Comparative investigation of methods for the numerical prediction of motion of asteroids that approach the Earth: Example of the 99942 Apophis asteroid

Using the 99942 Apophis asteroid (currently known as one of the most dangerous asteroids that is approaching the Earth) as an example, we estimate the error of predicting its motion with the use of several integrators over the time interval from 2012 to 2029. The minimum distance (and its error) between the Earth’s center and Apophis was estimated for the rendezvous moment on April 13, 2029. It is shown that this error for various integrators is comparable in the order of magnitude with the influence of certain components of the dynamic model of motion, such as, for example, the influence of harmonics of the Earth’s gravitational filed, solar-light pressure, the Jarkowski effect, etc.