Abstract
Context. The ephemerides of natural satellites resulting from numerical integration have a very good precision on the fitting to recent observations, in a limited interval. Meanwhile, synthetic ephemerides like the Théorie Analytique des Satellites de Saturne (TASS) by Vienne and Duriez describe in detail the dynamical system by a representation based on the combinations of the proper frequencies. Some theoretical studies need to have both advantages. For example, to study the rotation of Titan, one needs to know the representation of its longitude. Aims. We aim to use these two types of ephemerides in order to rebuild a long-lasting and high-precision ephemeris with proper frequencies based on the numerical integration ephemeris. The aim is to describe the numerical ephemerides with formulas similar to analytical ones. Methods. We used the representation of the orbital elements from the TASS ephemeris analysed over 10 000 years as a reference template. We obtained the proper frequencies with both numerical and the TASS ephemeris over 1000 years only. A least-square procedure allowed us to get the analytical representation of an orbital element in this limited interval. Results. We acquire the representation of the mean longitude of Titan from JPL ephemeris over 1000 years. For almost all components, the corresponding amplitudes and phases are similar to the relative terms from TASS. The biggest difference between our representation and the mean longitude of Titan of JPL is less than 100 km over 1000 years, and the standard deviation is about 26 km.
Highlights
Numerical ephemeris of natural satellites, which is widely used in research and space projects and conveniently available for download from the online service, based on the recent observations, is highly precise
Ω∗8 is the biggest component in the representation of the mean longitude of Titan, that the accuracy of its proper frequency has a significant influence on our final solution
It means that we can obtain the mean longitude of Titan in JPL at any time with our formula: nt λ6 = N × t + λ0 + Ai sin(ωit + φi)
Summary
Numerical ephemeris of natural satellites, which is widely used in research and space projects and conveniently available for download from the online service, based on the recent observations, is highly precise. Theory ephemeris includes all the details of the system motion in the representation with the proper frequencies It is helpful in the research of the influences between the different satellites in the planetary system. It provides access to key solar system data and flexible production of highly accurate ephemeris for solar-system objects (HORIZONS 2018) This includes 715 000+ asteroids, 3420 comets, 178 natural satellites, all planets, the Sun, 99 spacecraft, several dynamical points such as Earth-Sun L1 to L5 equilibriums, and system barycentres. The Horizon system presents ephemeris in classical orbital elements (a, e, i, ω, , M) in the ecliptic plane. It is the normal form of ephemeris, but different from the one we used. FA is the abbreviation of the frequency analysis (Sect. 2), LSM means the least-square method (Sect. 3)
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