On a ring origin of the equatorial ridge of Iapetus Options

[tasp]

Found some rough estimates I did (my fault if I slipped a decimal along the way) of what the27 km sphere would shape out as a disk.

A circular disk 112 km across, and 1 km thick, also, an 80 km disk 2 km thick.


Compare the disk sizes to crater volumes. Seems like there is no shortage of craters on Iapetus that plausibly could have been the possible 'source' crater for a ring system.

Keep in mind I have totally neglected the efficiency of an impactor in placing materials into orbit about Iapetus. Not sure how to proceed with that.

Would an oblique impact produce a spray of debris with a gaussian distribution of exit velocities? I dunno.

If it did, and the curve of velocities was from zero meters per second to perhaps something faster than Iapetan escape velocity, do we get the peak of the curve in the range of velocities needed to orbit Iapetus?

In this favorable scheme of things, maybe ~20% of the materials do what we want?

I have also neglected the fate of the impactor. Materials from the surface of Iapetus are going to be entrained along with the pulverized remains of the original impactor. Of course, the faster the impactor hits, the smaller it can be. As it's incoming speed increases, do we see a change in the velocity distribution of the ejecta? We might be able to come up with a minimum size of the incoming impactor if we look at at enough of the criteria. Far beyond my skills in any regard. Might stick with an impactor of around 27 km maximum size just for starters. Maybe someone can can get an idea of how efficiently such an object coming in at around ~5 degree angle to the surface can loft debris into orbit.

Also, what does the resulting crater look like? Elongated of course, but what kind of length to width ratio? 1:2? 1:3? Do we get an elongated central peak too? Hopefully we can get to the point where we have enough of this pinned down to go a little further than just saying the crater in the southern hemisphere on the eastern edge of Cassini Regio 'looks right'.

[tasp]

What was Iapetus' rotation rate at the time of ring formation?


OK, I don't have a number for this ( a guess would be 10-20 hours) but there might be a way to find out.

The impactor that lofted the ring material, also must have yielded a great many objects that did not achieve orbit (probably a pile of stuff at greater than escape velocity too), and all the slow stuff came back down on Iapetus.

If we can identify a population of secondary impact craters, and define the areal extent of the debris, we might be able to garner some statistics about the impacts. The ones on the shallower trajectories might also be expected to create elongated craters too, and the long axis of the craters will point back to the parent crater.

-but-

The point back angle will vary with distance from the crater. Iapetus might have been rotating on it's axis faster than once every ~80 days in that time period. The materials lofted further downrange will have had the Iapetan axis turn through a larger angle than the closer debris.

For materials destined to impact Iapetus 180 degrees around, the flight time will be just under 1 1/2 hours. If Iapetus rotated in 15 hours in those days, it will turn 36 degrees during that 1 1/2 hour period. This will also skew the footprint of the entire debris field.

If we can identify craters formed secondarily to the ring lofting impact crater, we could potentially know the rotation period of Iapetus in those days. The location and the orientation of that subset of Iapetan craters could yield an amazing piece of hard data.

Should an accurate timescale of the Iapetan tide lock / spin down period be known, (presumably this is a largish number), we might get a fairly precise date for the formation of the equatorial ridge structure.


Would this interesting bit of information be worth another Iapetan flyby during the Cassini extended tour?

Any chance we could discern the appropriate craters on Iapetus for this technique?

[tasp]

Thought of another way to get the symmetrical diverging attendent ridges, too.

{to reiterate, the attendant ridges might have formed as inclined elements in the outer ring system eventually came low enough to contact the existing 'high spot' along the equator. Or, during emplacement of the ring materials, toward the end of the process, Iapetus suffered a major (unrelated) impact that nudged the Iapetan rotation axis off a few degrees}

The new idea; there were two impacts that lofted ring forming materials into Iapetan orbit, seperated in time by virtually any conceivable amout of time consistent with the surface ages as determined by the crater counts on the various aspects of the ridge system. During the interim period of time, the Iapetan axis shifted a few degrees, either from another impact, or possibly long term effects on the Iapetan orbit of solar (or whatever) perturbations.

{it would even be possible in this epoch (send NASA lotsa money!) for us to nudge a smallish asteroid into a grazing collision with Iapetus, reloft some materials, and watch the whole ring forming and emplacement process at our convenience}

[tasp]

We can even run a slighty different kind of experiment and generate a variant type of ridge system.

Find a highly spherical object. Contrive a very tall mountain 5 degrees from the equator on this object. Have the grazing collision take place, and have the ring form. Perturb the ring to orbit inclined to the equator 10 degrees.

You now get a structure that does not have the central ridge, and the two diverging ridges that form will have unequal lengths, in proportion to the number of degrees off of the 180/180 degree equatorial sweep the current system shows.

