Predicting the Apophis Earth Encounters of 2029 and 2036
Giorgini, J.D.¹; Benner, L.A.M.¹; Ostro, S.J.¹; Nolan, M.C.²; Busch, M.W.^3
1Jet Propulsion Laboratory/California Institute of Technology; ²Arecibo Observatory; ³California Institute of Technology

Apophis was detected by the Arecibo radar at distances of 27 and 40 million km (0.192-0.268 AU) in 2005 and 2006 [1]. Incorporating radar astrometry in a new orbit solution reduced by 98% the uncertainty in Apophis' predicted location in 2029, when it will encounter the Earth at a minimum geocentric distance within the interval [5.62, 6.30] Earth-radii, a historically close encounter for an object so large (d ≤ 270 m). Passage through Earth's gravity field during this encounter will amplify prediction errors caused by forces not included in the standard dynamical model (SDM) normally used to estimate and predict small-body motion. The magnitude of these forces depends on as-yet unmeasured parameters. We find that solar energy could cause between 20 and 740 km of position change over the next 20 years leading into the 2029 Earth encounter. Seven years later, the effect on Apophis' predicted position can grow to between 520,000 and 30 million km (0.0035-0.2 AU). This range makes it difficult to predict if Apophis will have a close encounter with Earth in 2036 when the trajectories intersect and the SDM shows a small impact probability. Small uncertainties in the masses and positions of the planets and Sun can cause up to 23 Earth-radii of prediction error for Apophis by 2036. The SDM treatment of Earth as a point-mass can introduce up to 2.9 Earth-radii of prediction error by 2036; the Earth's oblateness must be considered to predict an impact. The gravity of other asteroids can cause up to 2.3 Earth-radii of prediction uncertainty for Apophis. By considering the possible range of Apophis' physical characteristics and these error sources, it was determined what new observations prior to 2029 will most effectively reduce prediction uncertainties. Apophis will be too close to the Sun for measurement by optical telescopes until 2010-2011, and too distant for useful radar measurement until 2013. Thereafter, the largest of these errors sources may be directly detectable as trajectory offsets from the SDM prediction. Observing criteria were developed that, if satisfied, could permit eliminating the 2036 impact possibility without further physical characterization of Apophis. Depending on their magnitude, such physical factors will affect trajectory prediction, hazard assessment, and mitigation feasibility not only for Apophis' potential encounter with Earth in 2036, but for a growing number of objects, as new surveys increase the rate of discovery.


[1] Giorgini JD, Benner LAM, Ostro SJ, Nolan MC, Busch MW, Predicting the Earth encounters of (99942) Apophis, Icarus 193 (2008), pp. 1-19.