Nonlinear impact monitoring: line of variation searches for impactors

Abstract

When a new Near Earth Asteroid is discovered, it is important to know whether or not there is the possibility of an impact with the Earth in the near future. In this paper, we describe the technical approaches employed by the two operational second-generation asteroid impact monitoring systems, CLOMON2 and Sentry, paying particular attention to the similarities and differences between these independent systems. The detection and characterization of a potential impact requires the propagation of the orbital probability density function from the time of discovery to the time of hypothetical impact. Since the N-body problem is not integrable, this can be done only by sampling the orbital elements space with a finite number of Virtual Asteroids (VAs), the orbit of each one being propagated numerically. Our methods, illustrated in this paper, use the Line Of Variation (LOV), a unidimensional subspace, to perform this sampling. The primary goal is to detect Virtual Impactors (VIs), which are regions in the initial conditions space leading to dynamically distinct collision solutions; then a probability integral needs to be computed on the volume of the VI. An important issue is how to assure completeness of such a search down to some impact probability threshold. This problem cannot be efficiently solved just by computing more VAs, but requires Email addresses: milani@dm.unipi.it (Andrea Milani), steve.chesley@jpl.nasa.gov (Steven R. Chesley), genny@pisces.eis.uva.es (Maria Eugenia Sansaturio), tommei@mail.dm.unipi.it (Giacomo Tommei), giovanni@rm.iasf.cnr.it (Giovanni B. Valsecchi). a geometric description of the behavior of the LOV in order to identify the critical segments of this curve. We have studied these behaviors on the Target Plane (TP) through our analytical theory and the output of many numerical tests. Assuming that the geometry is the simplest compatible with the data available from the sampling, we obtain a classification which allows us to use iterative methods, appropriate for each case, to find the closest approach distance possible along the LOV. After an LOV minimum has been identified, it is possible to use a probability density linearized at this point. However, when the cross section of the Earth is not crossed by the LOV, there is no guarantee that nonlinearity would be negligible in the direction on the TP transversal to the LOV. We describe how to test for such nonlinearity, and thus reduce or eliminate the possibility of spurious VIs. In this way, the performance of our impact monitoring systems has been significantly increased in comparison to the earlier and simpler solitary system. These more advanced systems have identified and then eliminated (through additional observations) more than one hundred cases of asteroids with VIs in the years 2002-2003.

The Pan-STARRS Synthetic Solar System Model: A Tool for Testing and Efficiency Determination of the Moving Object Processing System

“…One must also be able to rapidly recognize the object as a threat, in order to ensure adequate tracking and, in the event that an impact is confirmed, sufficient time for a suitable mitigation effort. To this end, after the discovery of a new Earth-crossing asteroid, the trajectory and associated uncertainty region of the object are routinely searched for future possibilities of impact (Milani et al 2005).…”

New methods for space debris collision assessment

“…Filter I Thanks to the ephemeris interpolation table, for each piece of space debris, it is possible to compute its geocentric distance r(t) and its time derivative˙ r(t) at any time t. We are interested in computing the maximum and minimum of this distance, which is equivalent to find the values where the derivative function˙ r(t) is equal to zero. This problem is solved by using a 'regula-falsi' algorithm similar to the one used in Milani et al (2005). So, given a pair of objects of index s 1 , s 2 , we compute the maximum and minimum values of their geocentric distances, named max(r sj ) and min(r sj ), for j = 1, 2.…”

Nonlinear impact monitoring: 2-dimensional sampling

“…In this way it is possible to interpolate between two consecutive VAs to prove the existence of a closest approach around a given encounter date. Using iterative algorithms it is possible to find the minimum approach distance and eventually a Virtual Impactor (VI) (Milani et al (2004b)). …”

“…Thus a corrective step was introduced, based upon differential corrections constrained on the hyperplane perpendicular to the weak direction. Milani et al (2004c) have formulated a new definition which does not require the presence of a nominal solution. The LOV, in fact, is defined as a set of points in which the gradient of the cost function is in the weak direction.…”