I discuss the diagrammatic approach to the conservative dynamics of coalescing binary systems within the effective field theory (EFT) framework applied to General Relativity (GR). In this setting, the Post-Newtonian (PN) expansion of the interaction potential can be systematically computed using techniques familiar from quantum field theory. Focusing on the static sector, I present the evaluation of the sixth-order PN correction, which requires the computation of six-loop two-point Feynman integrals. I review the main ingredients of the calculation and outline how the structure of the contributing diagrams enables a controlled organization of the computation. I will also discuss how a factorization theorem for the static potential can be exploited to extend the analysis to higher PN orders. Finally, I comment on general structural properties of Feynman integrals arising in GR-context, including their vector-space structure and their relations to D-modules theory.