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

Abstract: 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.

• The paper quantifies the impact of small asteroid collisions on Apophis’ trajectory using detailed dynamical models.
• It finds that a 0.3 mm/s velocity change shifts Apophis by about 200 km while a 5 cm/s change could trigger an Earth collision, both with extremely low probabilities.
• The study emphasizes the need for enhanced observational strategies post-2027 to promptly detect any significant trajectory perturbations.

On the Sensitivity of Apophis' 2029 Earth Approach to Small Asteroid Impacts

In the research article "On the Sensitivity of Apophis' 2029 Earth Approach to Small Asteroid Impacts," Paul Wiegert explores the potential effects of a small asteroid impact on the trajectory of the near-Earth asteroid 99942 Apophis. This study is crucial due to Apophis' projected close approach to Earth on April 13, 2029, at a distance of several Earth radii, which, while safe, raises concerns about unforeseen perturbations, such as those induced by an impact with a small asteroid.

The paper meticulously evaluates the likelihood and potential consequences of such a collision, focusing on two primary objectives:

1. Probability and Impact of Small Asteroid Collisions: The analysis concludes that the probability of an impact significant enough to displace Apophis into an Earth-threatening trajectory is exceedingly low. Specifically, the chance of an impact causing a notable deflection relative to its gravitational keyholes is estimated to be less than 1 in 10⁶. For an impact leading to a deviation compared to the miss distance in 2029, the probability is even lower, at less than 1 in 10⁹. This probability is well below the usual thresholds that trigger alerts in asteroid impact warning systems.
2. On-Sky Observations and Detection: The work stresses the challenges associated with detecting trajectory changes in Apophis due to its absence in the observable segment of the sky from mid-2021 until 2027. Single observations around 2027 may not be adequate to determine significant trajectory deviations unless they are substantial. However, notable deviations from its nominal path would manifest as positional shifts by tens of arcseconds in 2027, providing a critical detection mechanism for any significant impact-related deflection.

A significant part of the analysis involves models simulating impulsive velocity changes due to hypothetical asteroid impacts. The study estimates that an impact causing a 0.3 mm/s velocity change could shift Apophis by about 200 km on its target plane—a displacement associated with keyhole entry risks. A more pronounced velocity change of 5 cm/s could place Apophis on an Earth-colliding trajectory. Both scenarios, while possible, require very specific and unlikely conditions in terms of impact timing and direction.

Practical and Theoretical Implications:

• Astrodynamics and Risk Assessment: The research enhances our understanding of asteroid dynamics and provides valuable data for risk assessment regarding Apophis and similar near-Earth objects. It stresses the importance of continuous monitoring and the potential need for rapid response systems as Apophis re-enters the observable sky.
• Future Research and Observation Strategies: The study suggests the adoption of advanced observational strategies to detect any deviations in Apophis' trajectory upon its reappearance in 2027. These strategies will ensure any risks are mitigated well before its closest approach in 2029.

This investigation signifies a critical effort to prepare for potential atypical scenarios that, although statistically improbable, could have substantial implications. The detailed modeling and probabilistic assessments provide a framework for understanding and mitigating risks associated with the future paths of near-Earth objects.