The Monte Carlo method applied to the probability of an asteroid or comet falling onto the surface of the Earth

Abstract

Estimations state that, gradually, the chances of a celestial body an asteroid or a comet colliding with Earth's surface increase over time. This research aims to determine the probability associated with the impact of these objects by utilizing concepts and formulations derived from the Reliability of Components and Systems, specifically the Monte Carlo Process. The analysis was conducted through the formulation of the failure function and testing of the design variables, namely the minimum distance of the body to Earth and its relative velocity. The studied data was divided into two categories: existing objects mapped by NASA \cite{ref1} and randomly generated objects using sampling techniques involving the cumulative probability function in Excel and Matlab software. The results demonstrated similar failure probability values for both data sets, corresponding to the likelihood of the object impacting Earth's surface (0.113\% for real objects, 0.133\% for 15,000 points in Excel, and 0.141\% for 1,000,000 points in Matlab). Thus, this process was deemed viable for this study, allowing the probability to be calculated in both software programs with acceptable variations within observed limits. These findings are consistent with the approximations and techniques employed for a diverse range of celestial body numbers.