Chaos and secular variations of planar orbits in 2:1 resonance with Dione

Details Chaos and secular variations of planar orbits in 2:1 resonance with Dione Chaos and secular variations of planar orbits in 2:1 resonance with Dione

Jun 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987a%26a...179..304f&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 179, no. 1-2, June 1987, p. 304-310.

Astronomy and Astrophysics

Astronomy

14

Chaos, Dione, Orbit Calculation, Orbital Resonances (Celestial Mechanics), Planetary Orbits, Resonance, Secular Variations, Differential Equations, Eccentric Orbits, Euler-Lagrange Equation, Saturn (Planet), Time Dependence, Saturn, Satellites, Dione, Resonance, Astronomy, Orbits, Calculations, Models, Perturbations, Eccentricity, Numerical Methods, Energy, Periods, Evolution, Procedure, Techniques, Celestial Mechanics, Time Scale, Motion, Enceladus, Parameters

Scientific paper

In the first part of the paper the authors derive the secular equations for planar satellite orbits in 2:1 resonance with Dione. A simplified model of the perturbing function R is used taking into account the secular, long periodic and critical terms of lower degrees in the eccentricities; the J2 term of Saturn has also been included. The authors end up with four first order differential equations integrated in numerical experiments with a Lie series integration method. In the second part they study the secular evolution of planar satellite orbits in the first order resonance (2:1) with Dione. The elliptic orbit of Dione leads to the rise of a region of chaotic motions in the transition region between libration and circulations. The integrations were performed over periods reaching up to 2×104years or 4 million periods of a typical satellite in 2:1 resonance with Dione. The secular variations of the satellite eccentricity are given as functions of time and are comparable to phenomena in asteroidal motions in resonance with Jupiter.

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