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# 4. Model refinement

As discussed in the previous item, the model for the Standard Weighted Global Solution might favourably admit additional unknowns. Here, thus, we consider additional unknowns, to better account for the treatment of the refraction and to investigate the correction to the obliquity of the ecliptic. These are:

(i) - A correction to the constant of refraction.

(ii) - A time variation of the correction to the obliquity of the ecliptic.

(iii) - Corrections to azimuthal anomalies of the refraction.

(iv) - A correction to the constant of nutation.

With the corrections defined as above a number of trials of the Standard Weighted Global Solution were run, admitting some or all of the additional unknowns. The results are expressed in Table 6.

Solutions 2 and 3 include a correction to the constant of refraction. The first one refers to the bulk of the observations while the second one corrects only the OCA data. In both cases small corrections, at the level of upon the constant of refraction are obtained, without any major modification upon the other unknowns.

Solution 4 includes the coefficient for the time derivative of the obliquity of the ecliptic. The value of the correction to the obliquity of the ecliptic turned out to be , for the epoch 1990.0 (the approximate average epoch of the observations), with an additional yearly rate of . This result must be taken cautiosly, since the time interval is small and, to this purpose, the Northern and Southern data may lack in sincronicity. Taken at its face value, the negative sign of the time derivative would weaken the hypothesis that the high value found for the obliquity of the ecliptic itself might be due to an increasing trend not yet recognized.

Solutions 5 to 9 include unknowns of the type and , for P egual to 2 and 3, where Z is the azimuth. These terms represent azimuthal anomalies of refractive origin, that may arise from the characteristics of each site. Solutions 6 and 9 refer only to the high zenith distance subsets (, hence for the OCA only), that are more prone to present such refraction anomalies. In the other solutions of this kind (that is, 5, 7 and 9) the same azimuth dependent unknowns are applied to all the observations. They are probably less realistic, since they do not account for the local characteristics. Only the correction to the equator suffers changes, eventhough at a level smaller than .

Solution 10 includes a correction to the constant of nutation in obliquity. It takes advantage of the fact that the observational period (about 19 years) is comensurable to the period of retrogradation of the nodes of the lunar orbit. The correction obtainded is negligible and thus do not apport any change on the value of the correction to the obliquity of the ecliptic.

In general, it is seen that the modification introduced in the model did not affect but marginally the results obtained in the Standard Weighted Global Solution. The unknowns introduced are usually significant, thus well modelled, without casting new light upon the parameters originally researched.

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