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Small Body Grooves, Theories for the formation of grooves on Lutetia and Phobos
Hungry4info
post Jul 21 2010, 11:18 AM
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While I can see how that would apply to Phobos (though reorientation events would be required to explain the observed sets of grooves), I'm not sure it could be stretched to cover Lutetia. Lutetia, as far as we know, hasn't orbited a planet, and getting a situation to work where the asteroid would spend enough time in the vicinity of one to experience reorientation events would be difficult.

Furthermore, for ring impacts to create lines, the moon's orbit must be coplanar with the ring plane, otherwise an entire hemisphere gets blanketed when puncturing through the ring(s). In the case of Phobos, coplanarity with a ring would be best explained if Phobos formed from the ring. IIRC, Mars and Phobos are not believed to have the same composition, so having Phobos form from the ring is implausible. Another idea is that a hypothetical third moon could come in and get disrupted at the altitude where Phobos passed though on its current tidal inspiral toward Mars. This requires the hypothetical third moon to be coplanar with Phobos' orbit. If this is satisfied, we need a mechanism for reorientating Phobos. Interaction with a fourth moon that was since ejected?


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algorimancer
post Jul 21 2010, 03:06 PM
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Here's the mechanism proposed for Lutetia. Envision a low angle (non-equatorial) impact which hurls a debris cloud into orbit, then the debris condenses into a ring. The mechanism for this is well established. For a variety of reasons, the ring orbit decays over time until the ring intersects the surface, forming a groove and depleting the ring material closest to the surface. Repeat until multiple grooves have formed, bearing in mind that Lutetia is rotating beneath the ring. Here's an illustration:
Attached Image


For Phobos, the ring is postulated to have formed about Mars, not Phobos, an entirely different scenario.
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Hungry4info
post Jul 21 2010, 04:19 PM
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The bit about the body rotating beneath the ring puts a twist on the idea, I can see how it would create parallel grooves.

Such grooves would be distorted by the irregular shape of the body though. Do we see evidence for this on Lutetia?


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tasp
post Jul 21 2010, 04:41 PM
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Ring materials will preferentially strike the highest elevated spot(s) along their ground track, assuming circular orbits. As we consider primary objects that are successively smaller in size, the irregularity of the object, on average, will increase. For altitudes that are sufficient high, even a quite irregular object will manifest a gravitational field as emanating from a point source, as the altitude decreases, however, the irregularity of the object and the resulting gravitational field will cause increased dissipative losses in the ring plane materials as the orbiting particles 'feel' the irregularities and experience velocity changes, and even out of plane effects. The ring 'particles' will grind amongst each other more, and the angular momentum transfer process will increase in efficiency in dissipating the ring structure.

For scenarios that might require considerable time for successive realignments of the spin axis, the rapid dissipation of the ring materials (either from the high or low side) would seem to present a difficulty in having sufficient duration while the materials are available.

Another complication, for orbiting materials to collapse to the LaPlacian plane, my understanding is the oblateness of the primary is the key factor in facilitating the process. For grossly non-spherical objects, I am not sure how oblateness might be characterized. Perhaps there might be some guidelines on how close the measurements of a triaxial ellipsoid have to be to each other for the LaPlacian process to commence.
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Phil Stooke
post Jul 21 2010, 05:03 PM
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The first point of difficulty will be explaining how the debris forms a ring. Normally one would say that every piece of ejected material will be on a path that either escapes the object or falls back to the surface after less than one orbit. How is that changed to leave an orbiting ring?

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algorimancer
post Jul 21 2010, 05:22 PM
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QUOTE (tasp @ Jul 21 2010, 10:41 AM) *
...
For scenarios that might require considerable time for successive realignments of the spin axis, the rapid dissipation of the ring materials (either from the high or low side) would seem to present a difficulty in having sufficient duration while the materials are available...

