Moonlet Stability


  • Varying geometry (sphere vs. Ellipsoid)
  • Varying constituent particle size
  • Varying density
  • Solid core
        • Put down a lattice of small particles and then add a single large particle in the lattice (done in that order for ease of programming, and to test the non-stable state)
        • Build moonlet with larger r0
  • Immerse in Background particles (this work is being continued through summer 2011, Particle Adhesion is the link to the continued experiment)

Simulation and data analysis has now started for this experiment. We will be varying several parameters from the command line each time we run a new simulation. The format is
../RingsSim Density Rx Ry Rz rsmall-particles Rnaught > log.

  • The first few runs with individual particle density 0.4-0.8 but almost identical other parameters (excepting R naught, which was different by 0.5) show no indications of stability late into their orbits. The lattice structure seems completely unstable outside of the first few frames of the simulation. The same is true for larger Rx, by frame 1000 the lattice has become a stream of individual particles smeared out around the orbit path. The presence of a large core particle in these moonlets is looking more and more likely, either that or the possibility of a size distribution of smaller particles instead of all one radius. This latter option could possibly change the amount of gravitaional perturbation that the lattice could sustain before disintegrating.
  • Moonlet stability into later orbits has started occurring at individual density of about 0.8, and has also been shown to occur at at density of 1. The moonlets are still together at frame 10000 of the simulations, although their structure has changed significantly.
  • Increasing the value of R naught to that of the F ring (140000 km) changed the stability of the moonlet significantly, though the change caused a decrease instead of an expected increase in stability. The moonlet in this simulation was simply a stream of particles by frame 5000, indicating the importance of R naught. (further investigations have revealed that the size of the simulation timestep might actually be the culprit)
  • Note the apparent reconfiguration of Z axis structure throughout the orbits of "stable" moonlets. Some of the moonlets in the 0.7-0.8 range stay together through almost the whole simulation but break up by frame ~7000 or so. It seems to be related to this apparent reorganization of the moonlet lattice.
  • Initially we were assuming a 3:2:2 ratio for the ideal stable moonlet geometry, but the moonlets in the simulation have been deforming throughout their orbits to closer to a 2:1:1 ratio, which is what we are using for the newest simulations. This change has noticeably increased the stability of the lattice structure, causing less deformation throughout their orbits (with this new geometry,0.8 is the new threshold for individual particle density sufficient for moonlet stability throughout 10000 frames of the simulation).
  • Having explored a range of individual particle densities of 0.5-1.2, our investigation continues with variation in radius (both of the individual particles in the lattice and of the moonlet). Ideally, we want to see how big of a role each of these variables have in determination of moonlet formation stability. While radius is not particularly important to our work, it would help to set up a baseline influence (provided by variation in structure/stability with radius) to compare the rest of the variables to. The difficulty is going to be in quantifying these relationships.
  • Decreasing the individual particle radius from 0.5 to 0.25 e -7 while maintaining the 0.8 value for particle density caused another formation of an extended lobe structure after the collape of the particle lattice at frame 5000. It might be possible that some of these half-formed moonlets on the verge of staying together show up as some ring structures in Cassini images for the small window that they still have some vertical structure, but so far this is just speculation based on simulation results. Further thought on the matter leads to a problem: these structures are too short-lived to be possible because we would have witnessed the events that led to their formation.More interesting is the seemingly large variety in physical characteristics that give rise to the lobed structure at some point in the simulations. This will be explored further depending on how narrowly the stable moonlet characteristics are restricted by the end of the experiment.
  • There seems to be a proportional relationship between the radius of the moonlet and the required particle density to sustain its lattice structure, since the threshold stability density increases as the radius of the moonlet increases. While 0.8 was a good threshold for the 1.2e-6 moonlet, it does not work as such with the 2.4e-6 moonlet. This relationship must also change depending on R naught (the distance out from Saturn) because the amount of tidal forces exerted at various locations in the ring system change with r0, and these forces are going to affect the moonlet stability to various degrees depending on location.
  • A concern when running these particle simulations is the size of the timestep. When we talk of a moonlet surviving through "frame 5000", this means nothing unless we discuss the amount of time chosen to elapse between frames. A new adjustment in the lengh of this timestep can seriously change the resulting figures. Because we want to make sure we don't miss anything happening in the simulation, we have been slowly shortening the timesteps throughout the investigation of moonlet stability to get a feel for the timeframes over which these moonlets form and stay stable.
  • Changing the timestep seems to have messed up the code of the particle simulation, because now we are seeing virtually no change in moonlet structure over the course of 10,000 frames. This is obviously not accurate, so steps are being taken to try and remedy the situation. Currently there are 3 simulations that have finished running that have this problem.
  • We went back into the program file and corrected the previous inaccuracy by increasing the amount of frames that the simulations run, and so far the moonlets have still remained surprisingly stable throughout the simulation, but not without some slight reconfiguration of the lattice structure.

Solid Core Work:

  • New .cpp file called SolidCore, same variable syntax as before except with the addition of a particle density and radius of the core. The first simulations seem to indicate a decrease rather than increase in stability for a given particle density (kept at the same value as that of the lattice), but this could be either because the geometry of those moonlets is set up improperly, or possibly because there is a different particle density in the core than that in the outer layers. Next simulations with experiment with a solid rock core encompassed by ice.
  • Encountered difficulties finding the right relationship between individual particle size, core size, and moonlet size. As a result, some moonlets with solid rock cores were incredibly stable, while others did not last halfway into the simulation. As a whole, these types of moonlet exhibit more stability than their lattice counterparts. An even more interesting thing to note is that these types of moonlets can shed material quite easily (shedding events, see propeller photometry) when exposed to collisions with ring particles and self gravity, which would make them ideal candidates for propellors. The questions remaining: how much of this material is shed? How it is replaced? How does it interact with the ring particles? More important and more relevant at this point is the idea of finding some cutoff point for stable solid core moonlet density, radius, particle size etc.
  • New simulations seem to indicate that the stability of solid core moonlets does not rely on either symmetric particle density (same for both individual particles and core particles) or asymmetric particle density (indicates the presence of two different materials in the moonlet's composition). This is supported by the lack of change in stability when we switched from simulating an ice over a solid rock core to a rock lattice over an ice core. Both of these scenarios are apparently feasible, at least insofar as they are physically possible, but more thought needs to be put in to what situations would allow for the formation of a core of ice for a moonlet.
  • Unless otherwise indicated, these moonlet simulations are done at roughly the R naught value of the A ring (130,000 km), which also happens to be the area where propellers are usually found. This is done mainly to focus on our area of interest in the rings, but the later simulations will explore a range of R naught values.
  • Our latest efforts have been focused on encoding movie files that contain frames of our simulation, so we can watch step-by-step as the moonlets either stabilize their structure or slowly disintegrate. The purpose of this procedure is to nail down our lower threshold for stability density. This key point seems to be when the lower of the 2 particle densities drops below about 0.7, and that corresponds to a total surface density of about 0.5 g/cm^3, but we would like a more accurate value.


  • New modifications to .cpp files for both solid and no core: increased simulation run time and time between outputs, re-running simulations at or above 1.0 density values. This was done due to the fact that none of the simulations seem to be running long enough for the moonlets to accrete fully, and there is no use for half-formed moonlets in our work. We have also started looking at values of Rnaught that are different than 140000 km to give a range of radii around the A-ring.

DDA Poster

This is the poster that was presented at the 2011 DDA meeting on this topic.