A NEW WAY OF THINKING ABOUT IMPACT MONITORING OF NEAR-EARTHOBJECTS

G. Tommei

Department of Mathematics, University of Pisa, Pisa, Italy, Email: giacomo.tommei@unipi.it

ABSTRACT

An asteroid just been discovered has a strongly undeter-mined orbit, being weakly constrained by the few avail-able astrometric observations, and there is a set of possi-ble orbits, all compatible with the observations, forminga Confidence Region (CR) in the 6-dimensional orbitalelements space. The goal of Impact Monitoring (IM) isto understand whether the CR contains subsets of initialconditions leading to a collision with the Earth in the fu-ture (Virtual Impactors, VIs) and to estimate the ImpactProbability (IP). Once defined the CR, the crucial stepsare the sampling of the uncertainty region, the propaga-tion of the so called Virtual Asteroids (VAs) searchingfor VIs and the computation of IP. Two automatic sys-tems, CLOMON2 (at University of Pisa/SpaceDyS/ESA-NEOCC) and Sentry (at JPL/NASA), have been devel-oped for this purpose. Both generate VAs by applying a1-dimensional sampling of the CR based upon the LineOf Variations (LOV), that is a differentiable curve rep-resenting a kind of spine of the uncertainty region. TheLOV method is very useful when the CR is elongated andthin, but this is not the case when the observed arc is veryshort: the uncertainty results to be wide in at least twodirections and the LOV is not a reliable representativeof the entire region. Unfortunately, this is precisely thecase of very small asteroids observed only shortly beforea close approach or an impact with the Earth (imminentimpactors). The problem has been faced recently andthree systems were developed, SCOUT (at JPL/NASA),NEORANGER (at University of Helsinki) and NEOScan(at University of Pisa/SpaceDyS): we will focus on thelatter. NEOScan consults the NEO Confirmation Page(NEOCP) of the Minor Planet Center (MPC) every twominutes, extracting data and running the algorithms basedon the Admissible Region (AR), a tool widely used alsoin the space debris orbit determination. Once an objectgoes away from the NEOCP obtaining a designation, theIM systems switch to “classical” 1-d algorithms. In thisprocedure, essentially dictated by the rules of the MPC,there is a flaw, in the sense that there are objects, witha very well-defined orbit, remaining on the NEOCP, and,on the contrary, there exist designated objects with a greatuncertainty. Thus, there are a certain number of cases thatare not properly processed. In this paper, after a reviewof the IM algorithms developed at the University of Pisa,

we will present the idea of a new automatic system capa-ble, starting from the astrometric observations, to decidewhat is the right algorithm in order to reach reasonableresults for each kind of orbit.

Keywords: Near-Earth Objects; Impact Monitoring; Im-minent Impactors; Astrometry; Line Of Variation; Mani-fold Of Variation.

1. INTRODUCTION

Every night professional and amateur astronomers ob-serve the sky searching for new natural objects (asteroids,comets) or already discovered objects. The observationscollected are sent to the Minor Planet Center (MPC),that, under the auspices of the International AstronomicalUnion (IAU), computes orbits and try to define the type ofobject. New discoveries that could be NEAs (Near-EarthAsteroids) are posted by the MPC on the NEO confirma-tion page (NEOCP, [6]). Once additional observations arecollected and an orbit calculated, the object is added tothe catalog of known objects, and such data are releasedthrough a Minor Planet Electronic Circular (MPEC). Thediscovery of a NEA is a process requiring the distinctionbetween known and unknown objects, and then follow-ing up (obtaining additional observations) any unknowntargets with the aim of extending the arc of observationsand determining the orbit ([20]). Once an asteroid is dis-covered, it is important to clarify if it represents a riskfor the Earth in a near or remote future: this is the goalof Impact Monitoring (IM), a relative young field of re-search. Since a significant amount of new observationsare submitted every day, this activity requires an auto-matic system scanning continually the NEA catalog. Thisrequirement has been achieved by CLOMON2 and Sen-try, two independent IM systems that are operational atthe University of Pisa/SpaceDyS/NEOCC (since 1999)and at NASA Jet Propulsion Laboratory (since 2002), re-spectively. During the time span over which observationsare collected, CLOMON2 and Sentry outcomes ([9]),eventually with the announcement that some asteroid hasthe possibility of impacting, are published on the web:CLOMON2 results are published in the on-line infor-mation system NEODyS (newton.spacedys.con/neodys)and in the ESA portal (neo.ssa.esa.int), while Sentry re-

Proc. 1st NEO and Debris Detection Conference, Darmstadt, Germany, 22-24 January 2019, published by the ESA Space Safety Programme Office

Ed. T. Flohrer, R. Jehn, F. Schmitz (http://neo-sst-conference.sdo.esoc.esa.int, January 2019)

sults are available at CNEOS (cneos.jpl.nasa.gov/sentry).These two systems, whose output is carefully compared,now guarantee that the potentially dangerous objects areidentified very early and followed up. The input datacomes from the MPEC, thus an object is processed onceis a confirmed NEO. Unfortunately there is the possi-bility that a small object discovered and listed on theNEOCP would strike the Earth in a near future. Theseobjects are called imminent impactors and deserve a dif-ferent treatment. For this reason, new mathematical algo-rithms and three automatic systems were developed re-cently, SCOUT (at JPL/NASA, [4]), NEORANGER (atUniversity of Helsinki, [13]) and NEOScan (at Univer-sity of Pisa/SpaceDyS, [14]).

