Analytical formulation of lunar cratering asymmetries

摘要

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 venc is higher than the lunar orbital speed vM, we rigorously integrated the lunar cratering distribution, and derived its approximation to the first order of vM/venc. Numerical simulations of lunar bombardment by the MBAs during the LHB were performed with an Earth–Moon distance aM = 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 + A1cosβ), 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 + A2cos2?), which decreases as the latitude modulus | ? | increases. The amplitudes A1,2 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 A1 ∝ vM/venc, 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 aM. Estimates of A1 for crater density distributions generated by the MBAs and the NEOs are 0.101?0.159 and 0.117, respectively.