Crater ejecta scaling laws - Fundamental forms based on dimensional analysis

A model of crater ejecta is constructed using dimensional analysis and a recently developed theory of energy and momentum coupling in cratering events. General relations are derived that provide a rationale for scaling laboratory measurements of ejecta to larger events. Specific expressions are presented for ejection velocities and ejecta blanket profiles in two limiting regimes of crater formation : the so-called gravity and strength regimes. In the gravity regime, ejecta velocities at geometrically similar launch points within craters vary as the square root of the product of crater radius and gravity. This relation implies geometric similarity of ejecta blankets. That is, the thickness of an ejecta blanket as a function of distance from the crater center is the same for all sizes of craters if the thickness and range are expressed in terms of crater radii. In the strength regime, ejecta velocities are independent of crater size. Consequently, ejecta blankets are not geometrically similar in this regime. For points away from the crater rim the expressions for ejecta velocities and thickness take the form of power laws. The exponents in these power laws are functions of an exponent, α, that appears in crater radius scaling relations. Thus experimental studies of the dependence of crater radius on impact conditions determine scaling relations for ejecta. Predicted ejection velocities and ejecta-blanket profiles, based on measured values of α, are compared to existing measurements of velocities and debris profiles.

[1]  E. Buckingham.  On Physically Similar Systems; Illustrations of the Use of Dimensional Equations , 1914 .

[2]  H. J. Moore,et al.  Spray Ejected from the Lunar Surface by Meteoroid Impact , 1963 .

[3]  D. Gault,et al.  Impact cratering mechanics and structures , 1968 .

[4]  Ferris Wheel Series Air Vent/Flat Top Events , 1968 .

[5]  David Braslau,et al.  Partitioning of energy in hypervelocity impact against loose sand targets , 1970 .

[6]  C. Teitelboim.  RADIATION REACTION AS A RETARDED SELF-INTERACTION. , 1971 .

[7]  D. H. Scott,et al.  Multiringed basins - Illustrated by Orientale and associated features. [geologic mapping and photographs of lunar ejecta] , 1974 .

[8]  V. Oberbeck.  The Role of Ballistic Erosion and Sedimentation in Lunar Stratigraphy , 1975 .

[9]  G. Polkowski,et al.  Experimental hypervelocity impact into quartz sand: Distribution and shock metamorphism of ejecta , 1975 .

[10]  V. Oberbeck,et al.  Candidate areas for in situ ancient lunar materials , 1976 .

[11]  Review and comparison of hypervelocity impact and explosion cratering calculations , 1977 .

[12]  Experimental hypervelocity impact into quartz sand. II - Effects of gravitational acceleration , 1977 .

[13]  H. Cooper.  A summary of explosion cratering phenomena relevant to meteor impact events , 1977 .

[14]  W. Hartmann.  Planet formation - Mechanism of early growth , 1978 .

[15]  P. Schultz,et al.  Orbital infrared observations of lunar craters and possible implications for impact ejecta emplacement , 1978 .

[16]  William K. Hartmann,et al.  Planetesimals to planets: Numerical simulation of collisional evolution , 1978 .

[17]  K. Holsapple,et al.  A material-strength model for apparent crater volume. , 1979 .

[18]  D. Gault,et al.  Atmospheric effects on Martian ejecta emplacement , 1979 .

[19]  Jacques E Schoutens.  Nuclear Geoplosics Sourcebook. Volume IV. Part II. Empirical Analysis of Nuclear and High-Explosive Cratering and Ejecta , 1979 .

[20]  Alan W. Harris,et al.  Collisional evolution of asteroids - Populations, rotations, and velocities , 1979 .

[21]  R. M. Schmidt,et al.  Meteor Crater: Energy of formation - Implications of centrifuge scaling , 1980 .

[22]  A. J. Piekutowski,et al.  Formation of bowl-shaped craters , 1980 .

[23]  Y. Langevin,et al.  A Model for Small Body Regolith Evolution: the Critical Paramters , 1980 .

[24]  S. Croft.  The excavation stage of basin formation - A qualitative model , 1981 .

[25]  D. Gault,et al.  Laboratory simulation of pelagic asteroidal impact Atmospheric injection, benthic topography, and the surface wave radiation field , 1982 .

[26]  K. A. Holsapple,et al.  On the Scaling of Crater Dimensions 2. Impact Processes , 1982 .

[27]  K. Housen,et al.  REGOLITHS ON SMALL BODIES IN THE SOLAR SYSTEM , 1982 .