On the impact of the Yarkovsky effect on Apophis’ orbit

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 Rus sian 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 com ponent A 2 in the orbital coordinate system. The presence of this acceleration can be interpreted as the Yark ovsky effect. The statistical properties of distribution of A 2 for asteroids, for which it is determined quite reli ably, evidence in favor of this interpretation. The value of additional acceleration for bodies the size of Apo phis 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.

A thermophysical analysis of the (1862) Apollo Yarkovsky and YORP effects

“…The Yarkovsky effect has been detected by sensitive radar ranging for (6489) Golevka (Chesley et al 2003) and (101955) 1999 RQ36 , by deviations from predicted ephemerides over a long time span for (152563) 1992 BF ) and for 54 other near-Earth asteroids Nugent et al 2012;Farnocchia et al 2013), and indirectly through the observed orbital distribution of the Karin cluster asteroid family (Nesvorný & Bottke 2004). The Yarkovsky effect adds significant uncertainties to predictions of the orbits of potentially hazardous asteroids during very close encounters with the Earth, such as (99942) Apophis (Chesley 2006;Giorgini et al 2008;Shor et al 2012), and adds complications for determining the ages of unbound asteroid pairs (Duddy et al , 2013.…”

Impact trajectories of the asteroid Apophis in the 21st century

“…Obviously, in developing methods to prevent a collision in 2036, these events must be taken into consideration despite their low probability. The estimates for the probability of a collision of Apophis with the Earth are very sensi tive to initial data, as is shown in (Vinogradova et al, 2008;Kochetova et al, 2009;Shor et al, 2012) and, therefore, exhibit a large spread. Shor et al (2012) analyzed the results of the latest refinements of Apo phis' orbit based on the most complete set of observa tional data.…”

“…The estimates for the probability of a collision of Apophis with the Earth are very sensi tive to initial data, as is shown in (Vinogradova et al, 2008;Kochetova et al, 2009;Shor et al, 2012) and, therefore, exhibit a large spread. Shor et al (2012) analyzed the results of the latest refinements of Apo phis' orbit based on the most complete set of observa tional data. The possible trajectories of Apophis have become somewhat closer to the gravitational keyhole leading to a collision in 2036, but, due to the reduced size of the path tube, the probability of an impact is negligible.…”

“…Researchers should also consider the possibility of additional non gravitational accelerations, in particular, those relat ing to the Yarkovsky effect. If the most hazardous value of an additional nongravitational acceleration is selected within the possible range, the probability of a collision may be as high as 0.0022 (Shor et al, 2012). As noted in (Huebner et al, 2009), because the poten tial consequences of a collision with a hazardous object are global, speaking about its low probability is irrelevant.…”

“…Currently, the condi tions for observations of Apophis are unfavorable (Chesley, 2006;Harris, 2006). The accuracy of its orbit is analyzed, in particular, in the works of Russian authors (Yagudin and Shor, 2005, Vinogradova et al, 2008Kochetova et al, 2009;Shor et al, 2012). The research on the possible strategies for deflecting the asteroid's orbit shows that deflection efforts may be effective only if they are made well in advance of the 2029 approach (see, e.g., Sokolov et al, 2008a).…”