In this paper, after a brief review of IM tools and tech-niques (Section 2), we will focus on the problem of immi-nent impactors describing the algorithms implemented inNEOScan and showing how it worked in a real case (Sec-tion 3). In Section 4 we will explore some possible futuredevelopments and the idea of building an unique auto-matic system capable of treat both imminent impactorsand classical IM cases.

2. IMPACT MONITORING OVERVIEW

Impact Monitoring (IM) is the set of mathematical toolsand techniques used to study the possibility of impact ofan asteroid/comet with our planet. The output of an IMalgorithm is a Virtual Impactor (VI) representative, thatis an explicit set of initial conditions compatible with ob-servations and leading to a collision at a given date. Themain goal of IM is to solicit astrometric follow-up to ei-ther confirm or more likely dismiss the announced riskcases: this is achieved by communicating the impact date,the impact probability and the estimated impact energy.The steps of an IM procedure are the following.

1. Acquisition of astrometrical data. The observa-tional data are acquired through the MPEC or scan-ning the NEOCP.

2. Orbit Determination (OD). Starting from the as-trometry, it is possible to compute a preliminaryorbit, using for example classical methods like theGauss’ one ([11]). Then a weighted Least Squares(LS) method has to be performed searching for aminimum x∗ of the target function

Q(x) =1

mξ(x)TW ξ(x)

where ξ = (ξi), i = 1, . . . ,m is the vector of as-trometrical residuals (depending on the orbital pa-rameters x) and W is a square, symmetric, positive-definite m × m matrix reflecting the a priori RMSand correlations of the observation errors.

If such minumum x∗ does exist, we can expand the

target function in a neighborhood of x∗:

Q(x∗) = Q(x∗) +1

m(∆x)T C (∆x) + . . .

= Q(x∗) + ∆Q(x) ,

where C = BT W B si the normal matrix and itsinverse is the covariance matrix Γ = C−1. A Con-fidence Region (CR) Z(χ) is defined by setting anupper limit to the penalty ∆Q:

Z(χ) ={X | ∆Q(X) ≤ χ2/m

}.

If the CR and the residuals are small, then all thehigher order terms in the target function are negligi-ble and the confidence region is well approximatedby the confidence ellipsoid ZL(χ) defined by thequadratic inequality

ZL(χ) ={x : ∆xT C(x∗) ∆x ≤ χ2

}.

This geometrical object is just used for local com-putations because the hypothesis on the smallnessof the residuals is not applicable in general.However the previous algorithms could fail, when,for example, we have to process a Very Short Arc(VSA), that is a sequence of typically 3 to 5 obser-vations with one hour between the first and the lastobservation. In most of these cases the arc is tooshort for a full orbit determination (computation ofa LS orbit). When this is the case, the set of obser-vations is called a Too Short Arc (TSA). As it is wellknown from the theory of preliminary orbit determi-nation, when three observations are used to computean orbit, the curvature of the arc appears as a divisorin the orbit solution of Gauss’ method. The smalleris the curvature, the less accurate is the orbit; takinginto account the observational errors, in most casesit turns out to be impossible to apply the usual al-gorithm, consisting of a preliminary orbit determi-nation by means of Gauss’ method followed by adifferential correction to obtain a LS orbit. Whenstarting from a TSA, either Gauss’ method fails orthe differential correction procedure does not con-verge. For this reason the TSAs are not considereddiscoveries, but just detections. This does not in-dicate that the observed object is fictitious, but justthat its nature cannot be determined with the infor-mation available, that is not possible to discriminateamong different classes of object. In [7], the authorsfaced the problem created by the existence of largedatabases of TSAs proposing a solution with the in-troduction of the concept of attributable. A TSA isrecorded as a set of N observations, which meansthat a set of points on a straight line is what is actu-ally detected, with deviations from alignment com-patible with the random observational error. Thuswe can compute the straight line, using a linear re-gression or something similar. Then a TSA is repre-sented by an attributable, defined in this way:

Definition 1. We call attributable a vector

A = (α, δ, α, δ) ∈ [−π, π)× (−π/2, π/2)× R2,

representing the angular position and velocity of thebody at a time t in the selected reference frame.

The attributable could also contain an average ap-parent magnitude h, if there is at least one measure-ment of the apparent magnitude available. Note thatthe information contained in an attributable leavesunknown the topocentric distance ρ (the range) andthe radial velocity ρ (the range rate) of the objectat the reference epoch. If ρ and ρ were known,we would have a full description of the asteroid’stopocentric position and velocity in polar coordi-nates (α, δ, α, δ, ρ, ρ), called also attributable ele-ments, which can be easily converted to a Cartesianheliocentric state if the position and velocity of theobserver are known.Given an attributable A, we define the followingconditions on ρ and ρ:

(a) D1 = { (ρ, ρ) : E⊕ ≥ 0 } (A is not a satelliteof the Earth);

(b) D2 = { (ρ, ρ) : ρ ≥ RSI } (the orbit of A isnot controlled by the Earth);

(c) D3 = { (ρ, ρ) : E� ≤ 0 } (A belongs to theSolar System);

(d) D4 = { (ρ, ρ) : ρ ≥ R⊕ } (A is outside theEarth).

