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Let's imagine (or do we know one?) a moon in a very eccentric orbit around a planet, with periapsis below the Roche Limit. How would it behave? Would it break apart when speeding past the planet, then reform back as it spends a long time near the apogee, as the debris and parts are pulled back together by gravity over and over until tidal forces circularize its orbit enough that it stabilizes, or is one of these states considerably dominant, and it would either never get to break apart in the short periods near periapsis, or maybe gradually break into a ring and never get to reform?

enter image description here

Bonus question: what considerations / problems would exploration of such a body (artificial satellites, landers, rovers, maybe even a base) face comparing to similar endeavors involving a typical moon?

SF.
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    I'm having a little difficulty visualizing the situation. Could you post a picture/diagram for the moon's orbit, showing the planet's Roche limit, and other needed parameters? – WarpPrime Jan 28 '21 at 13:29
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    @fasterthanlight Done. Red line would be Roche limit, grey - moon orbit. – SF. Jan 28 '21 at 14:07
  • How far in does the moon go under the Roche Limit? Also, are there any specifications for the apoapsis, periapsis, and orbital period? It seems like those parameters are necessary to determining whether or not the moon survives long term, or is that up to the answerer to decide? – WarpPrime Jan 28 '21 at 15:08
  • @fasterthanlight If "how far does the moon go under the Roche Limit" is an important factor, I'd love the answer to discuss the different outcomes and how that factor matters. Similarly for other parameters - discussing their importance and various thresholds. I'm after a general problem answer, not a specific solution to one specific body. – SF. Jan 28 '21 at 16:01
  • There has to be an interesting prequel to this story. As you note, highly eccentric orbits tend to get circularized, so this moon must have been perturbed somehow in relatively recent times, and that perturbation was likely to have caused some stress to the moon's structure. – PM 2Ring Jan 28 '21 at 18:45
  • @PM2Ring I'd imagine one freshly captured through interaction (slingshot) with an older moon. Possibly ejecting the old moon or crashing it into the planet in the process. – SF. Jan 28 '21 at 20:02
  • As far as I know, the Roche-Limit is only defined for circular orbits, isn’t it? – Hartmut Braun Jan 29 '21 at 06:50
  • Sorry, I retract my comment. There are two different definitions for Roche limit. – Hartmut Braun Jan 29 '21 at 06:55
  • Extreme example: the hill sphere of the ISS is smaller than its actual size. – Joshua Jan 29 '21 at 17:32
  • Roche limit and Hill sphere are different things. – fraxinus Jan 29 '21 at 18:56

1 Answers1

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Comet Shoemaker-Levy 9 (SL9 for short) is a great example of a moon in a highly eccentric orbit that passes through the Roche limit at periapsis.

SL9 was discovered in 1993, but is thought to have been orbiting Jupiter for 20-30 years prior to discovery. It passed through Roche limit of the Jupiter/Comet pair and is thought to have broken apart in July of 1992. The pieces then collided with Jupiter in July of 1994.

SL9 had an extremely eccentric orbit ($e \approx 0.9986$), with apojove of almost a 1/3 AU! This "loose" orbit allowed massive orbital perturbations by the Sun at apojove, which eventually led to its demise. Here is a nice figure of its last passes:

enter image description here

Note:

  1. In this case, the tidal forces were dominant over the gravitational forces, so the SL9 fragments never came back together once they were broken apart. But SL9 passed deep into the Roche boundary of Jupiter prior to its collision. This may only be a partial answer to the above question. If SL9 had grazed the Roche boundary just enough to be barely broken apart, I don't know if it would have come back together prior to hitting Jupiter.

  2. After SL9 was split apart by tidal forces, as is shown in the above image, the pieces got further and further apart. This is exactly what we expect to happen since the pieces in higher orbit have a slower orbital speed and the pieces in lower orbit have a faster orbital speed. If SL9 had been in a stable eccentric orbit, the fragments would have continued to break up until they were small enough to withstand the tidal forces. Over many orbits, they would spread out and intermingle into an eccentric ring.

