A semi-analytical solution for the eccentricities and longitudes of the pericenter of the Uranian satellites

Astronomy and Astrophysics – Astronomy

Scientific paper

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Orbital Elements, Orbital Mechanics, Periodic Variations, Uranus Satellites, Double Cusps, Eccentricity, Laplace Equation, Longitude, Secular Variations, Uranus, Satellites, Eccentricity, Longitude, Astronomy, Motion, Period, Oscillations, Orbital Elements, Celestial Mechanics, Theoretical Studies, Calculations, Procedure, Numerical Methods, Miranda, Ariel, Umbriel, Titania, Oberon

Scientific paper

Semi-analytical solutions for the variations in time of the eccentricities and longitudes of the pericenter are developed as part of a complete semi-analytical theory for the motion of the Uranian satellites. All the long and short period variations of these elements, up to the order of 10-5, are considered. The results show that the oscillations around the mean value obtained by other authors through the analysis of the observations of Uranus' system, are significant. A discussion on the importance of the determination of osculating orbital elements, in order to obtain integration constants consistent with the real movement of Uranian satellites, is presented.

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