Analytical formulation of lunar cratering asymmetries
Analytical formulation of lunar cratering asymmetries
复制标题
月球陨石坑不对称性的分析公式
DOI：
10.1051/0004-6361/201628598
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发表时间：
2016-08
影响因子：
6.5
通讯作者：
Ji-Lin Zhou
中科院分区：
文献类型：
--
作者：
Nan Wang;Ji-Lin Zhou
上下文。卫星撞击的不对称性既与其轨道有关，也与撞击器有关。太阳系内部的撞击群体，即主带小行星(MBA)和近地天体(NEO)，分别在LHB后期和此后一直占据主导地位。目标。我们描述了月球陨石坑的分布，并验证了MBA和近地天体产生的陨石坑不对称性。方法：研究方法。基于一个不考虑地球引力和月球引力的平面模型，并假设撞击器与地球相遇的速度高于月球轨道速度vM，我们对月球陨石坑的分布进行了严格的积分，并导出了它的一阶近似值。在地月距离为M=20−60地球半径的5种情况下，对MBAS对月球的轰击进行了数值模拟。结果。该分析模型直接证明了超前/拖尾不对称的存在以及近/远不对称的存在。前导/拖尾不对称的近似形式为(1+A1 cosβ)，它随着顶点距离β的增加而减小。数值模拟显示了极/赤道不对称性和前导/拖尾不对称性，前者被经验地描述为(1+A2 cos 2ϕ)，它随着纬度模数|ϕ|的增加而减小。振幅A1，2是不对称性的可靠测量。我们的分析明确指出了陨石坑分布与A1∝v M/v enc等轰击条件(撞击器特性和月球轨道状态)之间的定量关系，从而得到了一种通过测量不对称性来再现轰击条件的方法。分析模型和数值模拟结果相互印证了陨石坑的分布及其随M的变化。MBA和近地天体产生的陨石坑密度分布的A1估计分别为0.101−0.159和0.117。
Context. The cratering asymmetry of a bombarded satellite is related to both its orbit and impactors. The inner solar system impactor populations, that is, the main-belt asteroids (MBAs) and the near-Earth objects (NEOs), have dominated during the late heavy bombardment (LHB) and ever since, respectively. Aims. We formulate the lunar cratering distribution and verify the cratering asymmetries generated by the MBAs as well as the NEOs. Methods. Based on a planar model that excludes the terrestrial and lunar gravitations on the impactors and assuming the impactor encounter speed with Earth v enc is higher than the lunar orbital speed v M , we rigorously integrated the lunar cratering distribution, and derived its approximation to the first order of v M / v enc . Numerical simulations of lunar bombardment by the MBAs during the LHB were performed with an Earth–Moon distance a M = 20−60 Earth radii in five cases. Results. The analytical model directly proves the existence of a leading/trailing asymmetry and the absence of near/far asymmetry. The approximate form of the leading/trailing asymmetry is (1 + A 1 cos β ), which decreases as the apex distance β increases. The numerical simulations show evidence of a pole/equator asymmetry as well as the leading/trailing asymmetry, and the former is empirically described as (1 + A 2 cos2 ϕ ), which decreases as the latitude modulus | ϕ | increases. The amplitudes A 1,2 are reliable measurements of asymmetries. Our analysis explicitly indicates the quantitative relations between cratering distribution and bombardment conditions (impactor properties and the lunar orbital status) like A 1 ∝ v M / v enc , resulting in a method for reproducing the bombardment conditions through measuring the asymmetry. Mutual confirmation between analytical model and numerical simulations is found in terms of the cratering distribution and its variation with a M . Estimates of A 1 for crater density distributions generated by the MBAs and the NEOs are 0.101−0.159 and 0.117, respectively.
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