*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
© European Southern Observatory (ESO) 1997
Online publication: May 26, 1998
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