Analytical Representation of Saturnian Satellite Numerical Ephemerides over Limited Time Spans

Numerical integration ephemerides are highly valued in both research and engineering due to their exceptional precision. However, their application in theoretical studies, particularly in the investigation of rotation and evolution, is constrained by their finite available time spans. In our previous work, we effectively explored the analytical representation of the mean longitude of Titan from the Jet Propulsion Laboratory (JPL) ephemeris. We established this representation as a function of combinations of proper frequencies and related the results with what is given in the synthetic ephemerides obtained by the Théorie Analytique des Satellites de Saturne (TASS).

In this study, we extend our analytical representations beyond the mean longitude to the other osculating elements of the Titan ephemeris. This allows us to create new synthetic representations that combine the benefits of both systems: the enduring stability and system intricacies of TASS, along with the exceptional precision characteristic of numerical integration ephemerides. These combinations encompass vital dynamical information, including the proper frequencies, which will be valuable for theoretical research.