Model for the Atmospheric Fragmentation and Scattering of a Small Celestial Body

Abstract

This paper considers the interaction of a small celestial body with a planetary atmosphere, which is treated as a two-stage process: the first stage is the fragmentation of the parental body (a model for this stage was developed by the authors) and the second stage involves breakup and scattering of the fragments. A model for the second stage is proposed in which the breakup is treated as a two-phase process of macrodisplacement of the fragments resulting from the fracture of the parental body. In the first phase there is accelerated rotation of the fragments around their centers of mass with preservation of contact between them. By the moment the contact ceases, they acquire a transverse velocity and there comes the second phase -the dispersion of the fragments, which ends with their scattering on the ground. A feature of this model is that the breakup occurs by an aerodynamic mechanism. In an analysis of the first phase of breakup, a system of differential equations for the kinetostatics of the fragments is formulated. Calculations are performed using as an example the atmospheric breakup of the Sikhote Alin meteoroid and the scattering of its fragments on the ground. It is shown that along with the numerical method for solving the system, an approximate analytical method is also possible. Calculation results for both methods are close and are in good agreement with observations of the indicated phenomenon.The space safety of the Earth is one of the most important and vital problems of the present time. In this connection, predicting the possible consequences of atmospheric entry of a small celestial body (SCB) is of significant interest. 2 Important aspects of this problem are the fragmentation of a SCB and the scattering of its fragments in the atmosphere and on the surface of the planet.At present, a number of computational and theoretical models for the fragmentation stage have been developed using various physical backgrounds (see, for example, [1][2][3][4][5][6][7][8][9][10][11]). A common feature of the models 1 Institute of Experimental Physics, Russian Federal Nuclear Center, Sarov 607190; root@gdd.vniief.ru. 2 Recall the dangerous consequences of the fall of the Tungus (1908) and Sikhote Alin (1947) meteoroids on the Earth's surface or imagine what would have been if the ShoemakerLevy 9 comet had fallen not on the Jupiter (1994) but on the Earth! of [1 -5] is that they use the fracture criteria adopted in the mechanics of materials although here brittle fractures (SCBs are brittle) are considered inadmissible. As a result, the fragmentation is regarded as a single total breakup [2, 3] with undeterminable number and dimensions of the fragments or as a sequential avalanche breakup in which the events of gradual reduction in fragment size continuously follow one after another [1,4,5]. Previously [8-11], we proposed a different model for the sequential fragmentation of a SCB based on the energy criterion of fracture developed using the integral approach of modern fracture mechanics [12]. Therefore, the f...