不规则形状小天体重力位的蒙特卡洛估算方法及其应用

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

  • 摘要: 当前小行星探测任务空前热烈,不规则外表形状对重力位估算的影响较大,常用的多面体算法因复杂度较高不利于算法设计。针对不规则外表形状小天体重力位估算的问题,提出基于蒙特卡洛积分的重力位估算算法,以便降低重力位估算的复杂度,促进相关理论研究和工程任务的开展。结果表明:(1)蒙特卡洛算法与多面算法在模型重力位估算中具有良好的一致性,表明本文算法具有一定的合理性。尽管球谐算法在重力位估算方面具极高的计算效率,但因数据转换和有限外表形状数据无法准确表征小天体形状而产生不可避免的偏差,该算法不太适合于不规则形状小天体重力位的估算; (2) Phobos和彗星67P重力位估算结果表明蒙特卡洛算法与多面体算法具有较好的一致性,再次表明蒙特卡洛算法具有一定的合理性,但蒙特卡洛算法因极大地降低重力位估算的复杂度更具适用性;(3)将蒙特卡洛算法应用于Psyche重力位的估算,发现Psyche赤道和两极的重力异常存在明显的带状分布。Psyche重力异常分布的差异性表明类似小天体的扁率摄动可能是环绕探测器轨道确定的主要影响因素,类似小天体的着陆采样任务在极区开展有助于降低燃料消耗。鉴于蒙特卡洛算法的良好表现及低复杂度,可广泛地应用于具有不规则形状小天体重力异常的估算中,可为类似理论研究和工程应用提供一定的参考。

     

    Abstract: 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.

     

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