**4.1 (99942) Apophis**

Table 8 lists orbital elements of (99942) Apophis performed using all observations available to 1st Oct., 2011. There were 1481 optical observations (of which 8 were rejected as outliers), and also seven radar data points on 2005/01/27, 2005/01/29, 2005/01/31 and 2005/08/07. The orbit was computed by the author using the OrbFit software v. 4.2. The JPL NASA Ephemerides DE405 and additional perturbations from massive asteroids: (1) Ceres, (2) Pallas, (3) Juno, (4) Vesta and (10) Hygiea were used.


Table 8. (99942) Apophis: orbital elements together with theirs 1- variations. 1488 observations from 2555 days (2004/03/15.10789 – 2011/03/14.12528 ), *rms*=0.389". Nominal orbit: epoch 2011 Aug. 27.0.

Actually, both the Yarkovsky/YORP effect, which are part of a set of other astrodynamical effects that were taken summary only into account to prepare the present analysis, but that seems to be of significant influence in the orbital evolution of such objects. The preliminary results are in Table 9. The Yarkovsky and YORP (Yarkovsky-O'Keefe-Radzievskii-Paddack) effects are thermal radiation forces and torques that cause a drift of semimajor axes (computed value of **da/dt** in present work) of small asteroids and meteoroids and a change their spin vectors (obliquities). Because the Yarkovsky force depends on the obliquity, we can expect a complicated interplay between the Yarkovsky and YORP effects . Therefore it is difficult to estimate the influence of the Yarkovsky and YORP effects on the motion of asteroids separately. The result of the Yarkovsky effect is removal of small asteroids from the main belt to chaotic mean motion and secular apsidal or nodal resonance zones. Then they can be gradually transported to Earth-crossing orbits. Therefore the Yarkovsky and YORP effects are now considered in relation to objects crossing the Earth orbit, particularly they are important in the motion of potentially dangerous asteroids for the Earth.

The NEODyS presents only impact solutions based on 1399 optical observations (of which 5 are rejected as outliers) from 2004/03/15.127 to 2008/01/09.666 and also on seven radar data points on 2005/01/27, 2005/01/29, 2005/01/31, 2005/08/07 and 2006/05/06. The NEODyS lists possible impact in 2036, 2056, 2068 – two solutions, 2076 and in 2103. Their solutions are based on Monte Carlo method, including a probabilistic model of the Yarkovsky effect. In this way impact solutions are model dependent. Without any nongravitational perturbation model they found possible impact in 2068/04/12.632 with the probability of about 3.81 10-6. Similar impact solutions are from the JPL NASA.

Using all 1490 observations of Apophis and the OrbFit software I computed value of the semimajor axis drift of Apophis equal to **da/dt**=+180 10-4 AU/Myr connected with the Yarkovsky/YORP effects and got following impact solutions as are presented in Table 9. Additional perturbations from (1) Ceres, (2) Pallas and (4) Vesta are included.


Table 9. (99942) Apophis. Impact solutions with the Earth using semimajor axis drif, **da/dt**= =+180 10-4 AU/Myr, computed by the author. Similar value of **da/dt**= (235+/-50) 10-4 AU/Myr has computed Grzegorz Sitarski (private information).

To compute impact solutions of Apophis we must know exact uncertainty from the Yarkovsky effects and physical parameter uncertainties of Apophis together with the astrometric biases and radiation pressure (Giorgini et al. 2007).
