Completeness of Impact Monitoring

TL;DR

This paper enhances impact monitoring by improving sampling methods in the LOV, significantly increasing the system's completeness while managing computational costs, and analyzing the distribution of virtual impactors.

Contribution

It introduces a novel LOV sampling approach with variable step-size and extended interval, improving impact detection completeness and providing empirical and analytical insights into impactor distribution.

Findings

Completeness limit IP* decreased by a factor of ~4.

Detection of virtual impactors follows a power-law proportional to IP^{-2/3}.

Power-law related to impactor accumulation over time.

Abstract

The completeness limit is a key quantity to measure the reliability of an impact monitoring system. It is the impact probability threshold above which every virtual impactor has to be detected. A goal of this paper is to increase the completeness without increasing the computational load. We propose a new method to sample the Line Of Variations (LOV) with respect to the previously one used in NEODyS. The step-size of the sampling is not uniform in the LOV parameter, since the probability of each LOV segment between consecutive points is kept constant. Moreover, the sampling interval has been extended to the larger interval [-5,5] in the LOV parameter and a new decomposition scheme in sub-returns is provided to deal with the problem of duplicated points in the same return. The impact monitoring system CLOMON-2 has been upgraded with all these features, resulting in a decrease of the generic completeness limit IP* by a factor $\simeq 4$ and in an increase of the computational load by a factor $\simeq 2$. Moreover, we statistically investigate the completeness actually reached by the system with two different methods: a direct comparison with the results of the independent system Sentry at JPL and an empirical power-law to model the number of virtual impactors as a function of the impact probability. We found empirically that the number of detected virtual impactors with $IP>IP^*$ appears to grow according to a power-law, proportional to $IP^{-2/3}$. An analytical model explaining this power-law is currently an open problem, but we think it is related to the way the number of virtual impactors within a time $t_{rel}$ from the first observed close approach accumulates, for which we prove the existence of a power-law proportional to $t_{rel}^3$. The power-law allows us to detect a loss of efficiency in the virtual impactors search for impact probabilities near the generic completeness limit.