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A Synthetic Theory of Motion for Titan-Hyperion

Published online by Cambridge University Press:  07 August 2017

L. Duriez
L. Duriez*
Affiliation:
Laboratoire d'Astronomie de l'Université des Sciences et Techniques de Lille-Flandres-Artois, 1 Impasse de l'Observatoire, F 59000 Lille, France

Abstract

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We present an iterative method allowing to synthetize a semi-numerical solution for the equations of motion of the resonant Saturn's satellites Titan-Hyperion (limited now to the planar problem). The current theory of Hyperion by Taylor, Sinclair & Message (1987) gives the greatest terms of the long-period part of the solution (depending on two angles: the libration angle τ, and the angular distance of the pericenters ζ). Using it as a first approximation, this solution is substituted numerically in the exact Lagrange equations of motion for Titan and Hyperion, computed for many values of the three angles: τ, ζ and ϕ (the mean synodic longitude). Then, a multivariable Fourier transform allows to reconstruct the equations in these three angles, that is in same form as the initial one with, in addition, the short-period terms. Then, a solution may be obtained and used as a better approximation in an iterative process. Besides a complete determination of the short-period perturbations of Hyperion obtained here completely for the first time, some long-period perturbations of Titan by Hyperion are also found which would be non negligible at the 10 km level.

Keywords

Titan-Hyperionsemi-numerical theoryresonance
Type
Part IV - Planetary Satellites
Information
Symposium - International Astronomical Union , Volume 152: Chaos, Resonance and Collective Dynamical Phenomena in the Solar System , 1992 , pp. 209 - 214
Copyright
Copyright © Kluwer 1992 

References

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