3 Comparison with theoretical positions

To compare our set of J2000 measured positions with those calculated using the GUST86 theory (Laskar & Jacobson 1987) which refers to the B1950.0 system, the following transformations were done. First, the positions of Uranus in J2000 were obtained from the DE403 ephemeris (Standish et al. 1995). These positions were converted to the B1950.0 reference system using the procedure described by Aoki et al. (1983, Appendix 2). To add on the e-term of the aberration in the transformation, a process of successive approximations (Rapaport 1996) was used. Therefore, the theoretical right ascensions and the declinations of the satellites were calculated in B1950.0 system. Using the Aoki procedure these coordinates were then computed in the J2000 system.

The mean residuals (O-C) and the standard deviations for each satellite are presented in Table 2. In order to compare these observations with those published in our previous papers, the means and standard deviations of our other photographic and CCD observations are added to the table. The residuals were compared with values of Jones et al. (1998). The residuals of their CCD observations are slightly smaller than the residuals presented in this paper. However, the two series of observations had been compared to different ephemeris and it is difficult therefore to analyze the significance of these differences, as stressed also by Jones et al. (1998).

  

Figure 2: Residuals for Miranda, Ariel, Umbriel and Titania referred to Oberon versus the date. The observations of this paper correspond to 1995-1998

  

Figure 3: Residuals for the observations presented in this paper for Miranda, Ariel, Umbriel and Titania referred to Oberon versus longitude

In Fig. 2, the residuals of all our observations for Miranda, Ariel, Umbriel and Titania referred to Oberon are presented as a function of the observational date. Observe that the vertical scale for Miranda is larger than the scale for the other satellites. It can be seen that the distributions of the residuals are uniform for these 16 years and very similar for the CCD observations (1989-1998).

The CCD residuals as function of the satellite longitude are shown in Fig. 3. It can be seen that there is in general a random distribution for the residuals. However, comparing this figure with Fig. 3 in Veiga & Vieira Martins (1995), a drift of the residual for Miranda can be seen in the X direction for the longitude range between $40^\circ$ to $100^\circ$. Two others drifts can also be seen in direction Y for the longitude intervals ($90^\circ$ to $160^\circ$) and ($300^\circ$ to $320^\circ$).