The Moons Of Saturn : Orbital Motion

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The moons of Saturn are numerous and diverse ranging from tiny moonlets less than 1 kilometer across to the enormous Titan, which is larger than the planet Mercury. Saturn has 62 moons with confirmed orbits, 53 of which have names and only 13 of which have diameters larger than 50 kilometers (Porco 2009). Twenty-four of Saturn 's moons are regular satellites; they have prograde orbits not greatly inclined to Saturn 's equatorial plane, while the other 38 are irregular satellites (Turrini et al. 2009; Grav et al. 2015), whose orbits are much farther from Saturn, have high inclinations, and mixed between prograde and retrograde orbits. 3.2.2 Theories of Saturnian’ Satellites
Several theories have described the orbital motion of the eight major satellites of Saturn (Mimas, Enceladus, Tethys, Dione, Rhea, Titan, Hyperion and Japetus). Because of resonances, the theories by Struve (1898 and 1933), Woltjer (1928) and Senclair (1977) described the motions of satellites in pairs (e.g.: Mimas-Tethys, Enceladus-Dione, Rhea-Titan and Titan-Hyperin). Kozai(1957) and Rapaport(1977) have improved such theories and adjusted their constants. Taylor (1984), Taylor et al. (1987) and Harper (1988) have developed the theory of Hyperion and Iapetus by adding some of missing terms. However, the above theories still not accurate and the residuals with observations from the Earth are about (~1400 km) in the Saturnian system.
Duriez and Vienne (1991a) introduced a new general analytical theory
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