  3. This may not be the only time an object is first broken up and then later collides with a larger body. Check out this set of craters on Ganymede!

enter image description here

Connor Garcia
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    If the orbit wasn't so extremely eccentric, it would be more stable and the comet could orbit Jupiter much longer - right? – SF. Jan 28 '21 at 18:24
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    @SF. It's really a function of apoapsis distance. Orbits get unstable around 1/2 to 1/3 of Hill Sphere radius. Jupiter's Hill Sphere radius is about 0.3381 AU. SL9's apojove was theorized to be about 0.33 AU prior to collapse. Even if SL9 had a perfectly circular orbit at 0.33 AU, its orbit would have been unstable. In order for SL9 to have a stable orbit it would have needed a much lower apojove and at least a little bit less eccentricity (so that it didn't hit Jupiter at perijove). Your question is outstanding, by the way. – Connor Garcia Jan 28 '21 at 18:40
  • Eh, if it had any less eccentric orbit with apojove near Hill sphere it's perijove wouldn't be anywhere near Roche limit. I'm more interested in possible longevity of situation as stated in the original question. e≈0.9986 is truly extreme. – SF. Jan 28 '21 at 20:25
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    Oh this is such a cool answer! :-) – uhoh Jan 28 '21 at 23:05
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    I've just asked What calculations show that Comet Shoemaker-Levy 9 orbited Jupiter for several decades before its spectacular impact? (Chodas, Sekanina & Yeomans) – uhoh Jan 28 '21 at 23:50
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    Gotta love the Ganymede picture! – armand Jan 29 '21 at 01:47
  • Okay, except Shoemaker-Levy 9 was not a moon before it broke apart, was it? It was always a comet. Unless it was just an undiscovered moon before? – Darrel Hoffman Jan 29 '21 at 14:24
  • @DarrelHoffman That depends on how you define "moon", which is still a matter of debate. – Philipp Jan 29 '21 at 15:26
  • @Philipp I guess my definition would be - was it always (for certain definitions of "always" - let's say at least a century?) orbiting Jupiter until it crashed? Or was it captured more recently? If it just came in out of the Oort cloud, did a couple loops and crashed, it's a little hard to call it a moon. – Darrel Hoffman Jan 29 '21 at 15:41
  • @DarrelHoffman Though also a comet, SL9 certainly qualified as a moon using our conventional definition: https://en.wikipedia.org/wiki/Natural_satellite#Definition_of_a_moon: "Every natural celestial body with an identified orbit around a planet of the Solar System, some as small as a kilometer across, has been considered a moon." If time-in-orbit is a relevant criteria, please provide a reference. – Connor Garcia Jan 29 '21 at 17:36
  • @ConnorGarcia That definition would include every speck of dust in Saturn's rings. (We just haven't identified anything smaller than 1km yet.) And what classifies as an orbit? SL9 doesn't appear to have completed even a single orbit between its discovery and its destruction. If you include that, you could count ʻOumuamua since its trajectory was at least slightly affected by Earth's gravity, but nowhere near close to a full orbit. You have to draw the line somewhere. – Darrel Hoffman Jan 29 '21 at 17:47
  • @DarrelHoffman In the above wikipedia definition, I think "identified" implies you have to be able to pick out the specific body (so far excluding ring dust), and "around" implies that the orbit has an eccentricity of less than one (thereby excluding Oumuamua as a moon of Earth). – Connor Garcia Jan 29 '21 at 18:08
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    "Jupiter's Roche limit" - Shouldn't that be "The Roche limit for the Jupiter-Comet pair"? (because it depends on the size and cohesion of the comet) – David Tonhofer Jan 29 '21 at 19:13
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    @DavidTonhofer Yes, a bit sloppy of me. Edited. – Connor Garcia Jan 29 '21 at 19:36
  • Is the first sentence in present tense just so it doesn't spoil the narrative, or are there pieces of it still out there? – Mazura Jan 30 '21 at 02:24