Acceleration of Numerical Integration of the Equations of Motion of Asteroids

Abstract—

Finding and studying possible collisions of asteroids approaching the Earth requires a significant amount of computation. This paper describes the R⁰ program created to calculate the trajectories of a large number of virtual asteroids and the parameters of approaches with the bodies of the Solar System: planets, the Moon, and the Sun. The program uses the DE430 ephemeris and the Gauss–Everhart integration method. Comparison with the previously developed v19 software package in different tests showed an increase in performance by an order of magnitude or more. When integrating the motion of one asteroid, a lower acceleration was achieved; however, this problem was already solved in an acceptable time. Optimization was carried out for a large number of asteroids. We estimated the probability of collision of 200 asteroids by the Monte Carlo method using the new program. The results are compared with those obtained by NASA.