Abstract
We present an approach to estimate an upper bound for the impact probability of a potentially hazardous asteroid when part of the force model depends on unknown parameters whose statistical distribution needs to be assumed. As case study, we consider Apophis’ risk assessment for the 2036 and 2068 keyholes based on information available as of 2013. Within the framework of epistemic uncertainties, under the independence and non-correlation assumption, we assign parametric families of distributions to the physical properties of Apophis that define the Yarkovsky perturbation and in turn the future orbital evolution of the asteroid. We find {mathrm{IP}}le 5times 10^{-5} for the 2036 keyhole and {mathrm{IP}}le 1.6times 10^{-5} for the 2068 keyhole. These upper bounds are largely conservative choices due to the rather wide range of statistical distributions that we explored.
Highlights
In risk analysis, uncertainties are generally classified into two categories: aleatory and epistemic
For each keyhole, we compute a reference impact probability corresponding to fixed distributions derived by the ones used in Farnocchia et al (2013a)
The distributions associated with the reference and to the maximum impact probability for the 2036 and 2068 keyholes are displayed
Summary
Uncertainties are generally classified into two categories: aleatory and epistemic. Tardioli and Vasile (2016) have presented an approach to the design of optimal collision avoidance and reentry maneuvers under uncertainty. They considered a dynamical model with six aleatory variables (the three components of the position and velocity vectors of the spacecraft) and four epistemic variables (some model parameters). In this paper, we use a parametric distribution approach to include epistemic uncertainties in the estimation of impact probabilities for potentially hazardous asteroids. Further observations reduced Apophis’ orbital uncertainty and ruled out any impact possibility for 2029, the asteroid remains an interesting object worth investigating. For some near-Earth asteroids, the orbital drift associated with the Yarkovsky effect can be measured from the orbital fit to the observations (Farnocchia et al 2013b). That was the case of Apophis as analyzed by Farnocchia et al (2013a), which we revisit within the epistemic uncertainty framework in this paper
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