3 Comparison between the observed and the theoretical positions

We compared the measured and theoretical positions of the Saturnian satellites. The theoretical positions for Mimas, Enceladus, Tethys, Dione, Rhea, Titan, Hyperion and Iapetus were calculated using TASS1.7 (Vienne & Duriez 1992, 1998; Duriez & Vienne 1997a, 1997b). For the residuals ($\rm O{-}C$), the number of positions, the means and the standard deviations for each satellite referred to Titan are presented in Table 3. Only the residuals smaller than 1$^{\prime\prime}$ were considered. The residuals referred to Saturn were not computed because the center of the planet could not be determined from its saturated image.

  

Table 3: The observed minus calculated means and standard deviations, in arcseconds, referred to Titan. N is the number of positions referred to Titan

It can be noticed that, for Mimas, there are few positions of the satellite and the mean and the standard deviation in the right ascension direction are comparatively large. As mentioned above, this follows from difficulty to observe this satellite due to its small distance from the planet bright rings. The right ascension standard deviations for Enceladus share nearly the same problem but in general its elongation is larger and its right ascension residuals are smaller than Mimas' are.

The residuals for the other satellites have all close values. For Hyperion the residuals in right ascension are larger than the residuals for the others external satellites. This value agrees with the results in Table 9 in Duriez & Vienne (1997). For almost all satellites, one can observe that, in general, the residuals in declination are smaller than in right ascension. This happens also for the photographic positions of Saturn satellites in Table 2 in Harper & Taylor (1994). Probably, this is due to errors in the guiding procedure during the observations.

The positions of the satellites were taken in respect to Titan and this choice might have introduced some bias on our results. To avoid this problem we computed the intersatellite positions too that is, the relative positions between each satellite against Enceladus, Tethys, Dione, Rhea, Titan, Hyperion and Iapetus. This procedure was not applied in reference to Mimas since this satellite doesn't present good positions as seen in Table 3. These results are presented in Table 4. The comparison between Table 4 and Table 3 shows them not be essentially different. Finally, we computed also the intersatellite positions, taking only Tethys, Dione, Rhea and Titan. The residuals are almost the same. Therefore, it is shown that the choice of Titan as reference satellite doesn't introduce any bias on our results.

  

Table 4: The observed minus calculated means and standard deviations, in arcseconds, for intersatellites positions. N is the number of intersatellite calculated positions

Figure 3 presents the histogram of the residuals for our positions referred to Titan. It can be observed that, but for the Mimas right ascension, the residuals for the satellites have distributions similar to a normal distribution.