If you contrive the mountain at 10 degrees, you again only get one ridge, but it will make a beautiful sweep
(~) relative to the equator. (it will still follow a great circle path though)

[tasp]

One aspect of the ring emplacement I have not covered in too much detail is just what happens as the ring particles contact Iapetus.

I will attempt to flesh out some thoughts I have had about this.


As the ring particles orbit Iapetus, various drag forces act upon the ring system (Poynting/Robertson, solar wind effects, Saturnian magnetspheric drag, etc.) and sap energy from it. These forces probably would not be terribly effective upon a solid object 27 kilometers in diameter, but since it is in a disconsolidated form with an enormous surface area, these forces are of sufficient magnitude to dissipate the orbital velocity of the ring mass in considerably less time than the age of the solar system.

As the ring materials collapse to the Laplacian plane, I expect them to be rather pulverized. A precise size might be a little iffy, but somewhere between bowling ball and Volkswagen size is my guess. Seems the physics of all this won't be affected too much by scaling effects. Also, while cryogenic water ice (best guess for the ring composition) is quite sturdy, I don't think the mechanical properties of the material are too different from ordinary materials we are familiar with.

So, what happens as the materials descend towards the surface of Iapetus?

The dynamical ring spreading process occurs, and transfers momentum from the 'low' side of the ring system towards the 'high' side. As a result the materials at the low edge of the ring, slowly descend towards the surface. But as they do this they maintain their circular orbits. (if you watched in time lapse, the paths would be a very, very tight spiral, but we can consider it a circle with out being to far off).

I expect the particles to be in a rough equilibrium with each other in regards to their individual rotation rates. That is, particles in the lowest orbits are going to be rotating individually in about 3 hours as they revolve around Iapetus in 3 hours. Various particles may jostle and bump, but for the most part, we can consider the lumps to be not spinning as they orbit.

How fast do they descend?

I consider an absolute minimum time to emplace the ridge structure at 350 years. This is a 1 cubic meter per second emplacement rate. The actual rate is probably vastly slower, and is regulated by drag effects on the ring system as a whole. 0.1 cu/meters per second implies deposition in 3500 years, and 0.01 cu/meters per second implies 35,000 years.

At the low deposition rates, we must also consider extremely slow descent rates for the ring system. Individual chunks of 1 cu/ meter size might be coming down once every minute and 40 seconds or so.

I had imagined in the higher depostion rates something occuring very much like bowling balls smacking and shattering upon a sturdy cliff edge, with still orbiting ring particles immediately above the 'splat'.

This might be too simplistic. At very low sink rates, the individual ring chunks will graze the highest spot along the Iapetan equator. Imagine, if you will, a 1 meter sized sphere of ice, traveling ~1500 kph intersecting an icy plane with only millimeters of intersection.

What happens?

Even cryogenic ice will experience friction, and the ice chunk, once it contacts the surface, will not be in orbit anymore, it will become a hockey puck. Its' forward velocity will assure it will continue on downrange, and the mounting deceleration forces and frictional contact with the surface will tend to break it up as it skitters along the ground. Additionally, you have cryogenic ice, contacting a cryogenic surface, in a cryogenic environment. Kinetic energy of the incoming lump is going to be dissipated over time and distance, and the materials (already thermo processed in the original impact event that lofted them into orbit in the first place) are going to experience low melting and micro vaporization.

Repeat a few zillion times, and you get a ramp shaped snow bank, dead straight, aligned perfectly with the Laplacian plane (equator), and tapered downwards from the contact spot downrange.

[alan]

Another object with an equatorial ridge
http://www.news.cornell.edu/stories/Nov06/kw4.arecibo.html
Movies here
http://echo.jpl.nasa.gov/~ostro/kw4/index.html

[TritonAntares]

Cornell University - Chronicle Online - Nov. 15, 2006:

...
The researchers were able to reconstruct the orbit, mass, shape and density of KW4's two components, Alpha and Beta.
They found an oddly shaped pair of dance partners, with Alpha, by far the larger (1.5 kilometers in diameter) of the two,
spinning as fast as possible without breaking apart, and the smaller and denser Beta wobbling noticeably as it orbits its partner.
...

Nice finding, but Alpha is not comparable to Iapetus concerning diameter and rotation period, apart from being part of a close binary, I guess...

Bye.

[nprev]

Hmm...interesting, Alan, thanks.

I think that NH may make or break this conjecture after all. Pluto is probably the closest analog to the "ringed Iapetus scenario" we're likely to see in many ways: it almost certainly had rings at some point(s) after the event(s) that created its satellite system, and may still have them today. The satellite system can be considered a well-preserved dynamical artifact because, of course, there's no Saturn to mess things up. If Pluto has a fossil equatoral ridge, that would provide a strong argument for a formerly ringed (and mooned?) Iapetus.

[volcanopele]

hmm, "Alpha" looks an awful lot like Pan.