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What is Time Dependent Nature of the Neptune's Arc Configuration about?

By distinguishing the main arc Fraternite from the minor arcs Egalite (2,1), Liberte, Courage, the restricted three-body system is extended to a non-conservative restricted four-body system with the central body Neptune S, the primary body Galatea X, a minor body Fraternite F, and a test body s. Through the equations of motion, it is shown that the locations where the force is null along the orbit of s correspond to the locations of Egalite (2,1), Liberte, and Courage. Even if all the arcs were captured by CER sites initially, the orbits over the CERs would be unstable for the minor arcs due to the disturbing force of Fraternite, allowing them to be relocated to the null points. On the other hand, the minor arcs do not have the mass to destabilize Fraternite from its CER site, which is enlarged from 8.37 degrees to 9.7 degrees thus accounting for the Fraternite's span. In this restricted four-body system, s is under the effects of the potentials of X and F. The potential of X drives a long period harmonic pendulum oscillation of $(n+1)\theta_{s}$ of the test body s with respect to $n\theta_{x}$ of X centered over a local CER site with period $T=1,000\,d$, while the potential of F d

Author

Tsui, K. H.

Published

2018

Language

EN