The two-parameter family of hamiltonians systems defined by $$H_{(a,\alpha )} (r,\theta ,p_r ,p_\theta ) = (p_r^2 + p_\theta ^2 r^{ - 2} )/2 - ar^{ - \alpha } ,\alpha ,a \in \Re ^ +$$ is considerated. For every value of $$(a,\alpha ) \in \Re ^ + \times \Re ^ + ,H_{(a,\alpha )}$$ is integrable, the energy H(a,α) and the angular momentum C(r,θ,pr,pθ)=pθ being two independent first integrals. Using appropriate coordinates, the natural foliation ofI h = ∪ c I hc is found-up to now, the sets Ih∩{c≥0} and Ih∩{c≤0} were studied separately and then their boundaries identified ([CLL], [D], [LL], for instance). As a corollary to this topological description, we obtain a relation between the value of the parametre α and the variation of the θ-coordinate along an orbit while it stays near collision or infinity.