Near-Earth Asteroid impact dates: A Reference Ideal Method (RIM) approach

Abstract

The dynamics of asteroids’ trajectories constitute potential threats to the Earth in the hypothetical case where the orbit of such an object crosses the orbit of the Earth. For this reason, advanced monitoring systems such as NASA JPL Sentry continually scan trajectories of Near-Earth Asteroids (NEAs), in addition to other celestial bodies. A large amount of data concerning NEAs is provided by such systems, including estimations of the impact probabilities as well as predictions of impact dates. In this paper, we apply a novel methodology to rank the impact dates of NEAs based on the data provided by Sentry. This approach carries out a comparison process via a novel Multi-Criteria Decision Making (MCDM) method named the Reference Ideal Method (RIM). It takes into account several NEA features, such as distance to the Earth, width, and impact energy, and establishes comparisons with respect to the impact dates of a population of non-small NEAs with those ones from noteworthy objects 410777 (2009 FD), 29075 (1950 DA), and 101955 Bennu (1999 RQ36). The obtained results have been found to be quite consistent, allowing the authors to present this methodology as a novel metric to assess impact dates of hazardous NEAs.

Introduction

The so-called Near Earth Objects (NEOs) are comets and asteroids with perihelion distances $<$ 1.3 AU. The following orbital elements: semi-major axis (a), perihelion distance $\left(q\right)$, and aphelion distance $\left(Q\right)$, are used to classify NEOs into the two following categories (Chodas, 2017a, Perna et al., 2013). The first one, consisting of Near-Earth Comets (NECs), is described by values of $q<1.3$ AU and an orbital period $<$ 200 years. The second category is comprised of Near-Earth Asteroids (NEAs), characterized by values of $q<1.3$ AU. In this paper, we focus primarily on NEAs. NEAs are further divided into five subcategories as follows. The Atiras group, whose name derives from object 163693 Atira, is characterized by values $a<1.0$ AU and $Q<0.983$ AU. Objects in this class are NEAs with orbits entirely contained within the Earth’s orbit. Objects with values $Q>0.983$ AU form the Atens group, named after asteroid 2062 Aten. This group consists of NEAs crossing the Earth’s orbit with semi-major axes smaller than that of the Earth. For objects with values $a>1.0$ AU, we can distinguish the Apollos group (named after object 1862 Apollo), with values $q<1.017$ AU, and the Amors group (whose name derives from asteroid 1221 Amor), with $1.017<q<1.3$ AU. It is worth pointing out that objects in the Apollos group are NEAs crossing the Earth’s orbit with semi-major axes larger than that of the Earth, whereas objects in the Amors group consist of NEAs with orbits exterior to the Earth’s orbit but interior to Mars’ orbit. Finally, PHAs (Potentially Hazardous Asteroids) are NEAs with a Minimum Orbit Intersection Distance (MOID) with the Earth $\le$ 0.05 AU and a brightness given by an absolute magnitude of $H\le 22.0$. According to the previous classification, monitoring of non-small objects, i.e., NEAs with estimated diameters $>50$ m, is necessary to predict close approaches to Earth, and hence, identify potential impact threats (Chapman and Morrison, 1994). With this aim, the NASA JPL Sentry System continually scans the trajectories of NEOs and updates their orbital parameters. As a result, this system displays lists of potential impact dates for each NEA, in conjunction with their corresponding impact probabilities. Among the population of non-small NEAs, three objects captured the attention of the authors: 410777 (2009 FD), 101955 Bennu (1999 RQ36), and 29075 (1950 DA). It is worth mentioning that they exhibit the greatest impact probabilities (cum.) according to Sentry and also display high scores in the Palermo scale (Chodas, 2017a, Chesley et al., 2002). It is worth pointing out that the Palermo Technical Impact Hazard Scale is a logarithmic scale allowing to rate the potential hazard of a NEO impact. Thus, they were selected as the main reference objects to apply a Multi-Criteria Decision Making (MCDM) approach in this study. In fact, techniques based on decision analysis, in particular, MCDM methods, may be applied to assess potential NEA threats (Lee et al., 2014) as an alternative to classical metrics, such as the Palermo Scale (Chesley et al., 2002).

