Determination of the height of the “meteoric explosion”

Abstract

When cosmic bodies of asteroidal and cometary origin, with a size from 20 to approximately 100 m, enter dense atmospheric layers, they are destroyed with a large probability under the action of aerodynamic forces and decelerated with the transfer of their energy to the air at heights from 20–30 to several kilometers. The forming shock wave reaches the Earth’s surface and can cause considerable damage at great distances from the entry path similar to the action of a high-altitude explosion. We have performed a numerical simulation of the disruption (with allowance for evaporation of fragments) and deceleration of meteoroids having the aforesaid dimensions and entering the Earth’s atmosphere at different angles and determined the height of the equivalent explosion point generating the same shock wave as the fall of a cosmic body with the given parameters. It turns out that this height does not depend on the velocity of the body and is approximately equal to the height at which this velocity is reduced by half. The obtained results were successfully approximated by a simple analytical formula allowing one to easily determine the height of an equivalent explosion depending on the dimensions of the body, its density, and angle of entry into the atmosphere. A comparison of the obtained results with well-known approximate analytical (pancake) models is presented and an application of the obtained formula to specific events, in particular, to the fall of the Chelyabinsk meteorite on February 15, 2013, and Tunguska event of 1908, is discussed.