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We study the time evolution of the impact probability for synthetic butrealistic impacting and close approaching asteroids detected in a simulatedall-sky survey. We use the impact probability to calculate the impact warningtime as the time interval between when an object reaches a Palermo Scale valueof -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-skysurvey could require many days or weeks to establish an imminent impact forasteroids >100m diameter that are discovered far from Earth. Most closeapproaching asteroids are quickly identified as not being impactors but asize-dependent percentage, even for those >50m diameter, have a persistentimpact probability of >10^{-6} on the day of closest approach. Thus, a singleall-sky survey can be of tremendous value in identifying Earth impacting andclose approaching asteroids in advance of their closest approach but it can notsolve the problem on its own: high-precision astrometry from other optical orradar systems is necessary to rapidly establish an object as an impactor orclose approacher. We show that the parallax afforded by surveying the sky fromtwo sites is only of benefit for a small fraction of the smallest objectsdetected within a couple days before impact: probably not enough to justify theincreased operating costs of a 2-site survey. Finally, the survey cadencewithin a fixed time span is relatively unimportant to the impact probabilitycalculation. We tested three different reasonable cadences and found that oneprovided ~10x higher (better) value for the impact probability on the discoverynight for the smallest (10m diameter) objects but the consequences on theoverall impact probability calculation is negligible.

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