Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-13T11:18:39.619Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Chapront, J., Bretagnon, P., Mehl, M.: 1975, ‘Un formulaire pour le calcul des perturbations d'ordre élevé dans les problèmes planétaires’, Celes. Mech. 11, 379–399 Google Scholar
Message, J.P.: 1989, ‘The use of computer algorithms in the construction of a theory of the long-period perturbations of Saturn's satellite Hyperion’, Celes. Mech. 45, 45–53 Google Scholar
Taylor, D.B., Sinclair, A.T., Message, P.J.: 1987, ‘Corrections to the theory of the orbit of Saturn's satellite Hyperion’, Astron. Astrophys. 181, 383–390 Google Scholar
Vienne, A., Duriez, L.: 1991, ‘A general theory of motion for the eight major satellites of Saturn. II: short-period perturbations’, Astron. Astrophys. 246, 619–633 Google Scholar
Woltjer, J.: 1928, ‘The motion of Hyperion’, Ann. Sterrewacht Leiden XVI-3,Google Scholar