GaussGrav: Gravity Field and Density Reconstruction of Small Bodies via Learnable 3D Gaussian Densities

Accurate gravity modeling near the surfaces of small solar system bodies remains one of the core challenges for spacecraft proximity operations, as demonstrated by missions such as Hayabusa2 at Ryugu [1] and OSIRIS-REx at Bennu [2]. Existing approaches, including polyhedral gravity models [3], mascon grids[4], and neural density fields [5,6], face trade-offs between computational cost, geometric flexibility, and physical interpretability. Near-surface gravity accuracy is particularly critical for safe landing and sample collection, yet most methods degrade rapidly as altitude decreases.

We present GaussGrav, a gravity field model that represents a small body's interior as a cloud of learnable three-dimensional Gaussian density blobs. Each Gaussian carries a peak density parameter and a size parameter; their collective density field implicitly encodes the body's internal mass distribution, and the gravitational acceleration at any external point is computed analytically from this representation. The model is trained purely from simulated accelerometry observations and adapts through a densification strategy that progressively concentrates resolution in high-density regions.

We evaluate GaussGrav on two well-studied asteroid analogues: Eros (a highly elongated S-type body) and Bennu (a rubble-pile B-type body with pronounced mass heterogeneity). At an altitude of 5% of the body's characteristic radius, GaussGrav achieves a mean relative acceleration error below 0.11%, representing an improvement of one to two orders of magnitude over a mascon grid approach [4]. For Bennu, the learned density field recovers the rank ordering of regional densities with a Spearman correlation of 0.87 against the heterogeneous mass distribution inferred fromOSIRIS-REx radio science data [2].

These results suggest that a Gaussian density formulation offers a promising path toward simultaneous gravity inversion and internal structure inference, with particular advantages for surface-proximity navigation in future small body missions.

References

[1] Watanabe, S., et al. (2019). Hayabusa2 arrives at the carbonaceous asteroid 162173 Ryugu. Science, 364, 268–272.

[2] Scheeres, D.J., et al. (2020). Heterogeneous mass distribution of the rubble-pile asteroid (101955) Bennu. Science Advances, 6, eabc3350.

[3] Werner, R.A., & Scheeres, D.J. (1997). Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia. Celestial Mechanics and Dynamical Astronomy, 65, 313–344.

[4] Fanti, E., & Izzo, D. (2025). MasconCube: Fast and accurate gravity modeling with an explicit representation. arXiv:2509.08607.

[5] Izzo, D., & Gómez, P. (2022). Geodesy of irregular small bodies via neural density fields. Communications Engineering, 1, 48.

[6] Martin, J.R., & Schaub, H. (2022). Physics-informed neural networks for gravity field modeling of small bodies. Celestial Mechanics and Dynamical Astronomy, 134, 46.