Theory of motion and ephemerides of Hyperion.

Abstract

Wepresent here anew theoryofmotion forHyperion, the seventh major satellite of Saturn. The Hyperion’s motion is defined like in TASS1.6 for the other satellites (Vienne&Duriez 1995), by the osculating saturnicentric orbital elements referred to the equatorial plane of Saturn and to the node of this plane in the mean ecliptic for J2000.0. These elements are expressed as semi-numerical trigonometric series in which the argument of each term is given as an integer combination of 7 natural fundamental arguments. These series collect all the perturbations caused by Titan on the orbital elements of Hyperion, whose amplitudes are larger than 1 km in the long-period terms and than 5 km in the short-period ones. However, the convergence of these series is so slow that, in spite of several hundreds of terms, their internal accuracy over one century is about 200 km only. These series have been constructed in such a way that the fundamental arguments and the amplitude of each term depend explicitly on 13 parameters (the twelve initial conditions of the motions of Titan and Hyperion and the mass of Titan). Taking also account of the perturbations from other satellites and Sun, we have fitted these series to 8136 Earth-based observations of Hyperion in the interval [1874-1985], giving a set of better values for these parameters. In particular the mass of Titan is found equal to (237.399 ± 0.005) 10−6 (in units of the Saturn’s mass) and we discuss this value in comparison with that [(236.638 ± 0.008) 10−6] obtained by Campbell & Anderson from their analysis of the Voyager missions to Saturn. The resulting fitted series allows us to produce new ephemerides for Hyperion. Their comparison to those from Taylor (1992) shows that, with the same set of observations and the same way to weight them, we obtain a root mean square (o−c) residual of 0′′ .156 while the ephemerides of Taylor gives 0′′ .203.