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 meteoroid mass to current mass of considered fragment. To compute trajectory divergence for newly-formed splinters we introduce the repulsive force, dependent on impact pressure, cross sectional areas of mutually repulsing bodies and distances between them. The set of mathematical models is implemented as the program complex. Preliminary computational results show that fragmentation altitude, terminal velocities and maximum splinter masses are in good agreement with corresponding observations and measurements.