General planetary theory extended to the case of resonance and application to the Galilean satellite system of Jupiter

Details General planetary theory extended to the case of resonance and application to the Galilean satellite system of Jupiter General planetary theory extended to the case of resonance and application to the Galilean satellite system of Jupiter

Mar 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..26..231d&link_type=abstract

(Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets, Facultes Universitaires Notr

Astronomy and Astrophysics

Astronomy

10

Astronomical Models, Jupiter (Planet), Natural Satellites, Orbital Mechanics, Planetology, Solar Orbits, Callisto, Europa, Ganymede, Io, Libration, Periodic Variations, Planetary Systems, Resonance, Planets, Theoretical Studies, Resonance, Jupiter, Satellites, Techniques, Procedure, Mathematical Models, Parameters, Harmonics, Resolution, Oscillations, Librations

Scientific paper

A planetary system defined by a given distribution of mean mean motions and masses is considered through the representation of the osculating elliptic elements of their heliocentric orbits by quasi-periodic functions of time, using a method adapted to the commensurability case. The functions are the sum of the general solution of a critical system, expressed in long-period terms, and the critical system contains the secular terms, the long-period terms, and the resonant terms. The particular solution consists of short-period terms only, whose amplitude is a function of the critical system's solution. A differential system is obtained for the case of the Galilean satellites of Jupiter, with constant coefficients, whose linear part concerns all the variables and yields as a first approximation the great inequalities, the free oscillations, and the libration.

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