Definition 2. Given an attributable A, we define asAdmissible Region (AR) the domain

D = { D1 ∪ D2 } ∩ D3 ∩ D4.

The AR is a compact set, being the inside of a finitenumber of closed continuous curves, and it can haveat most two connected components (proof in [7]).Note that in setting the conditions (a)-(d) we haveintroduced the following assumptions:

– The observer is assumed to be at the geocenter.– The orbits of asteroids passing close to the

Earth are affected by both the attraction of theSun and that of the Earth; taking into accounta complete three-body model would be verycomplicated. Thus conditions (a) and (b) areapproximated, and indeed there are objects inheliocentric orbit experiencing temporary cap-ture as satellites of the Earth, with E⊕ < 0.However, this can happen only for very lowrelative velocities Earth-asteroid, and the ob-jects found in these conditions are often artifi-cial.

– When the object is much farther away from theEarth than the Moon, that is ρ >> 60R⊕, weshould use for µ⊕ the ratio between the massof the Earth-Moon system and the mass of theSun.

– In computing the radius of the sphere of influ-ence we are neglecting the eccentricity of theorbit of the Earth.

3. Sampling of the uncertainty region using aswarm of Virtual Asteroids (VAs). Once the ODprocedure is complete (either with a LS orbit anda CR or only with an AR) we would like to ex-plore the uncertainty region (that in both cases isdefined as a compact set) sampling it with a finiteset of orbits, called Virtual Asteroids (VAs). Buthow to select the VAs? There are essentially twoclasses of methods: random or Monte Carlo (MC)ones, and geometric sampling methods. The MCmethods use the probabilistic interpration ([11]) ofthe least squares principle, and, when the computa-tional resources are not a problem and the error mod-els are reliable, they are more rigorous and completewith respect to the geometrical methods. Currently,the operative IM systems use the Line Of Variations(LOV) to sample the CR when a LS orbit is avail-able. The LOV is a differentiable curve representingessentially the direction of greater uncertainty, thedefinition adopted ([8]) is the following.

Definition 3. The LOV is the set of points X suchthat

V1(x)||D(x)

where V1 is the unit eigenvector of the normal matrixC(x∗), computed at the nominal solution, relativeto the smallest eigenvalue and D = −BTWξ =

−m2∂Q∂x

T.

The equation V1(x)||D(x) corresponds to five scalarequations in six unknowns, thus it has generically asmooth one parameter set of solutions, i.e., a dif-ferentiable curve. However, we do know an an-alytic or anyway direct algorithm neither to com-pute the points of this curve nor to find some nat-ural parameterization (e.g., by the arclength). An al-gorithm to compute the LOV by continuation fromone of its points X is the following. The vector fieldF (x) = k1(x) V1(x), deduced from the weak di-rection vector field V1(x), is orthogonal to H(x).A step in the direction of F (x), such as an Eu-ler step of the solution of the differential equationdx/dσ = F (x), that is x′ = x + δσ F (x), is notproviding another point on the LOV, unless the LOVitself is a straight line; this would be true even ifthe step along the solutions of the differential equa-tion is done with a higher order numerical integra-tion method, such as a Runge-Kutta. However, x′will be close to another point x′′ on the LOV, whichcan be obtained by applying the constrained differ-ential corrections algorithm ([9]), starting from x′

and iterating until convergence.If x was parameterized as x(σ), we can parameter-ize x′′ = x(σ + δσ), which is an approximationsince the value σ+ δσ actually pertains to x′. As analternative, if we already know the nominal solutionx∗ and the corresponding local minimum value ofthe cost function Q(x∗), we can compute the χ pa-rameter as a function of the value of the cost functionat x′′:

χ =√m · [Q(x′′)−Q(x∗)] .

In the linear regime, the two definitions are relatedby σ = ±χ, but this is by no means the case instrongly nonlinear conditions. Thus we can adoptthe definition σQ = ±χ, where the sign is taken tobe the same as that of σ, for an alternate parameter-ization of the LOV.In the last year a new method to sample the LOVhas been implemented in CLOMON2 ([2], [3]) be-cause, considering that the probability density on theLOV is p(σ) := 1√

2πe−

σ2

2 , the uniform step in σadopted in the LOV sampling is not optimal; in fact,the probability of each sampling interval would behigh around σ = 0, whereas it becomes too lownear the LOV endpoints. Therefore a better choicewould be to use a step-size that is inversely propor-tional to the probability density, small in the pointsaround the nominal solution, and larger towards thepoints with lower probability. This new samplingprocedure is such that the probability of the inter-val among two consecutive points of the samplingis constant. This means that if σi,i=1,...,N are thesampling nodes, then

P([σi, σi+1]) :=

∫ σi+1

σi

p(σ) dσ

does not depend on i. Moreover, to avoid too longintervals around the LOV endpoints, when the in-terval length exceeds a certain threshold ∆σmax thestep-size is set as uniform to this threshold value;this choice is necessary because if the step-size be-came too large, the last sampling node could fall af-ter the sampling interval endpoints, loosing a portionof the LOV of about the same length of the last step-size.The LOV method is very useful when the CR iselongated and thin, but this is not the case whenthe observed arc is very short (≤ 1◦). When theset of observations of an object covers only a veryshort arc, the confidence region results to be widein at least two directions and the LOV is not rep-resentative of the entire region: moreover its defini-tion strongly depends upon the coordinates and unitsused in the OD. In this case, both CLOMON2 andSentry do not perform very well and a 2-dimensionalmanifold should be used ([15]), as in the case of im-minent impactors that will be described in Section3.