An MCDM problem consists of a collection of alternatives to be classified according to a criteria set. All the information involved in such a problem is arranged into a decision matrix. The main goal of applying such techniques is to determine the best alternative according to a set of criteria. A wide collection of MCDM approaches has emerged since the late 1980s including ELimination Et Choix Traduisant la REalité (ELimination and Choice Expressing Reality, ELECTRE) (Roy, 1968); Preference Ranking Organization METHod for Enrichment of Evaluations (PROMETHEE) (Brans et al., 1984); Ordered Weighted Averaging (OWA) (Yager, 1998); Analytic Network Process (ANP) (Saaty, 1996); and VIseKriterijumska Optimizacija I Kompromisno Resenje (Multicriteria Optimization and Compromise Solution, VIKOR) (Opricovic, 1998), to name just a few. Among them, we would like to highlight the Analytic Hierarchy Process (Saaty, 1989) (AHP), applied in the first stage of the present study with the aim of determining the weights of the criteria, as well as the TOPSIS approach (Hwang and Yoon, 1981), both of which have been widely applied in several contexts (Mardania et al., 2015). Original MCDM procedures are still being contributed. For instance, recently the so-called D numbers were proposed to assess health-care waste treatment technologies (Xiao, 2018).

We would also like to mention that MCDM methods have been applied in the context of astrophysics. For instance, they allowed to deal with complex problems in space exploration projects at NASA (Tavana, 2003, Tavana, 2004, Tavana and Sodenkamp, 2009). It is also worth pointing out that both the AHP and (three variations of) TOPSIS were used to assess a series of preference models for the human exploration of Mars (Tavana and Hatami-Marbini, 2011).

In 2016, Cables et al. contributed a novel MCDM approach, namely, the so-called Reference Ideal Method (RIM for short, hereafter), allowing the information aggregation with respect to a reference ideal alternative. That approach exhibits a compensatory nature since it considers all the criteria simultaneously, weights their values, and provides an assessment for all the alternatives according to their distances to a reference ideal. As such, the RIM becomes a potential MCDM procedure to expand the range of TOPSIS applications to situations whose solutions lie between minimum and maximum values.

In this paper, we develop the first MCDM application of the RIM approach to rank a set of 4193 potential impact dates from a collection of 118 non-small NEAs (c.f. Section 3). With this aim, we surveyed a group of experts and carried out a detailed sensitivity analysis involving all the alternatives. In this way, the criteria weights were varied and the reference ideals were interchanged among a set of three distinguished objects, namely, NEAs 29075 (1950 DA), 101955 Bennu (1999 RQ36), and 410777 (2009 FD). It should also be added that an additional comparison with respect to a combined AHP–TOPSIS was performed to highlight the differences between both methodologies (c.f. Section 4).

As such, this paper is structured as follows. First of all, Section 2 is devoted to presenting the basics regarding the methodologies applied throughout the paper. More specifically, in Section 2.1, we describe the Analytic Hierarchy Process (AHP), whereas in Section 2.2, all the steps to effectively apply the Reference Ideal Method (RIM) in applications are provided. Next, in Section 3, we focus on the structure of our decision problem to carry out an assessment of potential impact dates of a NEA population with respect to the three distinguished objects listed above (c.f. Section 3.1). In Section 3.2, we describe in detail each of the criteria involved in the present study. It is worth mentioning that the weights of the criteria were determined by means of an AHP-based approach (for additional details, we refer the reader to Section 3.3). As such, we are ready to assess our list of potential impact dates through the RIM procedure (an example of application of the RIM approach is given in Appendix A). The results obtained are described in Section 3.4. To conclude this paper, we conducted a detailed sensitivity analysis with a triple purpose. In fact, we compared the results obtained by varying the weights of the criteria (c.f. Section 4.1), interchanging the ideal reference alternatives (c.f. Section 4.2), and further applying a combined AHP–TOPSIS methodology. It is worth pointing out that all such comparisons were carried out involving all the 4193 potential impact dates considered in this paper. To deal with these, Spearman rank correlation coefficient was used to analyse the correlation between each pair of rankings and support the robustness of our results. Section 5 highlights the main conclusions achieved by this paper. Two appendices are also included. As such, Appendix A contains an easy example described in detail to illustrate the reader how RIM method works, whereas, Appendix B provides the basics on TOPSIS method.