On the directional nature of celestial object's fall on the earth (Part 1: distribution of fireball shower, meteor fall, and crater on earth's surface).

This paper investigates the directional distribution of extraterrestrial objects (meteors, fireballs) impacting Earth's surface and forming craters. It also introduces a novel directional statistical mixture model to analyze their falls, validated through rigorous testing. First, we address whether these falls follow non-uniform directional patterns by explicitly employing directional statistical tools for analysing such data. Using projection techniques for longitude and latitude and more importantly, a general spherical statistical approach, we statistically investigate the suitability of the von Mises distribution and its spherical version, the von Mises–Fisher distribution, (a maximum entropy distribution for directional data). Moreover, leveraging extensive data sets encompassing meteor falls, fireball showers, and craters, we propose and validate a novel mixture von Mises–Fisher model for comprehensively analysing extraterrestrial object falls. Our study reveals distinct statistical characteristics across data sets: fireball falls exhibit non-uniformity, while meteor craters suggest a potential for both uniform and von Mises distributions with a preference for the latter after further refinement. Meteor landings deviate from a single-directional maximum entropic distribution; we demonstrate the effectiveness of an optimal 13-component mixture von Mises–Fisher distribution for accurate modelling. Similar analyses resulted in 3- and 6-component partitions for fireball and crater data sets. This research presents valuable insights into the spatial patterns and directional statistical distribution models governing extraterrestrial objects' fall on Earth, useful for various future works. [ABSTRACT FROM AUTHOR]