4. Propagation of the VAs. Once a set of VAs havebeen selected, each orbit is propagated forward tosome time in the future, storing all the close ap-proach information obtained during the numericalintegration. CLOMON2 propagates VAs until 2100and maps the linearized uncertainties, representedby the confidence ellipsoids, for all the VAs to thetime of each close encounter, allowing an early andquick assessment of whether a potential close en-counter could be threatening. The first output ofthe propagation is a collection of Earth encountersthat have been detected for each VA during the time

span of interest. If the close encounters set is notempty, the systems perform a sorting of the encoun-ters by date, splitting them into sets that are clusteredin time, called showers; then, according to the VAsLOV index, they re-sort the showers into contigu-ous LOV segments, called trails (or returns). Eachclose approach is carefully analysed on the corre-sponding Target Plane (TP), that is a plane passingthrough the Earth’s center and orthogonal to the un-perturbed velocity of the asteroid, i.e., orthogonal tothe incoming asymptote of the hyperbola definingthe two-body approximation of the trajectory at thetime of closest approach ([19], [16]).

5. Analysis of close approach and detection of Vir-tual Impactors (VIs). When there are many pointson the TP in a given return it is easy to understandthe LOV behaviour because the linear theory is lo-cally applicable. On the contrary, in strong non-linear cases the LOV has strange behaviours ([15])and a local analysis is necessary in the neighborhoodof each VA. The key point is that the VAs are not justa set of points but they sample a smooth curve, al-lowing us to interpolate between consecutive samplepoints. For instance, let us suppose that two consec-utive VAs xi and xi+1 have TP trace points yi andyi+1 straddling the Earth impact cross section. If thegeometry of the TP trace is simple enough (princi-ple of simplest geometry), an interpolation methodprovides apoint on the LOV xi+δ with 0 < δ < 1and such that yi+δ is inside the Earth impact crosssection: then, around xi+δ there is a VI.

6. Computation of Impact Probability. If a VI hasbeen found, by computing the probability densityfunction with a suitable Gaussian approximationcentered at xi+δ , it is possible to estimate the proba-bility integral on the impact cross section: this is theimpact probability associated with the given VI.

3. IMMINENT IMPACTORS

Small asteroids are expected to strike the Earth every fewyears and, since such objects are likely to be observedonly shortly before the impact, it is important to succeedin an early recognition of hazardous objects. When anobject is first observed, the available data are so few thatthe differential corrections procedure of finding a least-squares orbit could fail and thus they could not permitthe determination of a well-constrained six-parameter or-bit. Therefore, the short arc OD is a crucial issue and thetiming is essential because we are interested in a rapidfollow up of the object, to investigate whether could be ornot an imminent impactor. Three automatic systems weredeveloped recently, SCOUT (at JPL/NASA, [4]), NEOR-ANGER (at University of Helsinki, [13]) and NEOScan(at University of Pisa/SpaceDyS, [14]). We will focus onthe last one.

NEOScan consults the NEOCP of the MPC every twominutes, extracting data and running the algorithms based

on the AR (see previous sections), a tool widely used alsoin the space debris orbit determination ([18]). In par-ticular, the OD algorithm implemented in NEOScan hastwo choices: it explores a suitable grid in the topocen-tric range and range-rate space, producing a set of at-tributable elements, or uses a cobweb sampling of theconfidence region to obtain a set of VAs (if a least squareorbit does exist). The combination of this two techniquesprovides a robust short term orbit determination method,which ends with the computation of the Manifold OfVariations (MOV, [17]), a 2-dimensional compact man-ifold parameterized over the AR. The MOV representsthe 2-dimensional analogue of the LOV, thus it is used tosample the set of possible orbits as a starting point for theshort term impact monitoring. The goal of NEOScan isto detect all the possible VIs down to a probability levelof about 10−3, called completeness level ([3]): the choiceof 10−3 has been done because we are not interested inlower probability values, given that it is fundamental toavoid unjustified alarms.

Summarizing the algorithm, the steps are the following.

• Scanning of the NEOCP. The scan is every twominutes: new and old cases just updated are imme-diately run, to be confirmed or discarded.

• Computation and sampling of the AR. The algo-rithm provides a two-dimensional representation inthe (ρ, ρ) plane with either a cobweb, if a reliablenominal solution is available, or a double-iterationgrid if not. A reliable nominal solution is a nominalorbit (i.e., obtained by full differential corrections)with a geodesic curvature signal-to-noise ratio (S/N)χgeod greater than 3.

