Reconstruction of Lunar Gravity Anomalies and Heterogeneous Density Distribution based on Optical Guidance Information

Since the launch of China’s Lunar Exploration Program in 2004, the project has conducted a three-step approach of “orbiting, landing, and returning”. On June 2, 2024, the Chang’e-6 successfully landed in the South Pole-Aitken Basin on the far side of the Moon. To support future Earth-Moon space exploration, the prediction and selection of resource-rich regions are particularly crucial. In particular, the South Pole-Aitken Basin is not only the largest and deepest impact basin among terrestrial planets in the solar system but also the region with the highest density of impact craters on the lunar surface. Therefore, reconstructing lunar gravity anomalies and predicting heterogeneous density are of great significance for exploring deep planetary materials and internal structures, as well as guiding in-situ resource utilization on the Moon and other terrestrial planets. This study focuses on the Moon, using the LOLA digital elevation model to construct both a lunar shape model and a homogeneous Mascon model. The gravity acceleration results computed from the homogeneous Mascon model and the spherical harmonic model provided by the GRAIL mission are used as reference data. A fully connected neural network based on the Siren implicit neural representation with periodic activation functions is proposed to approximate the mass distribution within a closed cube. By encoding spatial coordinates within the cube, the network learns from the gravity acceleration dataset and backpropagates the differences to the acceleration calculated from the density represented by the network, thereby mapping positions within the cube to corresponding densities. Following this idea, instead of a simple reproduction to Moon, this paper is an important progress to future incorporation with autonomous guidance with two technical challenges explored, i.e., optical images by camera self-calibration in complex environments and uncertainty of gravity anomaly w.r.t heterogeneous density distribution. Final experiments show that, without the layered assumption, the network can implicitly learn the lunar surface shape, achieving a relative inversion error of 0.5% for the Mascon model and 0.76% for the spherical harmonic model. Under the layered assumption, the model successfully predicts the density of the lunar inner core (~7179 kg/m³⁾ outer core (~5379 kg/m³⁾ mantle (~3444 kg/m³⁾ and crust (~1958 kg/m³⁾ reducing the relative inversion error to 0.1%. Additionally, the study discusses the network's dependency on layer-specific factors and compares its performance with previous work. Ultimately, this research achieves simultaneous lunar gravity inversion and density distribution prediction.