Astron. Astrophys. 324, 366-380 (1997)

Theory of motion and ephemerides of Hyperion ^*

L. Duriez and A. Vienne

Université des Sciences et Technologies de Lille, Laboratoire d'Astronomie, 1 Impasse de l'Observatoire, F-59000 Lille, France (duriez@gat.univ-lille1.fr and vienne@gat.univ-lille1.fr)

Received 18 November 1996 / Accepted 10 February 1997

Abstract

We present here a new theory of motion for Hyperion, the seventh major satellite of Saturn. The Hyperion's motion is defined like in TASS1.6 for the other satellites (Vienne & Duriez 1995), by the osculating saturnicentric orbital elements referred to the equatorial plane of Saturn and to the node of this plane in the mean ecliptic for J2000.0. These elements are expressed as semi-numerical trigonometric series in which the argument of each term is given as an integer combination of 7 natural fundamental arguments. These series collect all the perturbations caused by Titan on the orbital elements of Hyperion, whose amplitudes are larger than 1 km in the long-period terms and than 5 km in the short-period ones. However, the convergence of these series is so slow that, in spite of several hundreds of terms, their internal accuracy over one century is about 200 km only. These series have been constructed in such a way that the fundamental arguments and the amplitude of each term depend explicitly on 13 parameters (the twelve initial conditions of the motions of Titan and Hyperion and the mass of Titan). Taking also account of the perturbations from other satellites and Sun, we have fitted these series to 8136 Earth-based observations of Hyperion in the interval [1874-1985], giving a set of better values for these parameters. In particular the mass of Titan is found equal to (in units of the Saturn's mass) and we discuss this value in comparison with that [ ] obtained by Campbell & Anderson from their analysis of the Voyager missions to Saturn. The resulting fitted series allows us to produce new ephemerides for Hyperion. Their comparison to those from Taylor (1992) shows that, with the same set of observations and the same way to weight them, we obtain a root mean square (o-c) residual of while the ephemerides of Taylor gives .

Key words: celestial mechanics planets and satellites Hyperion ephemerides

* The full Tables 3 to 8 of this paper are also available by anonymous FTP at cdsarc.u-strasbg.fr or ftp 130.79.128.5

Send offprint requests to: L. Duriez

Contents

• 1. Introduction
• 2. The interaction Titan-Hyperion
  • 2.1. Numerical integration
    • 2.1.1. Frequency analysis
    • 2.1.2. Digital filtering
  • 2.2. Synthesis of a semi-analytical representation
  • 2.3. The series
    • 2.3.1. Hyperion
    • 2.3.2. Titan
  • 2.4. Partial derivatives with respect to the parameters
• 3. Ephemerides of Hyperion
  • 3.1. Solar and other short-period perturbations
  • 3.2. Adjustment to observations
  • 3.3. Comparisons to previous works
• 4. Conclusion
• Acknowledgements
• Appendix A: features of the frequency analysis
• References

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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