• Computation of the MOV and generation of a setof VAs. Given a subset K of the AR, we definethe MOV M as the set of the points (A∗(ρ0),ρ0)in the orbital elements space such that ρ0 ∈ Kand A∗(ρ0) is the local minimum of the functionQ|ρ=ρ0 ; in addition, the value of the RMS of theresiduals is less than a given treshold Σ. In general,the MOV is a two-dimensional manifold, such thatthe differential of the map from the sampling spacetoM has rank 2. In our case, K is the AR, scannedwith this first regular semi-logarithmic or uniformgrid. For each sample point ρ0 = (ρ0, ρ0) we fixρ = ρ0 and ρ = ρ0 in the target function, and thenwe search the local minimumA∗(ρ0) with the sameprocedure used for classical systematic ranging, thatis by means of the doubly constrained differentialcorrections. That procedure works in a similar wayas the classical differential correction process, tak-ing into account that two variables are fixed andso working with four-dimensional subspaces: Thus,the normal equation to solve is

CA∆A = DA,

where

CA = BTAWBA, DA = −BTAWξ, BA =∂ξ

∂A.

We indicate asK ′ the subset ofK on which the dou-bly constrained differential corrections converge; inthis way, the sampling of the MOV is performedover K ′. For each point x on the MOV, we alsocompute a χ value

χ(x) =√m(Q(x)−Q∗), (1)

where Q∗ is the minimum value of the target func-tion: Q(x∗) if a reliable nominal solution x∗ exists,or the minimum value of Q(x) over K ′ otherwise.

• Propagation and detection of VIs. The VAs orbitsare progated in the future, currently for 30 days, andan analysis on the Modified Target Plane (MTP) isperformed in order to find possible impacts. We se-lect as VIs the VAs that, on the MTP, are inside theimpact cross section D⊕.

• IP computation. If a VI has been found on theMTP, it is associated with an IP computed in thisway. We begin assuming that the residuals are aGaussian random variable ξ, with zero mean and co-variance Γξ = W−1. Hence the probability densityfunction on the residuals space is

pΞ(ξ) = N(0,Γξ)(ξ) =

√detW

(2π)m/2exp

(−mQ(ξ)

2

)=

√detW

(2π)m/2exp

(−1

2ξTWξ

).

(2)

The method consists in a rigorous propagation ofthe density function according to the probability the-ory without any a priori assumption. The Proba-bility Density Function (PDF) is propagated fromthe residual space to the orbital elements space (pre-cisely, on the MOV), and then to the sampling space,according to the Gaussian random variable transfor-mation law. The fundamental difference in usingthis approach instead of the uniform prior distribu-tion (as done in [4]) is that we compute the Jacobiandeterminant of the transformation and it is not equalto 1. Anyway, the results are similar because, as amatter of fact, the Jacobian determinant is always anumber near to unity. To compute the PDF on S(the space of the sampling variables), we start con-sidering the following chain of continuously differ-entiable maps

Sfσ−→ R+ × R ⊇ K ′ fµ−→ x ⊇M F |M−−−→ V.

where

– K ′ is the subset of the points of the AR suchthat the doubly constrained differential correc-tions give a point on the MOV,

– M is the MOV,– V = F (x) is the manifold of the possible

residuals, which is a six-dimensional subman-ifold of Rm,

and we consider the product of the Jacobian deter-minants. Using the maps fµ and fσ , the VI is asso-ciated with a subset V ⊆ S of the sampling space,and hence its probability is given by

P(V) =

∫VpS(s) ds =

∫V exp

(−χ

2(s)2

)detMµ(ρ(s)) detMσ(ρ(s)) ds∫

f−1σ (K′)

exp(−χ

2(s)2

)detMµ(ρ(s)) detMσ(ρ(s)) ds

If for a given object we find impacting solutions, weassign to the object an impact flag, which is an inte-ger number related to the computation of the impactprobability ranging from 0 to 4 and depending on IPand geodetic curvature (see [14] for more details).

• Computation of object-category score. Each cat-egory of objects (NEO, MBO, DO, SO), given byconditions on the orbital elements, corresponds to asubset V ⊆ S of the sampling space, and hence thesystem has the capability to compute the probabilityof the object to belong to each category making useof the previous formalism.

At the end, the scan is re-scheduled after 2 minutes. Thetime required to run one target strictly depends on thecharacteristics of the object, but usually it is between 15and 20 minutes. When predicting possible imminent im-pacts, one of the most important requirements to fulfill isto minimize the number of unjustified alarms. It is de-noted as nonsignificant case an object for which there areless than three observations or the arc length is less than30 minutes, unless there exists a nominal solution witha geodesic curvature S/N greater than 1. The classifica-tion of an object as nonsignificant does not mean that thecomputation is skipped; all the steps of the algorithm areperformed in any case and the score and the impact flagare assigned to the object. Nevertheless, being nonsignif-icant automatically decreases the priority of the object incase of an alarm. Unfortunately, these techniques are notenough to remove all the spurious cases, they only lowerthe number. In fact, spurious cases usually occur whenthe astrometry is either known to be erroneous or noisy, oranyway not reliable. We cannot solve this problem, andwe acknowledge that the astrometric error models basedon large number statistic are not sufficient to distinguisherroneous and accurate astrometry in a small sample.

