Appendix A: Approximate Titan orbit

The orbit of Titan used in computing the perturbations in the simplified model is defined by a set of orbital elements which were derived from a fit to the SAT077 integrated Titan orbit. Because of Titan's small eccentricity and inclination, we adopted the equinoctial form of the elements (Broucke & Cefola 1972); Table 9 (click here) contains the elements. The table also gives the orientation angles for Titan's Laplacian plane in the Earth mean equator and equinox of J2000 system. The orbital longitudes () are measured from the ascending node of the Laplacian plane on the Earth mean equator of J2000. The root-mean-square of the differences between the Titan orbit defined by the elements and the integrated orbit are 72 km in the radial direction, 264 km in the in-orbit direction, and 210 km in the out-of-plane direction over the 1966 to 2013 time period.

When computing the perturbations on Phoebe, the Titan position relative to the Saturnian system barycenter is found with the elements, and then the position of Saturn relative to the barycenter is formed from the Titan position assuming that Titan and Saturn are the only massive bodies in the Saturnian system.

   

Element Value Units

a km deg deg/s deg/s deg/s

Laplacian plane pole deg right ascension

Laplacian plane pole deg declination

Table 9: Titan barycentric orbital elements at Julian ephemeris date 2451179.5 referred to Titan's Laplacian plane