Dynamic Falling of the Chelyabinsk Meteoroid: Sizes, Radiation, and Destruction

The purpose of this paper is to obtain refined altitude-time dependences of radiation intensity and mass of the Chelyabinsk meteoroid during the fall, determine the size of the bolide, and build a model of destruction with an estimate of the fragment distribution parameters by mass. The study into the impact of large celestial bodies on the environment is an urgent task for forecasting environmental consequences. The radiation intensity was calculated using the time dependence of the bolide's brightness and E. Epic's empirical formula. The Stefan-Boltzmann law and M. Planck's formula were used for the radiation model of a perfect black body in a limited range of wavelengths. A method was found to determine the size of the bolide according to published observations from the video recorder. For the construction of the model of continuous fragmentation, an adapted equation of individual fragments' motion was used. Three types of mass distribution of fragments were tested: logarithmically normal, power-law, and uniform. As a result of the numerical simulation, the contribution of radiation energy was determined. It was shown that 21% of the kinetic energy of a meteoroid was spent on radiation. The variations in the mass, altitude-time dependences of the bolide size, and the parameters for different distributions of fragments by mass were calculated. The diameter of the bolide head reached 2 km, and the length of the tail was 3.5-4 km. It was found that the results of fragmentation are described at the initial stage of motion by the power-law distribution, while the distribution is lognormal in denser layers of the atmosphere. The characteristics of the swarm of stone fragments that may have followed the meteoroid were estimated. The length of the swarm reached 30 km, the maximum mass of the swarm was estimated at 400 t, and the radiation energy was 0.6% relative to the initial kinetic energy of the meteoroid.