3.1. The latest impactor: 2018LA

Last year NEOScan had the opportunity to be real timetested on a real case of an imminent impactor: the aster-oid 2018 LA. This object, known as ZLAF9B2 prior tobeing designated, was a small Apollo-type NEA that im-pacted Earth’s atmosphere at roughly 16:44 UTC (18:44local time) on 2 June 2018 over Botswana, near SouthAfrica border, at the altitude of about h = 50 km. Theasteroid produced an explosion with an intensity of about

1 kiloton, which suggests an estimated size for the aster-oid of 3 to 5 meters in diameter, and it was discoveredonly 8 hours prior the impact by Richard Kowalski at theMount Lemmon Survey. The object approached the Earthwith a relative velocity of approximately 17 km/s fromthe night side: due to its size and high entry velocity, itcould not have been spotted before it was very close to theEarth, and it could only be detected on its final plunge toEarth. Indeed, when it was first detected, the asteroid wasnearly as far away as the Moon’s orbit and appeared as astreak in the series of time-exposure images taken by theCatalina telescope.

The first observations data were immediately submittedto the MPC and published on the NEOCP. In the follow-ing hours additional observations were made and, accord-ing to the system results, as the number of the observa-tions was increasing, it became extremely probable thatthe object would have collided with the Earth.

During the follow up, 4 tracklets of observations wereobtained: the first one was of 3 observations, the sec-ond and the third of 11 and 12 observations, respectively,and the last of 14 observations. Table 1 shows the out-comes of the software while observations were flowingin. Table 1 shows how the IP increased as new observa-

# of observations Impact Probability3 0.08%

11 5.1%12 38.3%14 100%

Table 1. Number of observations and corresponding val-ues of IP, impact flag and the score.

tions were added. By using the last tracklet, consistingof 14 observations, the system estimated that the impactwould have certainly occurred (IP = 100%), and thus,according also to the arc quality, gave the impact flag themaximum value.

Table 2 displays additional information for each track-let: details upon the corresponding arcs and results of thesoftware by means of the number of grid and MOV pointsand, among them, the impacting points. We recall that κis the geodesic curvature and η is the along-track accel-eration, while Overall indicates their chi2-value χ2

c . Theitem Arc Type in Table 2 indicates an integer number Ndefined as follows. An observed arc is an Arc of Type N ifit can be split into exactly N disjoint TSAs in such a waythat each couple of TSAs consecutive in time, if joined,would show a significant curvature. The computation ofthe arc type value depends upon the method by whichthe observed arcs are to be split into TSAs; the values inTable 2 have been computed by using the algorithm dis-cussed in [10].

We now report the results obtained by NEOScan for eachone of these observed arcs, thus revealing how the aware-ness of an impacting object increased as the observationswere flowing in ([1]).

Significance of curvature

#Obs.

Timespan(h)

ArcType κ η Overall # of

pointsMOVpoints

Impactingpoints

3 0.38 1 0.22 1.78 1.82 10000 5304 16611 1.42 2 -0.42 61.21 61.39 10000 634 16812 1.42 2 -1.91 63.47 63.56 10000 584 17714 3.78 3 187.67 -369.07 409.56 10000 8811 8811

Table 2. For each tracklet, number of observations, arc data and specific results.

First observed arc: 3 observations The first three ob-servations were made in the early morning of Saturday2 June 2018, and covered a time span of 22.8 minutes;the absolute magnitude of the body was estimated be-tween a minimum value Hmin = 31.29 and a maximumvalueHmax = 34.39, thus indicating a small object. Thisbatch of observations was immediately submitted to theMPC NEOCP, where the object was temporarily denotedas ZLAF9B2; the NEOScan run started at 09:04 UTCand ended at 09:18 UTC. We refer to Table 1 and Ta-ble 2 for the main results and arc data. The observed arcwas an arc of type 1, since it had a non significant cur-vature. In this case, only the double grid sampling of theAR could be adopted because the observational data weretoo poor to compute a nominal solution; in particular, thesoftware computed a uniform densified grid in log10(ρ)for the AR.

Figure 1. Grid sample of the AR in the (ρ, ρ) space forthe first 3 observations of 2018 LA.

Figure 1 shows the uniform AR grid sampling obtainedwith NEOScan for the three observations tracklet:

• the red solid line represents the level curve of theheliocentric energy equal to −k2/(2amax), namely,the outer boundary of the AR;

• the green dashed line shows where the geocentricenergy is equal to 0, also taking into account thecondition about the radius of the Earth sphere of in-fluence;

• the magenta dashed line (which is parallel to the ρaxis) represents the shooting star limit condition;

• the magenta solid lines (which are parallel to the ρaxis) represent different values of the absolute mag-nitude;

• the dots are indicated in blue if χ(x) ≤ 2, green if2 < χ(x) ≤ 5 and black if χ(x) > 5;

• the points corresponding to a VI are representedwith red circles.

The grid consists of 10000 points while, as displayed inTable 2, the corresponding MOV consists of 5304 points(the coloured points in Figure 1); among them, there are166 impacting points (the red circles in Figure 1), whichlead to an impact probability value IP = 0.08%. There-fore, due to this IP value, the system assigned impact flag1 to the object. Furthermore, with such a grid sampling,the score of the object to be classified as a NEA was100%. In Figure 2 it is easy to see that there are some

Figure 2. Projection on the MTP of the VAs obtained withthe first 3 observations of 2018 LA.

blue points leading to an impact, and thus correspondingto a VI.

With these first three observations available only, the ob-ject was claimed as nonsignificant because the arc lengthwas ∆t = 22.8 min, that is less than the minimum estab-lished (30 minutes) in order to avoid unjustified alarms.Nonetheless, the impact flag value 1 and NEA score

100% produced an alert for the observers, and a followup of the object was immediately started.

