2 The observations, measurements and reductions

All the observations were made at the Cassegrain-focus of the 1.6 m Ritchey-Chretien reflector of the Laboratório Nacional de Astrofísica in Brazil (geographical longitude: $3^{\rm h}02^{\rm m}19^{\rm s}$, latitude: $-22^{\circ}32'04''$ and altitude: 1872 m). The focal length of the Cassegrain combination is 15.8 m, which results in a plate scale of 13 $\hbox{$.\!\!^{\prime\prime}$ }$0/mm in the focal plane. No filter was used. In order to avoid saturation in the CCD due to the light from the planet, a round mask was put on the CCD window and the frames were made with Saturn's image behind this mask. Since the distance from the camera window to the CCD surface is small, the penumbra region is negligible.

During the missions, 4 CCDs detectors were used. In Table 1 the characteristics of these devices are given.

 

 

Table 1: Technical characteristics of the CCD devices. The "series'' column show the Code of the series given in Table 4.

Devices	Description	Series
CCD0048	EEV P88231	1-2-3-4-5-6-7-8
	(770 X 1152)
CCDCAM2(1)	SITe SI003AB(A1)	9
	(1024 X 1024)
CCD009	EEV-05.20.0.202	10-11-12-13-14
	(770 X 1200)
CCDCAM2(2)	SITe SI003AB(B2)	15-16
	(1024 X 1050)

Since the pixels dimension of every CCD used are about $22~\mu{\rm m}$ $\times$ $22~\mu{\rm m}$, the scale per pixel is about 0 $\hbox{$.\!\!^{\prime\prime}$ }$3 $\times$0 $\hbox{$.\!\!^{\prime\prime}$ }$3. Therefore, the field observed with these devices is about 4 $\hbox{$^\prime$ }$ $\times$ 5 $\hbox{$^\prime$ }$ and 5 $\hbox{$^\prime$ }$ $\times$ 5 $\hbox{$^\prime$ }$.

 

 

Table 2: Numbers of observed nights and useful positions in general referred to Rhea, for every satellite. We consider useful positions those with $\rm \vert(O{-}C)\vert$ smaller than 0 $\hbox{$.\!\!^{\prime\prime}$ }$5 in the case of the eight large satellites (S1-S8) and smaller than 2 $\hbox{$.\!\!^{\prime\prime}$ }$ for S12 and than 5 $\hbox{$.\!\!^{\prime\prime}$ }$ for S13 and S14.

Satellites	Positions	Nights
Mimas (S1)	329	18
Enceladus (S2)	419	23
Tethys (S3)	484	25
Dione (S4)	482	26
Titan (S6)	214	13
Iapetus (S7)	7	1
Hyperion (S8)	70	3
Helene (S12)	37	2
Telesto (S13)	24	4
Calypso (S14)	6	1

The numbers of observed nights and useful positions in general referred to Rhea, for each satellite, are presented in Table 2. We consider as useful positions those with $\rm \vert O{-}C\vert$ smaller than 0 $\hbox{$.\!\!^{\prime\prime}$ }$5 for the eight large satellites and smaller than 2 $\hbox{$.\!\!^{\prime\prime}$ }$0 for Helene and 5 $\hbox{$.\!\!^{\prime\prime}$ }$0 for Telesto and Calypso. It can be noted that the number of observations increases with the distance from Saturn. This is a consequence of the difficulty to observe faint satellites near bright planets. However, for the satellites with largest distance from the planet the number of observations decreases with the distance, mainly because the CCDs used are relatively small. In particular, Iapetus is too far from Saturn and so we have only 7 positions observed in our frames, where Saturn is always at the center of the CCD. For the very faint Lagrangian satellites we have small number of images since their observations result blurred in the neighborhood of the bright Saturn. The histogram of the number of frames with respect to the epoch of the observations is shown in Fig. 1. Each bar corresponds to one of the 10 observational missions.

Figure 1: Histogram of the observations with respect to time. Each bar corresponds to one mission.

 

 

Table 3: The mean, the root mean square and the standard deviation of the (O-C) (in arcseconds) for all satellites. The ephemerides compared were TASS1.7, and JPL positions for the Lagrangian satellites. The residuals are referred to S5 (if S5 is absent of the frame, we use S6, and so on with the ordering list: S5, S6, S4 and S3).

