Analytical Representation of Saturnian Satellite Numerical Ephemerides over Limited Time Spans

Abstract

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 an analytical representation of the mean longitude of Titan from the Jet Propulsion Laboratory (JPL) ephemerides. We established this representation as a function of combinations of proper frequencies and compared the results with those obtained from the synthetic ephemerides of the Théorie Analytique des Satellites de Saturne (TASS), Building upon this, we have extended our analytical representations beyond the mean longitude to the other osculating elements of the Titan ephemeris. This enables us to develop new synthetic representations that combine the strengths of both approaches: the long-term stability and system complexity inherent in TASS. In our current work, we have shifted our focus to the NOE ephemerides from the Paris Observatory. Unlike the JPL ephemerides and the synthetic TASS ephemerides, the NOE ephemerides account for Saturn’s tidal effects and long-period solar terms within their perturbation calculations. This results in a more complex analytical representation of the NOE ephemeris compared to the JPL ephemeris. Notably, these representations encapsulate crucial dynamical information, including proper frequencies, which are invaluable for theoretical research.