Monte Carlo Estimation of Gravity Potential for Irregularly Shaped Small Bodies and Applications

Objectives: The increasing focus on asteroid exploration missions has brought significant attention to the estimation of gravity potential for irregularly shaped small celestial bodies, as their irregular geometries greatly influence gravity calculations. Methods: The commonly used polyhedral model (PM), while accurate, presents substantial challenges in algorithm design due to its high computational complexity. To address these issues, this study introduces a Monte Carlo (MC) integration-based algorithm for estimating the gravity potential of irregularly shaped small celestial bodies. This approach aims to reduce computational complexity and support advancements in both theoretical research and engineering applications. Results: Our results demonstrate that: (1) The MC algorithm demonstrates good consistency with the PM in gravity potential estimation, validating the rationality of the proposed approach. In contrast, the spherical harmonic algorithm, though computationally efficient, is less suitable for irregularly shaped bodies due to unavoidable biases arising from data transformation and the limited ability of spherical harmonic expansions to represent irregular geometries. (2) The MC algorithm achieves robust consistency with the PM when estimating the gravity potential of Phobos and comet 67P, further confirming its reliability while significantly reducing computational complexity. (3) Applying the MC algorithm to estimate Psyche's gravitational potential revealed a distinct banded distribution of gravity anomalies between the equatorial and polar regions. These findings suggest that the oblateness-induced perturbations of similar celestial bodies could significantly impact the orbit determination for orbiting probes. Furthermore, conducting landing and sampling missions in the polar regions of such bodies may reduce fuel consumption. Conclusions: The MC algorithm, with its demonstrated robustness and low computational complexity, shows strong potential for widespread application in gravity anomaly estimation for irregularly shaped small celestial bodies. It offers valuable insights for related theoretical studies and engineering tasks, providing a reference for future exploration missions.