# On the impact of the Yarkovsky effect on Apophis’ orbit

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## Abstract

In October 2009, a new set of optical observations of Apophis, a potentially hazardous asteroid, was published. These data have significantly expanded the interval of observations and their total number. In the article we compare the results of refinement of Apophis’ orbit made at the Jet Propulsion Laboratory (JPL, United States), the University of Pisa (Italy), and the Institute of Applied Astronomy (IAA) of the Russian Academy of Sciences with consideration for new observations. New orbits lead to a significant decrease in the probability of Apophis’ collision with the Earth in 2036. As a result of processing a large number of observations of asteroids approaching the Earth and main belt asteroids less than 40 km in size, with a large number of optical and, in many cases, radar observations in different oppositions, one of the authors revealed that additional acceleration affects their motion. This acceleration can be represented by the transversal component *A* _{2} in the orbital coordinate system. The presence of this acceleration can be interpreted as the Yarkovsky effect. The statistical properties of distribution of *A* _{2} for asteroids, for which it is determined quite reliably, evidence in favor of this interpretation. The value of additional acceleration for bodies the size of Apophis falls in the range ±10^{−13} AU/day^{2}. In this paper we have calculated the probability of Apophis colliding with the Earth in 2036 at different values of the transversal component of additional acceleration *A* _{2}. For the resulting points, a plot of the probability of the collision against the *A* _{2} value has been constructed. At *A* _{2} = −8.748 × 10^{−14} AU/day^{2} (and zero values of the radial *A* _{1} and normal *A* _{3} components) the nominal solution for Apophis’ orbit on April 13, 2029, is only 90 m from the middle of a “keyhole” 600 m in width, which leads to a collision of Apophis with the Earth in 2036. Since the scattering ellipse in the target plane in 2029 significantly overlaps the keyhole, the probability of collision at the given additional acceleration value is 0.0022. This result has been verified by the Monte Carlo method. Tests of 10000 random sets of orbital elements, which were found taking into account their correlation, have shown that 22 cases have resulted in virtual asteroids colliding with Earth in 2036. A plot of the probability of the collision against the value of *A* _{2} has been constructed.

## Keywords

Orbital Element Solar System Research Semimajor Axis Optical Observation Radar Observation## Preview

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