Second observed arc: 11 observations Within twohours, additional observations of the object ZLAF9B2were provided, giving an amount of 11 total observations;the arc covered a longer time span, ∆t = 85.2 min, andthen the object was no longer classified as a nonsignif-icant case. The observed arc resulted an arc of type 2,with a significant curvature; moreover, the value of thegeodesic curvature S/N was χgeod < 3.

Figure 3. Grid sample of the (ρ, ρ) space for 11 observa-tions of 2018 LA.

Figure 4. Projection on the MTP of the VAs obtained for11 observations of 2018 LA.

The NEOScan software run started at 11:41 UTC andended at 11:57 UTC, giving results as displayed in Ta-ble 1 and Table 2. Again, a reliable nominal solutioncould not be obtained and thus the software had to ap-ply the double grid sampling of the AR, computing a uni-form densified grid in log10(ρ). With such a grid sam-pling, the score of the object to be classified as a NEAwas 100%. Figure 3 shows the uniform AR grid sam-pling obtained for this eleven observations tracklet; the

used colour scheme is the usual. Again, the grid con-sists of 10000 points while, as displayed in Table 2, thecorresponding MOV consists of 634 points only; amongthem, there are 168 impacting points, which lead to animpact probability value IP = 5.1%. Hence, accordingto this IP value and to the fact that χgeod < 3, the sys-tem assigned impact flag 3 to the object, thus increasingits priority in the follow up activities. Figure 4 representsthe projection on the MTP of the VAs. The colours ofthe points indicate their χ-value, according to the usualcolour code, while the dark green circle centerd in (0, 0)is the Earth cross section. Figure 4 clearly shows a num-ber of projected MOV points inside the Earth cross sec-tion, which form a VI and thus correspond to the red cir-cles in Figure 3.

Third observed arc: 12 observations In a matter ofminutes, one additional observation was provided; thus,with a total of 12 observations, the observed arc still cov-ered a time span ∆t = 85.2 min, and was an arc of type2, with a significant curvature. Indeed, its curvature isvery slightly different from the one of the tracklet with11 observations. NEOScan run started at 14:10 UTC andended at 14:26 UTC. Again, since it still could not beobtained a reliable nominal solution, the software had toapply the double grid sampling of the AR, and computeda uniform densified grid in log10(ρ) consisting of 10000points; with such a grid sampling, the score of the objectto be classified as a NEA was 100%.

Figure 5. Grid sample of the (ρ, ρ) space for 12 observa-tions of 2018 LA.

Figure 5 shows the uniform AR grid sampling obtainedfor this tracklet with 12 observations. According to Ta-ble 2, with a single additional observation the softwarewas able to compute a MOV consisting of 584 points,where the impacting points were 177, thus decreasing thenumber of VAs while increasing the number of impact-ing points. As a consequence, the impact probability in-creased significantly, reaching the value IP = 38.3%.Figure 6 represents the projection on the MTP of the VAs,using the usual colour scheme and a dark green circlecenterd in (0, 0) representing the Earth cross section; itclearly shows a number of projected MOV points inside

Figure 6. Projection on the MTP of the VAs obtained for12 observations of 2018 LA.

the Earth cross section, thus leading to an impact. Theseorbits form a VI and correspond to the red circles in Fig-ure 3. Again the system assigned impact flag 3 to theobject, since the observed arc still had χgeod < 3, and atthat point it was clear that every single additional obser-vation would have been critical to ascertain whether theimpact would occur or not.

Figure 7. The AR in the (ρ, ρ) space for 14 observationsof 2018 LA.

Fourth observed arc: 14 observations In about twohours, two additional observations of ZLAF9B2 were ob-tained, giving an amount of 14 total observations and de-termining a tracklet that covered a time span ∆t = 226.8min. This tracklet was an arc of type 3, and allowed thesystem to compute a reliable nominal solution x∗ withRMS = 0.571. Using the new observations, the abso-lute magnitude of the body was estimated more precisely,between Hmin = 30.55 and Hmax = 30.59, thus thesmall object resulted slightly bigger than was expectedinitially with only 3 observations. NEOScan run startedat 14:13 UTC and ended at 14:40 UTC; since a reliablenominal solution was available, the software performeda cobweb sampling of the AR in a neighborhood of x∗.

Figure 8. Cobweb sampling of the (ρ, ρ) space for 14observations of 2018 LA.

Figure 9. Cobweb sampling of the (ρ, ρ) space for 14observations of 2018 LA. Here the impacting points areshown.

Figure 10. Projection on the MTP of the VAs obtained for14 observations of 2018 LA.

In Figure 7 is shown the AR obtained with this trackletof 14 observations; around the point denoted with the or-ange star (that is the orbit with the minimum χ2 value)there are the points of the cobweb sampling, which isvery small with respect to the whole AR and thus it isnot visible in this graphic. Figure 8 and Figure 9 providea zoomed representation of the cobweb sampling insidethe AR. Figure 8 shows the cobweb sampling by denoting

points with colours indicating their χ-value; on the otherhand, Figure 9 shows the cobweb sampling indicating theimpacting orbits with red circles. The sample consistsof 10000 points while the MOV consists of 8811 points,which are all impacting orbits, as one can see in Table 2;indeed, the MOV is represented by green and blue dots(that is, the orbits having χ ≤ 5), and by comparing Fig-ure 8 and Figure 9 it is easy to see that all the MOV pointsare denoted with the red circles, that is they are all im-pacting orbits. Therefore, NEOScan computed an impactprobability value IP = 100%, and then, obviously, as-signed impact flag 4 to the object. Figure 10 representsthe projection on the MTP of the VAs; it shows that all theprojected MOV points are inside the Earth cross section,thus pointing out that the impact would certainly occur.At that point it was necessary to rapidly predict the im-pact corridor ([2]), to outline possible impact locationsin such a way to allow the organisation of quick securitymeasures.

