THE ORBITS OF THE MAJOR SATELLITES OF SATURN

Strugnell & Taylor's (1990) catalogue of observations of the major satellites of Saturn was augmented by several thousand additional observations. Theories of the motions of the satellites (excluding Hyperion) were fitted to these observations using a weighted least-squares procedure in order to derive improved values of the orbital elements and other parameters of the system, including the masses of the four inner satellites and the dynamical form factors J2 and J4 of Saturn. We find the following values: Mass of Mimas = (0.0646 +/- 0.0011) x 10(-6) Mass of Enceladus = (0.213 +/- 0.046) x 10(-6) Mass of Tethys = (1.076 +/- 0.018) x 10(-6) Mass of Dione = (1.916 +/- 0.036) x 10(-6) Dynamical form factor J2 = 0.016478 +/- 0.000038 Dynamical form factor J4 = -0.001 10 +/- 0.00028 Node of Saturn's equator plane = 168.8387-degrees +/- 0.0035-degrees Inclination of Saturn's equator plane = 28.0653-degrees +/- O.0016-degrees where the masses of the satellites are expressed in units of Saturn's mass and the dynamical form factors have been calculated assuming the equatorial radius of Saturn to be 60000 kilometres. The position of the equator plane of Saturn is referred to the mean ecliptic and equinox of the epoch B 1950. The masses of the satellites agree well with those determined by Dourneau (1987). The dynamical form factors agree well with those obtained from analysis of radio tracking data from the Pioneer and Voyager spacecraft. We also find that inclusion of the long-period terms calculated by Vienne et al. (1991) in the mean longitude of Mimas causes a small but significant reduction in the coefficient of the secular acceleration which was introduced by Kozai (I 957). This suggests that the discrepancy between observed and computed values of the mean longitude of Mimas may be due to the omission of terms of very long period, as proposed by Vienne et al. (1991)