Satellite	$\overline{x}$	$\overline{y}$	$x_\sigma$	$y_\sigma$
	(rms)	(rms)
Mimas	0.012	0.006	0.134	0.106
	(0.134)	(0.105)
Enceladus	0.019	-0.027	0.112	0.110
	(0.113)	(0.113)
Tethys	0.007	-0.003	0.111	0.090
	(0.111)	(0.090)
Dione	0.014	-0.021	0.096	0.089
	(0.097)	(0.091)
Titan	-0.018	-0.010	0.110	0.120
	(0.111)	(0.120)
Iapetus	-0.178	0.084	0.036	0.026
	(0.181)	(0.088)
Hyperion	0.191	0.143	0.105	0.099
	(0.218)	(0.173)
Helene	0.119	0.063	0.139	0.089
	(0.182)	(0.109)
Telesto	0.083	-1.177	1.391	0.938
	(1.365)	(1.493)
Calypso	0.539	0.227	0.128	0.228
	(0.552)	(0.228)

As mentioned above, a round mask was put on the CCD image in order to occult the planet image. However, the ring image was saturated since the mask does not hide them. Therefore, many of the stars in the field are not see and many others are immersed in the light scattered by the planet and its rings. Furthermore, the limit magnitude of a typical image is 14. Consequently, a small number of reference stars appear and so we decided to measure only the satellite positions and adopt an inter-satellite reduction.

 

 

Table 4: Extract of the catalog.

opp.	year	m	day(utc)	tt-utc	obs.	ref.	t	obj.	fl	obs1	obs2	s	f	o-c1	o-c2	r	-	se	xpix	ypix
				sec.						arcsec.	(degree for C*)			arc	sec.				pixel
118	1995	6	10.3052546	61.184	874	303	1	15	11	47.7194268	-4.1966535	2	1	0.147	-0.077	5	0	1	162.321	-13.471
118	1995	6	10.3052546	61.184	874	303	1	25	11	37.4313628	-3.7999220	2	1	0.022	-0.016	5	0	1	127.334	-12.294
118	1995	6	10.3052546	61.184	874	303	1	35	11	108.7209996	-8.5488541	2	1	-0.120	0.003	5	0	1	369.804	-27.252
118	1995	6	10.3052546	61.184	874	303	1	45	11	86.7859497	-8.0598588	2	1	-0.101	-0.057	5	0	1	295.215	-25.955
118	1995	6	10.3052546	61.184	874	303	1	65	11	-34.9822851	0.3491667	2	1	0.083	0.061	5	0	1	-118.949	0.599
118	1995	6	10.3052546	61.184	874	303	1	C5	11	61.1455158	-4.0790906	2	1	999.999	999.999	5	0	1	-208.070	12.836
118	1995	6	10.3052546	61.184	874	303	0	C*	11	355.5226507	-4.1351607	2	1	999.999	999.999	5	0	1	99 999.999	99 999.999
118	1995	6	10.3069907	61.184	874	303	1	15	11	50.4610858	-4.6822838	2	1	2.597	-0.532	5	0	1	171.656	-15.076
118	1995	6	10.3069907	61.184	874	303	1	25	11	37.5308699	-3.8116642	2	1	-0.093	-0.009	5	0	1	127.673	-12.332

Figure 2: Histogram for the $\Delta\alpha \cos\delta (X)$ and $\Delta \delta (Y)$ residuals of the observed satellites.

Figure 2: continued.

Figure 2: continued.

All frames were measured with the ASTROL software (Colas 1996), which allowed us to use a centering algorithm based on the adjustment of a point spread function. A second degree polynomial is also adjusted in order to remove the background which is affected by the light from the planet and its rings.

For the inter-satellite reduction, we used the method presented in (VTVAM) and (Vienne et al. 2001b). More details and discussions of the method can be found in these papers.

We divided our observations in 16 series that cover one or few nights. For every series we assume that the receptor has been mounted in the same way for all the frames of the series and so the scale and the orientation remains the same for all of them. We used TASS1.7 (Vienne & Duriez 1995; Duriez & Vienne 1997) for the saturnicentric positions of the satellites. The positions of Saturn are given by the ephemerides SLP96 from the "Institut de mécanique céleste (IMCCE)'' (available at ftp://ftp.imcce.fr/pub/ephem/sun/slp96/) found on the VSOP87 planetary theory (Bretagnon & Francou 1988), which precision is about . The frames registered and measured in pixels are not directly comparable with ephemeris, because they have been affected by some local effects. So first, we have to correct the computed coordinates with these effects due to refraction, stellar aberration, the projection of the celestial sphere on the tangential plane of the focal point, light-travel time between satellites and topocentric parallax. Comparing these apparent computed coordinates to the observed ones by a least square procedure, we deduced the scale factor and the orientation of the receptor. These two parameters are then free of these local effects. In the least square procedure, only the positions of Tethys, Dione, Rhea and Titan are used to calibrate because these satellites have the best ephemerides, and are thus probably affected by the smallest systematic effects.

The positions $(\Delta\alpha \cos \delta ,\Delta\delta)$ we give in Table 4 are really astrometric ones because they are given in the J2000 system and all significant astrometric corrections have been done. But, for a given series, they are given apart from a scale factor and from a rotation. As explained in Vienne et al. (2001b), if we want to compute the astrometric coordinates in any other way, for example with other ephemerides, we have only to touch up the scale factor and the orientation of the receptor.