Narrow rings have been discovered around Saturn, Uranus and the other gas giants. These structures are hundreds of thousands of km across yet only a few km wide. The most well-known radial confinement theory involves Shepherd moons in which each ring is bracketed by a pair of small satellites. Saturn’s F ring and the Uranian Epsilon ring have exactly such moonlet pairs. In other cases, two body resonances seem to be responsible for sculpting ring edges. However, for the vast majority of rings, neither of these machinists is active. We are investigating the possibility of three-body resonances inducing stability in narrow rings using a N-body code, hnbody. We modified the code to simulate narrow rings using a chain of particles by including the gravity from only the nearest neighboring particles. We study the strengths and limitations of this code by measuring the precession rate for rings modeled with different numbers of particles and/or nearest neighbors. We have developed graphic tools in Python to directly visualize the chain of particles using polar. The FFT is particularly useful for finding weak resonances caused by a distance satellite or the more exotic three-body resonances.
Link to PDF (may not be available yet): P12-10.pdf