The effect of parallax and cadence on asteroid impact probabilities and warning times

Abstract

We study the time evolution of the impact probability for synthetic but realistic impacting and close approaching asteroids detected in a simulated all-sky survey. We use the impact probability to calculate the impact warning time as the time interval between when an object reaches a Palermo Scale value of -2 and when it impacts Earth. A simple argument shows that warning time ~ D^x with the exponent in the range [1.0,1.5] and our derived value was $x=1.3\pm0.1$. The low-precision astrometry from the single simulated all-sky survey could require many days or weeks to establish an imminent impact for asteroids >100m diameter that are discovered far from Earth. Most close approaching asteroids are quickly identified as not being impactors but a size-dependent percentage, even for those >50m diameter, have a persistent impact probability of >10^{-6} on the day of closest approach. Thus, a single all-sky survey can be of tremendous value in identifying Earth impacting and close approaching asteroids in advance of their closest approach but it can not solve the problem on its own: high-precision astrometry from other optical or radar systems is necessary to rapidly establish an object as an impactor or close approacher. We show that the parallax afforded by surveying the sky from two sites is only of benefit for a small fraction of the smallest objects detected within a couple days before impact: probably not enough to justify the increased operating costs of a 2-site survey. Finally, the survey cadence within a fixed time span is relatively unimportant to the impact probability calculation. We tested three different reasonable cadences and found that one provided ~10x higher (better) value for the impact probability on the discovery night for the smallest (10m diameter) objects but the consequences on the overall impact probability calculation is negligible.