On the sensitivity of Apophis' 2029 Earth approach to small asteroid impacts

Apophis' current trajectory takes it safely past our planet at a distance of several Earth radii on 2029 April 13. Here the possibility is considered that Apophis could collide with a small asteroid, like the ones that frequently and unpredictably strike Earth, and the resulting perturbation of its trajectory. The probability of an impact that could significantly displace Apophis relative to its keyholes is found to be less than 1 in $10^6$, requiring a delta-v greater than 0.3 mm/s, while for an impact that could significantly displace Apophis compared to its miss distance in 2029 it is less than 1 in $10^9$, requiring a delta-v greater than 5 cm/s. These probabilities are below the usual thresholds considered by asteroid impact warning systems. Apophis is in the daytime sky and unobservable from mid-2021 to 2027. It will be challenging to determine from single night observations in 2027 if Apophis has moved on the target plane enough to enter a dangerous keyhole, as the deviation from the nominal ephemeris might be only a few tenths of an arcsecond. An impending Earth impact would, however, be signalled clearly in most cases by deviations of tens of arcseconds of Apophis from its nominal ephemeris in 2027. Thus most of the impact risk could be retired by a single observation of Apophis in 2027, though a minority of cases present some ambiguity and are discussed in more detail. Charts of the on-sky position of Apophis under different scenarios are presented for quick assessment by observers.