4. FUTURE OF IMPACT MONITORING

At the moment there are two types of automatic systemsdealing with IM of NEOs:

(1) those for already designated orbits, like CLOMON2and Sentry, and

(2) those for the detections of imminent impactors(SCOUT, NEORange, NEOScan).

Systems of class (1) use data from MPEC, and a geo-metrical sampling of the CR with the LOV, while thoseof class (2) scan the NEOCP and use systematic rangingmethods and/or geometric sampling with a 2-dimensionalmanifold.

The born of this two classes of systems has been essen-tially dictated by the history of searching for NEOs, bythe grow of observational facilities and by the amount ofdata available. When CLOMON2 and Sentry started theiractivities the scientific and public communities were in-terested in big objects that could have caused global dam-age, while, at the moment, the attention has moved tosmall objects and meteorites. Probably, the differentia-tion in this two classes are due also to the rules of theMPC, or better, how the automatic systems catch the datafrom it. In this processes there could be a flaw, in thesense that there are objects, with a very well-defined or-bit, remaining on the NEOCP, and, on the contrary, thereexist designated objects with a great uncertainty. Thus,there are a certain number of cases that are not properlyprocessed: object with a very well defined orbit shouldbe processed like ordinary cases using, for example, LOVmethods, while designated objects would deserve a treat-ment using a different sampling of the CR.

What we propose and what we will try to develop in thenext years is an unified system that, starting from NEOCP

data of an object, could decide the type of orbit and whatis the more corrected algorthm of OD to extract as muchinformation as possible.

The starting step should use the NEOScan algorithms togive a first insight to the observational data and to under-stand, using the score of the detection, the type of orbit.The score is the probability that an object belongs to theclasses listed below:

• NEO: Near-Earth Object, an object with periheliondistance q < 1.3AU ;

• MBO: Main Belt Object, an object belonging eitherto the Main Belt or to the Jupiter Trojans. In partic-ular, it has to fulfill the conditions{

1.7AU < a < 4.5AU

e < 0.4∨{

4.5AU < a < 5.5AU

e < 0.3

where a is the semimajor axis (in AU) and e is theeccentricity;

• DO: Distant Object, characterized by q > 28AU(for instance, a Kuiper Belt Object);

• SO: Scattered Object, not belonging to any of theprevious classes.

In case of a NEO probability greater than some thresold,the algorithms for searching VIs should start. The choiceof the more convenient algorithm should be based onsome facts and quantities:

• type of observational arc;

• geodetic curvature;

• presence or not of a reliable LS orbit.

Knowing the previous input, the system must be able todecide:

a) the way to sample the uncertainty region (AR orCR);

b) the duration of propagation;

c) how to detect potential impactors after the propaga-tion and the projection on the TP of an encounter.

Concerning a), a possible improvement is the use of aMonte Carlo (MC) sampling of the CR, when a nominalsolution exists. MC method start from a given probabilitydistribution of initial conditions and propagated forwardin time while recording the number of impacts. This kindof method has the advantage of making no simplifyingassumptions on how the orbital uncertainties are mappedinto the future. However, MC method is a very compu-tationally expensive technique because it requires prop-agating a large number of VAs, typically of the order of

the inverse of the target probability resolution. However,due to increase in the speed of processors, new MC-typemethods are being studied ([12]) in order to replace ge-ometrical sampling. A new automatic system, like whatwe have in mind, should have the capability of use botha geometrical sampling or MC method and above all un-derstand when to use one and when the other.

5. CONCLUSIONS

In the last twenty years there has been a huge progress inthe problem of assessing the asteroid impact hazard. But,as pointed out in [5], the story is not finished, the researchin this field must go on. Due to LSST and GAIA, therewill be a significant increase in the amount and quality ofdata and, both the mathematical algorithms and the pro-cessing strategies, should be improved. In this paper wepresented the state of art of IM systems, higlighting thefeatures of classical IM (LOV geometrical sampling) anddiscussing a new generation system, NEOScan, treatingimminent impactors. We showed also the analysis of areal case, 2018LA. At the end we proposed some possi-ble future developments in the field of IM, and the idea ofdeveloping a unique automatic system capable of summa-rize the features of CLOMON2 and NEOScan in itself.

ACKNOWLEDGMENTS

This conference paper is dedicated to Andrea MilaniComparetti (1948-2018) who was, without a shadow of adoubt, the founding father of impact monitoring and thefirst scientist to develop an automatic system for asteroidhazard. We should have written this work together and hewould certainly has enlightened me with new ideas thatwere never lacking. Unfortunately fate has decided oth-erwise, depriving us of his brilliant intuition and his ideasnever banal. But I am sure that what he has done will in-spire all future scientists who will dedicate to planetaryprotection.

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