Orbital dispersion and Earth-impact probability analysis for fragmented asteroids

This paper describes the orbital dispersion problem for a fragmented asteroid in an elliptical orbit. The use of a state transition matrix derived from the general relative equation of motion for an elliptical orbit is emphasized in this paper. The state transition matrix is used to propagate the orbital dispersion. The Earth-impact probability is then computed to obtain a measure of the likelihood of impact with the Earth after the asteroid is fragmented with a high-energy fragmentation method. The state transition matrix approach is also compared with numerical integration approaches that use the two-body equation and the general relative equations of motion. The computational efficiency of such a state transition matrix approach is verified with accuracy equal to the numerical integration approaches. The employed state transition matrix, known as the Cochran, Lee and Jo (CLJ) state transition matrix, is also evaluated for the numerous fragments with data from the burst.