, Volume 12, Issue 1, pp 89-99
Date: 21 Aug 2012

The Dynamics of Rings: From Benzene to Saturn

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In this paper I draw the connection between the chemist’s analysis of the vibrational dynamics of benzene and the analysis of dynamics of celestial rings. Chief among the results is the identification of the hip-hop orbit as the B 1g out-of-plane ring mode of benzene. Three additional periodic orbits are predicted to occur. These correspond to the A 1g breathing mode and the B 1u and B 2g in-plane ring modes. These last two are seen to be analogous to out-of-plane hip-hop orbit. The doubly-degenerate modes, E 1u , E 2u , E 2g give rise to one-parameter families of period orbits. These are also discussed. And finally the implications of these results for models of the rings of Saturn are also discussed.

To Kenneth R. Meyer for making his math accessible to chemists.