4 Analytical theory

The GUST86 analytical theory is firstly used in determining the scale and orientation of the CCD and secondly in the fitting to observations. In Paper I, we described several calibration methods suggested by previous authors. These methods include the "Double star method'' used by Jones et al. (1989) and the "Globular cluster method'' proposed by Colas & Arlot (1991). However, in Paper II we presented a more detailed analysis and discussion of the method called "Brighter moon calibration''. The use of the satellites themselves for the determination of calibration greatly simplifies the reduction of the observations (Harper et al. 1997), so we continue to prefer this technique in the present work.

An accurate ephemeris is most important for the "Brighter moon calibration'' method. In Paper II, we suggested that in order to reduce the effect of systematic errors in a single analytical theory, the use of the multiple-theories method may be feasible. However, for the Uranian satellites, analysis shows that GUST86 remains the analytical theory with the best dynamical and internal consistency, and thus the multiple-theories method can not be used. Table 4 gives observed-minus-computed residuals of inter-satellite positions, in separation ($\Delta S$) and position angle ($S\Delta P$), for each satellite based on GUST86. Oberon is excepted, because it was used as the reference satellite.