tokens: more complex calibration model may contribute to the degeneracy and, in the worst case, restore complete degeneracy. 4.5. Dependence on heliotropic coordinates The spherical coordinates , , introduced in Sect. 2.6 define the position of the solar system barycentre in the SRS. This is what matters for calculating the parallax effect, which depends on the observer’s displacement from the barycentre. On the other hand, the physical relevance of the modulation is connected with the changing illumination of the satellite by the Sun, which depends on the heliocentric distance and the heliotropic angles and that represent the proper direction towards the centre of the Sun at the time of observation. The difference between the heliotropic and barytropic coordinates is at most about 0.01 au and 0.01 rad, respectively. This is small but should be taken into account for an accurate modelling of the basic angle variations. In this context it can be noted that the expected thermal impact on the satellite scales as , whereas the parallax factor scales as . On the other hand, the scanning law is chosen to keep as constant as possible, whereas can vary at the level of 1%. If the basic angle varies as , it is no longer strictly of the form of Eq. ( 18 ). The resulting parallax bias can be estimated by means of Eq. ( 19 ). 4.6. Breaking the degeneracy? If the basic angle varies as a consequence of the changing solar illumination of the rotating satellite, we expect to see a parallax bias according to Eq. ( 19 ). However, as discussed above, the degeneracy with the parallax zero point is not perfect, and in principle this opens up a possibility to calibrate the basic angle variations from the observations. At least three different effects that contribute to breaking the degeneracy could be used: the finite size of the field of view (Sect. 4.4 ), the time dependence of due to the eccentricity of the Earth’s orbit (Sect. 4.3 ), and the difference between the barytropic and heliotropic angles (Sect. 4.5 ). Unfortunately all three effects only come in at a level of a few per cent of the variation, or less, which makes the result very sensitive to small errors in the calibration model. Moreover, the finite field of view is of little use if we have to calibrate complex periodic variations of optical distortions independently in each field of view. The best chance may be offered by the time variation of , for which the ratio of the parallax effect to the illumination strength goes as and consequently varies by % over the year. Thus the hope of breaking the degeneracy purely from the observations themselves, based on the self-calibration principle, is somewhat limited. 5. Conclusions We present an analysis of the effect of basic angle variations on the global shift of parallaxes derived from observations by a scanning astrometric satellite with two fields of view. The method of small perturbations was used to derive the changes in the four observables, the across- and
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