The Difference Between 6 and 7

by landonlehman

A ring system consists of n  “light” point masses orbiting around a “heavy” central mass. Assume that the orbit is circular and the light masses are equally spaced around the circle. The relevant physical force is Newtonian gravity.

Here is a ring system with n = 6:

6_rings

And here is a ring system with n = 7:

7_rings

 

The ring system with n = 6 is always linearly unstable, while the ring system with n = 7 can be stable (if the central mass satisfies a certain condition).

See the detailed analysis here: https://arxiv.org/abs/astro-ph/0606510, by Robert J. Vanderbei and Egemen Kolemen.

This is closely related to work done by Maxwell (yes, the electromagnetism Maxwell) on the stability of the rings of Saturn. Speaking of which, some amazing pictures have been taken of Saturn’s rings:

PIA21628_-_B_Ring_fine_structure_in_color

The above is a high-resolution image in the Solar System sense – each pixel corresponds to about 3 square kilometers! The image was taken by the Cassini Orbiter. (More info here: https://photojournal.jpl.nasa.gov/catalog/PIA21628).

 

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