Dynamics of Saturn’s Ring (I. Wake Structure)

What are Saturn's rings made from? It is known that the rings are made from countless, small, icy clumps with diameters ranging from dozens of centimeters up to several meters. When seen together, these form a ring. Moreover, pictures taken by spacecraft like Voyager and Cassini show that Saturn's rings have complicated structures. What mechanisms create such structures in the rings? Here we introduce one of the computer simulations which can give insight in to the mysteries of Saturn's rings.

Saturn's rings are made from innumerable ice particles, making it impossible to simulate the entire ring. Therefore, we take a part of the ring and perform a simulation of the particles in this region in order to understand what is going on.

First, let’s show a movie to explain our simulation. Inner moons orbit faster than the outer ones. The components of the rings, ice particles, follow the same motion. This motion is indicated by red arrows.
Let’s orbit around Saturn with the ice particles. Particles closer to Saturn move faster and outpace the camera. On the other hand, ones that are farther away from Saturn move slower and lag behind the camera. This is just like the cars in the inner lanes overtaking cars in the outside lanes on the freeway.
This movie shows a simulation following a part of the ring, a few hundred square meters in area, as it orbits around Saturn.
We can see complicated patterns. These patterns formed by the aggregation of numerous ice particles are called "wake structure."
These patterns are formed by the attractive effect due to the self-gravity of the particles and the shearing effect due to their differential rotation around Saturn.
It looks like the aggregates of ice particles are colliding at high speeds. But that is because this movie shows the motion over several days compressed into 2 minutes. The actual collision speeds of the aggregates are very slow.
Although these small scale structures cannot be seen directly by spacecraft such as Cassini, they have been observed indirectly by methods such as occultation. It is inferred that dense regions of Saturn's rings have such structures.
The stripes of Saturn's rings have a much larger scale than that of the simulation in this movie. In other words, we cannot simulate the stripes seen in the pictures taken from the spacecraft. Recent large-scale simulations are beginning to reveal the origin of those stripe structures.

Full version : 640x480, Windows Media Video

SaturnRingWake64x48Full_e.zip ( zip file : 88.5 MB)

Short version : 640x480, Windows Media Video

SaturnRingWake64x48Short_e.zip ( zip file : 77.9 MB)

Full version : 320x240, mpeg

SaturnRingWake32x24Full_e.zip ( zip file : 37.9 MB)

Short version : 320x240, mpeg

SaturnRingWake32x24Short_e.zip ( zip file : 33 MB)

Other file formats

  • 1024x768 (.avi) stereoscopic/non-stereoscopic
  • 2048x2048 Dome Master (.mp4, .tif sequence files) stereoscopic/non-stereoscopic
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Numerical Simulation Details

Basic ModelPeriodic boundary conditions + shearing box
ObjectDynamics in Saturn's rings
Calculation MethodGravitational N-body simulation + rubble pile model
Number of Particles:7×104 particles
Machine Used for SimulationGRAPE-6
Phenomena Timescale Several days
Phenomena Spatial ScaleSeveral ten meters to several hundred meters
AuthorHiroshi DAISAKA (Hitotsubashi University)
ReferenceH. Daisaka, H. Tanaka, and S. Ida, Icarus 154, 196, (2001)

Details of Visualization

In this simulation, there are not hard walls at the boundaries of the simulated area. Instead, it is assumed that the left boundary wraps around to connect to the right boundary and vice versa. (This assumption is known as periodic boundary conditions.) Hence, we can investigate a large-scale phenomenon by simulating a relatively small-scale region. In order to cover an area as large as possible, we make copies of the simulated region results and array them over a wide area to make the movie.


  • Simulation: Hiroshi DAISAKA
  • Visualization: Takaaki TAKEDA
  • 4D2U Project, NAOJ

Release Information

  • March 2016: This contents download page opened.