Structural Convergence of Mascon Gravity Models: A Comparative Study of (16) Psyche and (136108) Haumea

Abstract Mascon gravity models are widely used to represent the near-field gravity of small bodies, yet practical criteria to verify whether a given mascon resolution is sufficient for local dynamics are rarely quantified. We propose a reproducible convergence protocol centered on a dynamically meaningful feature that controls accessibility in the rotating frame: the four external saddle equilibria and the associated connectivity of equatorial zero-velocity curves (ZVCs). We build controlled mascon families for two contrasting bodies, the irregular asteroid (16) Psyche, represented by a convex triangular mesh, and the elongated dwarf planet (136108) Haumea, represented by a triaxial-ellipsoid model. For each resolution N = {500, 1000, 3000, 5000, 10 000, 15 000, 20 000}, we detect the external saddles and track them against a fixed reference set at Nref = 20 000 via a one-to-one three-dimensional matching. A resolution reproduces the external equilibrium-point configuration if all four saddles are matched within an acceptance radius dmax = αRmean, where Rmean is the volume-equivalent radius and α is a dimensionless tolerance. Using the conservative tolerance α = 0.05, full recovery, defined as nmatch = 4, is not guaranteed at low and intermediate N and can be non-monotonic. For Psyche, nmatch(N) = {1, 1, 2, 1, 2, 3, 4}; for Haumea, nmatch(N) = {0, 4, 2, 2, 4, 4, 4}. The external equilibrium-point configuration thus provides a sensitive diagnostic of mascon-resolution adequacy. Reporting nmatch(N) together with reference-based displacement metrics provides a compact verification step prior to downstream dynamical surveys.