Approximation of the observed motion of bolides by the analytical solution of the equations of meteor physics

A great volume of data has been accumulated thus far related to the photoregistration of the paths of meteor bodies in the terrestrial atmosphere. Most images have been obtained by four bolide networks, which operate in the USA, Canada, Europe, and Spain in different time periods. The approximation of the actual data using theoretical models makes it possible to achieve additional estimates, which do not directly follow from the observations. In the present study, we suggest an algorithm to find such parameters of the theoretical relationship between the height and the velocity of the bolide motion that help to fit observations along the luminous part of the trajectories in the best way. The main difference from previous studies is that the given observations are approximated using the analytical solution of the equations of meteor physics. The model presented in this study was applied to a number of bright meteors observed by the Canadian camera network and by the US Prairie network and to the Benesov bolide, which is one of the largest fireballs registered by the European network. The correct mathematical modeling of meteor events in the atmosphere is necessary for further estimates of the key parameters, including the extra-atmospheric mass, the ablation coefficient, and the effective enthalpy of evaporation of entering bodies. In turn, this information is needed by some applications, namely, those aimed at studying the problems of asteroid and comet security, to develop measures of planetary defense, and to determine the bodies that can reach Earth's surface.