Given a reductive group G and an affine G-scheme X, constellations are G-equivariant sheaves over X such that their module of global sections has finite multiplicities. Prescribing these multiplicities by a function h, and imposing a stability condition $\theta$ there is a moduli space for $\theta$-stable constellations constructed by Becker and Terpereau, using Geometric Invariant Theory. This construction depends on a finite subset D of the set of irreducible representations of G. By reformulating the stability condition $\theta$ and the GIT stability condition, in terms of a slope condition (say $\mu_{\theta}$ and $\mu_D$) we are able to construct Harder-Narasimhan filtrations from both points of view, and prove a precise relation between the two filtrations. Finally, we show that the associated polygons to the $\mu_D$-filtrations coverge to the one associated to the $\mu_{\theta}$-filtrations when D grows. These results are joint work with Ronan Terpereau.