The aim of this paper is the study of the impact that the consideration of different physical properties as magnitude and spectral type of stars has on the geometric relations between Hipparcos2 and UCAC4. In this sense, the pairs of residuals Δα* and Δδ can be considered as functions of (α, δ, r) and for each fixed r, we can fit a vector field on the sphere from which to obtain its components in the VSH basis. The same can be done by grouping the stars considering their magnitudes, spectral types (or mixing them) and then studying the variations in the mentioned geometry. We must not forget that Δα* and Δδ are numerical random variables whose regression on the magnitude m, for example, can be estimated. The results will be computed taking into account r as well as the physical mentioned properties. So, we avoid the assumption that the harmonic coefficients depend only on m.