I would postulate that these ring systems, formed by grazing impacts, may be relatively easy to form on bodies of the right size range ... say 100 to 1000 km (pure speculation) diameter airless bodies. Thus there is no need to realign the spin axis ... one grazing impact will form a ring yielding a distinct set of grooves, then assume that there have been multiple such impact scenarios, each yielding a ring in a slightly differently inclined orbit.

[from Phil]...The first point of difficulty will be explaining how the debris forms a ring. Normally one would say that every piece of ejected material will be on a path that either escapes the object or falls back to the surface after less than one orbit...[...]
It's been quite a few years since I read the papers on the lunar origin theory which bases the origin of the moon on a grazing impact (I recall a major paper in Icarus, plus I have a book on the topic somewhere), but as I recall: during a grazing impact there develops a plasma interaction between grazing impactor and the ground, the net result of which is a momentum exchange such that proportion of the impactor ends up in orbit, rather than being lost to escape velocity or impact. Presumably this generalizes to larger asteroids. Considering that many smaller asteroids are rubble piles, it may be even easier for a grazing impact by rubble pile asteroid to leave a substantial amount of material in orbit to form a ring.

Assuming that all of this isn't complete navel-gazing, there is presumably some optimal size/mass of asteroid for which this sort of thing is most common. Some group with the appropriate computational resources (say those who worked on the Lunar origin scenario or the Iapetus ridge-via-ring scenario), would be in a good position to determine this through a series of simulations.
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charborob
post Jul 21 2010, 05:38 PM
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I've been more or less following this discussion about ring systems around asteroids. Considering the number of asteroids out there, what would be the probability that a few actually exist at the moment? I suppose we would have to take into account the frequency of impacts and the life expectancy of a ring system.
Personally (and unscientifically), my feelings go to the "partially filled cracks" theory.
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fredk
post Jul 21 2010, 09:33 PM
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QUOTE (algorimancer @ Jul 21 2010, 04:06 PM) *
the ring orbit decays over time until the ring intersects the surface, forming a groove

How is the groove supposed to form? Impact of ring particles? At the very low Lutetia orbital velocity, wouldn't you expect the ring material to pile up in ridges, Saturn-moon style?
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tasp
post Jul 22 2010, 04:57 AM
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QUOTE (charborob @ Jul 21 2010, 11:38 AM) *
. . . I suppose we would have to take into account the frequency of impacts and the life expectancy of a ring system.



I did a little math on the the possible ring derived Iapetan equatorial ridge system, (volume vs. deposition rate), and assuming a few simplifications, a deposition rate of 1 cubic meter per second can 'install' the ridge system in less than a thousand years.

I have insufficient math skills to come up with some estimates for how fast a ring system can redistribute angular momentum to shed material onto the primaries' surface from the low side, but I suspect the 1 cubic meter per second to be extremely fast. But even a limit of .01 cubic meter per second only gets you out to 10,000 years duration when there would be something 'fun' to see. In a 4 billion+ year old solar system, you would need a pretty serious asteroid collision rate to assure something 'fun' to watch in our era. I also note, in the case of Iapetus, it appears an extreme upper limit for the number of times it plausibly had a ring system would be <or = to 1.

As for splatting collisional materials into orbit, grazing collisions would seem to offer a substantial 'braking' effect while the contact between the bodies is occurring. As the impactor grazes, and breaks up, it seems plausible a significant portion of the impactor might end up in the correct speed regime to achieve some kind of orbit. Granted, materials lost on hyperbolic trajectories following the graze are lost for good. I think examining the surface of the primary 180 degrees around from the grazing collision sight would be interesting. As the lofted materials 'process' per the LaPlacian collapse to the equatorial plane (see the Planetary Rings chapter in The New Solar System for a fuller description of this) undoubtedly, considerable materials are going to clobber the primary, but unfortunately for us wanting to study the process, these tertiary craters are going to be spread over a huge area on the primary and are going to be difficult to sort out from all the other craters. As we see from the depositional rate, an essentially planar ring system does not require much mass to be interesting, so even a somewhat inefficient process for orbiting the raw materials, and another somewhat inefficient process for cranking those materials down to the equatorial plane does not seem to be an insuperable barrier.

