Equations of state and impact-induced shock-wave attenuation on the moon

Abstract

Current equation-of-state formulations, used for finite-difference cratering flow calculations, are cast into a framework permitting comparison of peak pressures attained upon impact of a sphere, with a half-space, along the impact symmetry axis, to one-dimensional impedance match solutions. On the basis of this formulation and application of thermochemical data, the regimes of melting and vaporization are examined. For the purpose of identifying material which will, upon isentropic release from the impact-induced shock state, result in a solid just brought to its melting point, i.e., incipiently melted (IM), completely melted (CM), just brought to its boiling point, i.e., incipiently vaporized (IV), and completely vaporized (CV) state, the pressures at which the critical isentropes intersect the Hugoniots of iron and gabbroic anorthosite (GA) are examined in detail. The latter rock type is assumed to be representative of the lunar highlands. The Hugoniot pressures, for which IM, CM, IV, and CV will occur upon isentropic expansion, are calculated to range from 2.2 to 16.8 Mbar, respectively for iron. For the high-pressure phase (hpp) assemblage of GA, modelled as a mixture of plagioclase in the hollandite structure and pyroxene in the perovskite structure, IM, CM, IV, and CV are calculated to occur upon isentropic expansion from Hugoniot states ranging from 0.43 to 5.9 Mbar, respectively. The spatial attenuation of shock pressure along the impact axis is found to be clearly represented by two regimes, if the peak pressure, P, and radius normalized to that of the projectile, r, are fitted to expressions of the form P ∝ r^α. At distances from 2.2 to 5.6 projectile radii into a GA target, the constant, a, is on the order of -0.2. This low-attenuation rate, near-field regime, extends further into the target at the slower impact velocities and arises because of the slightly divergent flow associated with the penetration of a spherical projectile. For the near-field impact regime, an impact at 5 km/sec of an iron object with a GA surface will induce CM for GA but the iron will remain solid. At 15 km/sec, partial vaporization (PV) occurs for both GA and iron, whereas at 45 km/sec, CV occurs in both materials. Similar calculations are summarized for a GA meteoroid striking a GA surface at velocities ranging from 5 to 45 km/sec. At greater radii, in thefar-field regime, the exponent, a, varies systematically from -1.45 to -2.15 for impacts of GA onto GA as the impact velocity is increased from 5 to 45 km/sec. For an iron projectile impacting at speeds of 5-45 km/sec, the exponent, a, varies from -1.67 to -2.95. By comparison, the equivalent value of a, reported for both contained and surface explosions in various rocks is ~ -2. It is suggested that, given field data on shock attenuation (based on identification of various shock metamorphic features versus distance), overall crater size, and some chemical data as to the type of meteoroid which produced a crater, quantitative bounds on the impact velocity of the meteorite may be obtained.

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