eclipses on Saturn:

Seven of Saturn's satellites – Janus, Mimas, Enceladus, Tethys, Rhea, Dione and Titan – are large enough and near enough to eclipse or occult the Sun, or in other words to cast an umbra on Saturn.

Of the 7 listed above, Mimas and Tethys are in a 2:1 orbital resonance and so are Enceladus and Dione, however that doesn't stop either pair (or all 4 together) from eclipsing Saturn at the same time.

So, in theory, it is possible for all 7 moons to more or less line up together. Does this mean that during eclipse season on Saturn, there can be a septuple eclipse? If so, when is the next one going to happen?

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    $\begingroup$ Interesting question! What exactly is a septuple eclipse? Does it just mean that shadows of seven moons appear somewhere on Saturn's disk at the same time? They don't have to all fall on the same location, right? $\endgroup$
    – uhoh
    May 27, 2020 at 7:36
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    $\begingroup$ Yes, like you said, it means 7 simultaneous eclipses happening at once and thus 7 shadows somewhere on Saturn's disk. $\endgroup$
    – user177107
    May 27, 2020 at 11:43
  • $\begingroup$ So from one Saturnian observer's location, one eclipse and 6 transits. $\endgroup$
    – Carl Witthoft
    May 27, 2020 at 14:03
  • $\begingroup$ I suspect there’s something keeping it from happening… Anyhow, an interesting read, though not directly about that, is Mathematical Astronomy Morsels, by Jean Meeus, in which he addresses the possibility of having all planets lined up. He quickly concludes that it’s impossible. I suppose the same for Saturn’s seven “eclipsing” moons. $\endgroup$
    – Pierre Paquette
    Nov 21, 2020 at 17:52

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The short answer is no, septuple eclipses can’t happen.

Using a method described by Meeus in Mathematical Astronomy Morsels (p. 190), we find that while it is, in theory, possible, for the seven satellites to align, it happens only once per ~ 20 million years—and that’s among themselves only; I didn’t factor in the Sun’s position yet!

The possibility that the Sun is along the same line is $ \displaystyle \frac { \text {(angular size of the Sun as seen from Saturn)}°} {360°} = \frac {0.05} {360} $; let’s be generous and round it off to 1:10,000.

Multiplying 20 million years by 10,000 shows us that the seven satellites would line up with the Sun once in 200 billion years—longer than the life of the Universe!

Finally, the above was estimated by using circular orbits, which is not the case in practice. Plus, orbital parameters change (“chaotically”) over long timespans, so it would (at least currently) be impossible to compute the actual positions of satellites in the remote future on timescales such as the ones above.

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  • $\begingroup$ Late but thank you for the answer! $\endgroup$
    – user177107
    Apr 3, 2021 at 6:37
  • $\begingroup$ Always a pleasure! :) $\endgroup$
    – Pierre Paquette
    Apr 3, 2021 at 9:19

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