3 CCD observations

66 CCD images were exposed between 1990 July 10 and 18, two on 1990 October 21, and 71 between 1991 July 4 and 11. The Z filter ($\lambda \sim 0.9\ \mu$)was chosen primarily because the large amounts of methane in the atmosphere of Uranus make the planet faint at this wavelength, while the satellites are relatively unaffected. Further advantages are that, compared to other broad-band colours available to the CCD:- (1) moonlight on the image arises mostly by Rayleigh scattering which is smallest at this wavelength. Many of these observations were made with the full Moon close to the field. (2) the small atmospheric dispersion at this wavelength.

All the CCD reductions were done with IRAF. The CCD images were bias-subtracted, and flat-fielded with images of the twilight sky. The co-ordinates of the satellites and the secondary astrometric stars were found from PHOT, PSTSELECT, PSF and PEAK. PSTSELECT was used to identify the four brightest unblended stars from the list provided by PHOT. PSF derived the point-spead-function (psf), consisting of independent Gaussian distributions in x and y from these four stars. PEAK fitted the centres of all the images with the psf.

Miranda is more or less blended with Uranus depending on the seeing, although the use of the Z filter minimises the effect. Other observers working at shorter wavelengths have removed the blending by modelling and then subtracting the light of Uranus before centring on Miranda (Vieira Martins et al. 1986; Pascu et al. 1987; Veiga & Vieira Martins 1995a). Pascu et al. also cut down the light of Uranus with a coronagraph and Veiga and Vieira Martins simply rotated the image of Uranus through $180\hbox{$^\circ$}$ before subtraction.

We removed the variable background by subtracting an image smoothed with a ring filter following Secker (1995). From each CCD image we subtracted an image which had been smoothed with IRAF FRMEDIAN. The ring had a radius twice the full-width-at-half-maximum (FWHM) of the seeing disc and width one pixel.

During these observations Uranus was moving through rich star fields towards the centre of the Milky Way and on several occasions the satellites were blended with stars. Misshapen images could be identified from the value of ``chi" in PEAK. All satellite images with chi > 2.5 were rejected. Another symptom of blending is that the satellite appears abnormally bright. Table 3 gives the median and semi-inter-quartile (siq) Z magnitudes of the satellites from all our images; relative to Titania, the brightest. Any satellite which deviated by more than seven times the siq was rejected. Table 3 follows the IAU numbering system and also includes the (V-Z) colours formed by differencing these magnitudes with those given by Reitsema et al. (1978).

  

Table 3: Median magnitudes relative to Titania III

The images were reduced with ASTROM (Wallace 1994) to give the scale and orientation of each. Any proper motion of the stars between the epoch of the plates and the epoch of the CCD observations has been neglected. The goodness of fit in ASTROM is a combination of errors in the reference star positions and errors in extracting the image centres from the CCD. A well observed night was 1990 July 13/14 when 15 images were obtained with 12 reference stars common to all. For this and similar nights it is straightforward to separate the errors (Table 4).

  

Table 4: Rms errors of CCD observations

The star position errors roughly agree with the photographic measuring errors in Table 2. The CCD errors are 0.04 pixel which is three times the value found by Zacharias (1996). However, Zacharias made contiguous exposures with the telescope autoguided where our exposures are spread over five hours and without autoguiding.