L. I. Turchak

A comprehensive study of distribution laws for the fragments of Košice meteorite

In this study, we conduct a detailed analysis of the Kosice meteorite fall (February 28, 2010), to derive a reliable law describing the mass distribution among the recovered fragments. In total, 218 fragments of the Kosice meteorite, with a total mass of 11.285xa0kg, were analyzed. Bimodal Weibull, bimodal Grady, and bimodal lognormal distributions are found to be the most appropriate for describing the Kosice fragmentation process. Based on the assumption of bimodal lognormal, bimodal Grady, bimodal sequential, and bimodal Weibull fragmentation distributions, we suggest that, prior to further extensive fragmentation in the lower atmosphere, the Kosice meteoroid was initially represented by two independent pieces with cumulative residual masses of approximately 2 and 9xa0kg, respectively. The smaller piece produced about 2xa0kg of multiple lightweight meteorite fragments with the mean around 12xa0g. The larger one resulted in 9xa0kg of meteorite fragments, recovered on the ground, including the two heaviest pieces of 2.374xa0kg and 2.167xa0kg with the mean around 140xa0g. Based on our investigations, we conclude that two to three larger fragments of 500–1000xa0g each should exist, but were either not recovered or not reported by illegal meteorite hunters.

Consequences of collisions of natural cosmic bodies with the Earth’s atmosphere and surface

AbstactPossible consequences of collisions of natural cosmic bodies with the Earth’s atmosphere and surface are described. The methodological basis of classification of consequences is the solution of meteor physics equations characterizing the trajectory of a body in the atmosphere, namely, the dependence of the body’s velocity and mass on the flight altitude. The solution depends on two dimensionless parameters characterizing the drag altitude and the role of mass loss by a meteoroid during its motion in the atmosphere. Depending on values of these parameters, the degree of effect on the planetary surface considerably changes. In particular, the conditions of cratering and meteorite fall on the planetary surface are obtained. The results are presented in a simple analytical form. They quite match to the real events considered in the paper. Recommendations are given on further investigations into the important problem of interaction of cosmic bodies with planetary atmospheres.

Standards for crater formation and meteorite fallout by the light sector of an atmospheric trajectory

New application of the simple solution of meteor physics equations, which depends on two dimension� less parameters, the ballistic coefficient α and the massloss parameter β, is given in the paper. The solu� tion allows easily predicting important consequences of the entry of meteor bodies into the atmosphere and of their interaction with the surface of the planet. The matter concerns the forecast of the crater formation and meteorite fallout on the basis of observable prop� erties of the light sector of the atmospheric trajectory of the bolide. The problem of the approximation of the observed motion of the bolide in the atmosphere is reduced to the search for such values of parameters α and β at which the analytical solution of meteor physics equa� tions

Approximating the Solution of Meteor Physics Equations through the Use of Elementary Functions

In this paper we examine the possibility of using approximations of elementary functions for the analytical solution of meteor physics equations, used to describe the trajectory and to evaluate the defining parameters of meteoroids entering the Earth’s atmosphere. We show the possibility of replacing the analytical solution with the combination of two elementary functions along one parameter. We provide estimates for the error of the proposed replacement. We investigate the magnitude of error in the function which arises in the approximation of meteoric observational data.

Shape estimation for Košice, Almahata Sitta and Bassikounou meteoroids

This paper is concerned with a meteoroid shape estimation technique based on statistical laws of distribution for fragment masses. The idea is derived from the experiments that show that brittle fracturing produces multiple fragments of size lesser than or equal to the least dimension of the body. The number of fragments depends on fragment masses as a power law with exponential cutoff. The scaling exponent essentially indicates the initial form of the fragmented body. We apply the technique of scaling analysis to the empirical data on the mass distributions for Kosice, Almahata Sitta and Bassikounou meteorites.

Estimation of the initial shape of meteoroids based on statistical distributions of fragment masses

An approach to the estimation of the initial shape of a meteoroid based on the statistical distributions of masses of its recovered fragments is presented. The fragment distribution function is used to determine the corresponding scaling index of the power law with exponential cutoff. The scaling index is related empirically to the shape parameter of a fragmenting body by a quadratic equation, and the shape parameter is expressed through the proportions of the initial object. This technique is used to study a representative set of fragments of the Bassikounou meteorite and compare the obtained data with the results of statistical analysis of other meteorites.

Meteoroids Interaction With The Earth Atmosphere

Abstract In this study we evaluate meteoroid mass and its other properties based on the observed atmospheric trajectory. With account for aerodynamics, we formulate a problem by introducing key dimensionless parameters in the model, responsible for the drag, mass loss and rotation of meteoroid. The proposed model is suitable to categorize various impact events in terms of meteor survivability and impact damage and thus, to analyze consequences that accompany collisions of cosmic bodies with planetary atmosphere and surface. The different types of events, namely, formation of a massive single crater (Barringer, Lonar Lake), dispersion of craters and meteorites over a large area (Sikhote-Alin), absent of craters and meteorites, but huge damage (Tunguska) are considered as illustrative examples. The proposed approach helps to summarize the data on existing terrestrial impacts and to formulate recommendations for further studies valuable for planetary defence. It also significantly increases chances of successful meteorite recoveries in future. In other words, the study represents a ’cheap’ possibility to probe cosmic matter reaching planetary surface and it complements results of sample-return missions bringing back pristine samples of the materials.

Statistical approach to estimate initial meteoroid shape from empirical mass distribution of recovered fragments

We present a study on statistical approach to estimate initial meteoroid shape of the Sutter’s Mill meteorite, aiming to fit lognormal, Weibull and Grady statistical mass distributions to the recovered fragments. We show a good correspondence of the selected distribution functions to the experimental data, with the best fit obtained with exponential cumulative distribution function (as a special case of Weibull distribution). This allows us to implement a novel technique for meteoroid pre-entry shape estimation, based on the detailed data on surviving meteorite fragments recovered on the ground. In total, all the available 77 fragments of the Sutter’s Mill meteorite were analyzed. This recovered fragment set is proved statistically complete. From the results obtained in this study, we suggest that only one major fragmentation event occurred during the atmospheric passage of the Sutter’s Mill meteoroid. The scaling analysis reveals an elongated pre-fragmentation shape of the meteoroid, being an average bet...

Mathematical model for estimation of meteoroid dark flight trajectory

This paper is concerned with mathematical model for numerical simulation of meteoroid dynamics. The simulations of bolide ballistics are carried out via hard sphere approximation. System of differential equations for movement and heat transfer is solved in Lagrange variables via Runge-Kutta methods. The drag force of atmospheric air is computed via Henderson formula, valid for wide ranges of Reynolds and Mach numbers. The parameters of surrounding gas are obtained from standard atmosphere model. The impact pressure is computed taking into account entropy jump through bow head shockwave and consequent isentropic deceleration of the flow in the vicinity of streamlined sphere. Meteoroid fragmentation is modeled as sequential division of parent body into two parts using random weighting coefficient for parent mass. The condition for fragmentation event occur when the hemisphere-averaged value of impact pressure exceeds the threshold of relative body strength, which nonlinearly depends on ration of initial met...