5 The observations

Table 4 shows that the errors in the present observations arise mostly from errors in the star positions. Near opposition Uranus regresses by roughly one chip width per night so that each night's observations are measured relative to a nearly independent set of stars from the nights before and after. This was confirmed by breaking down the observations into separate nights which revealed significant night to night changes in scale and position angle.

Fundamental Right Ascensions and Declinations are not required for the satellites because their theory can be improved simply from observations of one satellite relative to another. In Table 7 (only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html) the satellite positions are presented as standard co-ordinates $(\xi , \eta)$ relative to a reference satellite which is usually Oberon, but otherwise the next satellite observed nearer the planet. In reducing the data the scale and rotation of position angle with hour angle were fixed for the whole series and separate zero points of position angle (J2000.0) were fixed for each year. The constants were found from weighted means over the separate nights. The formulae used were:

$$\theta = -88\hbox{$.\!\!^\circ$}8647 (\pm 26) + 0\hbox{$.\!\!^\circ$}00527 (\pm 106)\tau \;\;\;\; \mbox{(1990)}$$ (1)

$$\theta =\;\;\; 90\hbox{$.\!\!^\circ$}2214 (\pm 46) + 0\hbox{$.\!\!^\circ$}00527 (\pm 106)\tau \;\;\;\; \mbox{(1991)}$$ (2)

$$\xi = 0\hbox{$.\!\!^{\prime\prime}$}302763 (\pm 20) (\;\;\;\Delta x \cos \theta + \Delta y \sin \theta)\\$$ (3)

$$\eta = 0\hbox{$.\!\!^{\prime\prime}$}302763 (\pm 20) (-\Delta x \sin \theta + \Delta y \cos \theta)\\$$ (4)

where $\Delta x, \Delta y$ are measured in pixels on the chip relative to the reference satellite, and $\tau$ is the hour angle in hours. The standard errors are in units of the least significant digit. The standard co-ordinates were corrected for refraction under a pressure of 760 mBar; the results are presented in Table 7.