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1 Introduction

Helene, the faint Lagrangian satellite of Saturn-Dione, was discovered in 1980 during the Earth ring-plane crossing (Lecacheux et al. 1980). Its visual magnitude is about 17. Due to its faintness and its proximity to scattered light from the planet and rings, this satellite is very difficult to observe. Therefore the number of astrometric positions of Helene is not very large and the positions are not very accurate.

After its discovery, Helene was observed in 1980-81 (Reitsema 1981) and from 1981 to 1985 by Veillet (Oberti et al. 1989). In total, there are 233 published positions of this satellite. Some observations made in 1992 and 1994 are informed by Rodhe & Pascu (1993, 1994).

An analytical theory for the motion of Helene was presented by Oberti (1990). After 1995 a numerical integration of this longitude: $-3^{\rm h} 02^{\rm m} 19^{\rm s}$, latitude: $-22^\circ 32' 04''$ and altitude: 1 872 m. The plates are the same used in our observations of the large satellites of Saturn. All plates were hypersensitized and the exposure times have varied from 8 to 12 minutes. No filters or masks on the plates were used. For some details about the observations see Paper I.

Table 1: Observed positions of Helene. For each plate we present the year, month, day, and decimal fractions of TDT days, corresponding to the mean instant of the observation. The differential topocentric coordinates, $X (\Delta\alpha \cos\delta)$ and $Y (\Delta \delta )$, are referred to Titan. The reference system is defined by the mean equator and equinox J2000
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The images of the satellite, the stars and the other satellites of Saturn were digitized with the PDS 1010A of the Observatório Nacional-Brazil. For the images scans a square slit with 20 m$\mu$ of side was used. To find the center of these images, the ASTROL routines package (Colas & Serrau 1993) was employed and to determine each center, a two-dimensional Gaussian fitting on a small circular area around the image in which the background was removed by a second-degree polynomial, was used. The errors upon the centering procedure were smaller than 0 $\hbox{$.\!\!^{\prime\prime}$ }$03 for Helene.

For the astrometric calibration we used the method presented in Paper I. The observed positions of Helene are referred to Titan in the reference system J2000. In Paper I, it can be seen that the positions of the large satellites of Saturn have errors smaller than 0 $\hbox{$.\!\!^{\prime\prime}$ }$2 when their positions are compared with TASS1.7 (Vienne & Duriez 1998). Therefore, it is considered that the errors induced by the reduction procedure are smaller than 0 $\hbox{$.\!\!^{\prime\prime}$ }$2. In Table 1, our positions of Helene related to Titan are presented.

  \begin{figure}\includegraphics[width=8.8cm, clip]{}\end{figure} Figure 1: The observed minus calculated positions of our measured positions on the x and y directions. It can be observed a cluster of 22 positions near the origin. The other 10 positions appear scattered over the plane. Only the central cluster positions were considered in this paper

\includegraphics[width=8.8cm, clip]{}\end{figure} Figure 2: Histogram for the residuals of Helene referred to Titan ( $X=\Delta\alpha \cos\delta$ and $Y=\Delta \delta $)

The theoretical positions for Helene and Titan were provided by Jacobson from JPL (Jacobson 1999). We inspected all our plates of the Saturnian system (Paper I) in order to identify images of any faint image in the regions around the Dione's Lagrangian points. We found only 32 measurable objects in these plates.

To select the images of Helene from the 32 candidates measured, we compared these observed positions with the theoretical one. We can observe in a plot (Fig. 1) where the axes are the $({\rm O-C})_x$ and $({\rm O-C})_y$ that there is a cluster of points in the neighbohood of the origin, while the other points are spread over the plot. We considered only the positions belonging to the central cluster. These positions of the candidates to Helene images were also compared with the positions of stars (with B and R magnitudes smaller than 20) from the USNO A2.0 Catalog (Monet et al. 1998) in the same field, in order to insure that they are not stellar.

The residuals for our observed positions of Helene compared with theoretical positions have $\overline{x}=0\hbox{$.\!\!^{\prime\prime}$ }270$, $\overline{y}=-0\hbox{$.\!\!^{\prime\prime}$ }223$, $\sigma_x=0\hbox{$.\!\!^{\prime\prime}$ }320$ and $\sigma_y=0\hbox{$.\!\!^{\prime\prime}$ }278$. In Fig. 2 the histogram for the residuals x and y, is presented. It can be noted that the standard deviation in the x direction is larger than for the y direction. This is due to guiding problems.

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