# A moon in eccentric orbit dipping below Roche limit

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?

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?

• 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? Commented Jan 28, 2021 at 13:29
• @fasterthanlight Done. Red line would be Roche limit, grey - moon orbit.
– SF.
Commented Jan 28, 2021 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? Commented Jan 28, 2021 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.
Commented Jan 28, 2021 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. Commented Jan 28, 2021 at 18:45

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:

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!

• If the orbit wasn't so extremely eccentric, it would be more stable and the comet could orbit Jupiter much longer - right?
– SF.
Commented Jan 28, 2021 at 18:24
• @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. Commented Jan 28, 2021 at 18:40
• Oh this is such a cool answer! :-)
– uhoh
Commented Jan 28, 2021 at 23:05
• – uhoh
Commented Jan 28, 2021 at 23:50
• Gotta love the Ganymede picture! Commented Jan 29, 2021 at 1:47