The estimation of the motion model errors influence on precision of the building of confidence region for near-Earth asteroids

This paper deals with the method of accuracy estimation of using of asteroid motion models by comparing the size of confidence regions and offset of least square estimation of their nominal orbits determined for models of varying degrees of completeness. Comparing of perturbing forces models and selection of the best models in the task of constructing regions of object possible motions are based on indicator that has geometrically clear and simple form. If the value of this index is less than a certain threshold value, it is supposed that the offset of least square estimation can be considered as small compared to the size of confidence regions and exclusion of some factors has a negligible effect. In this study, the motion model has included gravitational perturbations from the principal planets, the Moon, Pluto, oblateness of Earth and relativistic effects from the Sun. The linear and nonlinear methods of presenting of confidence region by its boundary surface are also investigated. Investigation of the Newton’s iteration method, which has used for mapping points in non-linear case, has been made. The estimates of the influence of the motion model errors on the accuracy of constructing confidence regions are provided on the example of near Earth asteroids 2011 MD and 1998 QE2. The paper states that no complete account of the disturbing forces and inexact representation of the observations may lead to unreliable determination of confidence region for small bodies’ motion.