3 Measurement and calibration

In previous years, the positions of the satellites in each CCD frame were measured manually using the IRAF (Image Reduction and Analysis Facility) software. This is a laborious and time-consuming task, and it was decided to develop software which would automate the process. This software is described elsewhere (Harper, in preparation); it was tested on the 1993 and 1994 data and found to produce pixel coordinates identical to those obtained manually and published in Harper et al. (1997).

The 1995 and 1997 observations are published in the form of raw pixel coordinates in order that future investigators can make direct use of the CCD images if they wish.

The orientation of the CCD in both years is such that the column coordinate ($\xi$) increases eastwards and the row coordinate ($\eta$) increases southwards . However, the axes of the device are not aligned exactly in the north-south and east-west directions and a small rotation is therefore required to convert row and column coordinates into differential coordinates referred to the true equator and equinox of date.

Let $\Delta\xi$ and $\Delta\eta$ represent the column and row coordinates, measured in pixels, of one satellite relative to another. These may be converted to differential coordinates $\Delta\alpha\,\cos\delta$ and $\Delta\delta$ referred to the true equator and equinox of date by the following transformation:

$$\left( \begin{array} {c} \Delta\alpha\,\cos\delta \\ \Del... ...{array} {c} \Delta\xi \\ -\Delta\eta \\ \end{array} \right).$$

The scale ($\rho$) and orientation ($\delta P$) of the CCD were determined empirically for each observing campaign by comparing the positions of the satellites Tethys, Dione, Rhea and Titan with those calculated from the theories of Harper & Taylor (1993) as described in Sect. 3 of Harper et al. (1997). In Table 4 we give the values of $\rho$ and $\delta P$ together with their standard errors from the least-squares fitting process. This method was first used for CCD observations by Colas & Arlot (1991) in their reduction of observations of the satellites of Mars.

  

Table 3: Data sets obtained in 1997 October

  

Table 4: Calibration parameters for the observations

The 1997 data are treated as three separate sets, corresponding to the three nights on which observations were obtained. During the observing run, engineering work was in progress on the telescope following a major refurbishment of the primary mirror, and it could not be determined whether the CCD camera had been dismounted from the telescope during the daytime. It was therefore decided to calibrate and analyse each night's data separately. The 1997 data sets are summarised in Table 3.