Detection of Asteroid Impact Orbits Using Conditional Minimization of the Distance to the Earth

Abstract—A method has been developed for detecting impact orbits of asteroids in the confidence ellipsoid of the initial parameters of motion. The method consists in conditionally minimizing the distance from the asteroid to the Earth in any of its approaches to the Earth. The method imposes a restriction on the so-called “confidence coefficient,” i.e., the factor of increasing the size of the confidence ellipsoid. The limitation consists in setting a certain constant value for this coefficient, which determines a certain normalized distance from the center of the ellipsoid in the six-dimensional space of the initial parameters of motion. The method consists in finding the initial parameters of the motion corresponding to this distance and leading to the collision of the asteroid with the Earth. Varying the confidence coefficient with a sufficiently small step makes it possible to reveal such parameters at all corresponding distances, i.e., to obtain a picture of the location of the impact initial parameters of motion in the entire confidence ellipsoid. The method was tested for three potentially dangerous asteroids (2001 VB, 2005 WG57 and 2008 JL3) in their upcoming encounters with the Earth.