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4. Format of the observations

The data in this paper are published in the form of raw pixel coordinates which were determined by the centre-finding tool of the IRAF (Image Reduction and Analysis Facility) software. Publication of the data in this format will enable future investigators to make direct use of the original CCD images if they so wish.

We use tex2html_wrap_inline1167 to denote the column coordinate and tex2html_wrap_inline1169 to denote the row coordinate in the CCD array. In the data tables, the satellite positions are given as tex2html_wrap_inline1171 pairs.

The orientation of the CCD device changes from one year to another, depending on how the device was mounted by the Observatory staff. However, one axis of the device is always aligned roughly north-south. We therefore use x to denote a direction parallel to the axis of the CCD which is nearest to the east-west direction, with x increasing eastwards (i.e. in the direction of increasing Right Ascension). Likewise, y is parallel to the axis of the CCD which is nearest to the north-south direction, with y increasing northwards (i.e. in the direction of increasing Declination).

Table 3 shows the approximate directions of the CCD coordinate axes in each year, together with the transformation from tex2html_wrap_inline1181 to (x,y).

Table 3: Orientation of the CCD device and transformation from tex2html_wrap_inline1185 coordinates to (x,y)

Table 4: Calibration parameters for the observations

Let tex2html_wrap_inline1193 denote the position of satellite B with respect to satellite A in raw pixel coordinates. Further, let tex2html_wrap_inline1195 denote the scale of the CCD device in units of arc-seconds per pixel. This assumes that the pixels are square; we have run calibration trials with different scales in the tex2html_wrap_inline1197 and tex2html_wrap_inline1199 directions but have found no significant difference between the two scales. Let tex2html_wrap_inline1201 denote the position angle of the north-south axis of the CCD with respect to the true pole of date, measured positive towards the East.

Table 5: Example transformations from pixel coordinates to true equator and equinox of date

First calculate tex2html_wrap_inline1205 and tex2html_wrap_inline1207 according to Table 3. Then the differential coordinates tex2html_wrap_inline1209 and tex2html_wrap_inline1211 referred to the true equator and equinox of date are calculated from

4.1. Values of tex2html_wrap_inline1241 and tex2html_wrap_inline1243

The parameters tex2html_wrap_inline1245 and tex2html_wrap_inline1247 have been determined empirically for each observing campaign by comparing the observations with the orbital theories of Harper & Taylor (1993, 1994) and determining the values of tex2html_wrap_inline1249 and tex2html_wrap_inline1251 which yield the best fit between the observations and the theories. Work is in progress to obtain independent values of these parameters from observations of globular clusters and other fiducial star fields (Jones 1996).

The values which we have adopted at present are given in Table 4. They are based upon measurements of the positions of Tethys, Dione, Rhea and Titan.

The 1990 data has been divided into three subsets. Set (a) covers 10-18 July and represents the main observing programme in that year. Set (b) covers 26 July to 3 August, whilst set (c) covers 15-17 August. The CCD detector was removed between sets (b) and (c) while a different instrument was in use. In addition, it is not possible to guarantee that the CCD was not rotated between sets (a) and (b); the difference in the tex2html_wrap_inline1253 values for these sets is tex2html_wrap_inline1255, which is eleven times the standard error of set (a), suggesting that some alteration of the alignment may have occurred.

4.2. Example calculation

In order to assist the reader in checking the validity of the formulae, we present four sample calculations in Table 5. In each case, the example is taken from the first image listed for the given year.

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