Grazing collisions are quite interesting, the degree of overlap of the primary and the impactors radius, the approach angle, the differential velocity, the similarity of the compositions of the two bodies, are all going to make modeling these events rather complicated.


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bk_2
post Jul 22 2010, 08:24 AM
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QUOTE (Hungry4info @ Jul 21 2010, 12:18 PM) *
While I can see how that would apply to Phobos ...

Furthermore, for ring impacts to create lines, the moon's orbit must be coplanar with the ring plane ...


That is the sine qua non of this hypothesis. I see two possible origins for rings coplanar with a moon. A grazing impact, as described by Tasp above, would produce a cone of debris with some distribution of particle size and velocity but essentially symmetrical. If some of the debris that didn't escape or fall back, coalesced into a moon, while the rest formed a ring, they might well be coplanar.

The other possibility is a disruptive capture of an asteroid, with some of the original mass torn off by tidal force in passes beneath the Roche limit, providing the raw material for the ring. This too is likely to result in coplanar ring and moon.
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Hungry4info
post Jul 22 2010, 10:37 AM
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The Roche limits of the kind of bodies we're talking about are probably close enough to it that the irregular shape of the body is going to pose an immediate obstacle to forming a ring system.


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bk_2
post Jul 23 2010, 09:55 AM
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If the grooves on Lutetia were caused by the mechanism I propose for those on Phobos, the question is how Luetia could ever have been in orbit around a large body with rings.

We have evidence for a candidate large body in the asteroids, M and C types. The differences imply the existence of a large, fully differentiated body with a metallic core, that subsequently disintegrated. Perhaps there were several of these large doomed globes. Their disintegration must have involved catastrophic impacts, but it seems likely that before that there were many smaller, but significant grazing impacts giving rise to moons and rings in coplanar orbits. Lutetia could have been part of this.

It will be interesting to see how common the phenomenon is as we explore more of the asteroid belt.
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Hungry4info
post Jul 23 2010, 01:54 PM
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There's still the problem of forming the ring in the first place. The irregular shape of the body (Lutetia in this case) would being any such rings down quickly unless the impactor hit the highest elevation point, which in itself is an improbable event. Impact velocity is also an issue. These bodies have very low (and irregular) surface gravities, getting the particles to make a nice neat line is going to be a problem.

Speaking of nice neat lines, how do you propose for the ejecta to form such a narrow, confined line? Debris spreads out after a collision, yet the grooves on Phobos, Lutetia are linear instead of fan shape.

And why would your mechanism be confined to small bodies? Why not larger bodies like the various moons in the solar system, who have stronger surface gravities to help encourage such secondary impacts and as well as pull in impactors?


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bk_2
post Jul 23 2010, 11:28 PM
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Perhaps I didn't make myself clear. Impacts on Lutetia played no part in the formation of its grooves. It was an impact on the body it was orbiting that formed rings and Lutetia itself. The ejecta coalesced into moon and rings, with the moon in an elliptical orbit coplanar with the rings.

I'm worried now that there may not be enough matter in the asteroid belt to account for a planet of sufficient size to support this hypothesis. It was big enough to differentiate. What is the minimum mass for a body to differentiate?
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DFinfrock
post Jul 24 2010, 12:54 AM
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I was showing these images of Lutetia to my son and he remarked that the grooves were reminiscent of the concentric "shock waves" that appear when you toss a rock into viscous mud.

Could an impact into a compacted rubble pile produce shock waves that would show up as "grooves"? If that is possible it would make sense to see if any of the grooves align concentrically at a distance around large impacts. Of course if the grooves are really straight, rather than showing slight curvature, then that hypothesis dies quickly.
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