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 to denote the column coordinate and to denote the row coordinate in the CCD array. In the data tables, the satellite positions are given as 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 to (x,y).
Table 3: Orientation of the CCD device and transformation from coordinates to (x,y)
Table 4: Calibration parameters for the observations
Let denote the position of satellite B with respect to satellite A in raw pixel coordinates. Further, let 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 and directions but have found no significant difference between the two scales. Let 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 and according to Table 3.
Then the differential coordinates and referred to the true equator and
equinox of date are calculated from
The parameters and 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 and 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 values for these sets is , which is eleven times the standard error of set (a), suggesting that some alteration of the alignment may have occurred.
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.