# An efficient algorithm for prioritizing NEA physical observations

M. Cortese, E. Perozzi, M. Micheli, B. Borgia, E. Dotto, E. Mazzotta Epifani, S. Ieva, M. Barucci, D. Perna

► To cite this version:

M. Cortese, E. Perozzi, M. Micheli, B. Borgia, E. Dotto, et al. An efficient algorithm for prioritizing NEA physical observations. Meteoritics and Planetary Science, 2017, 52 (3), pp.522-531. 10.1111/maps.12810. hal-02265977

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# An efficient algorithm for prioritizing NEA physical observations

M. CORTESE<sup>1,2*</sup>, E. PEROZZI<sup>1,3,4</sup>, M. MICHELI<sup>3</sup>, B. BORGIA<sup>2</sup>, E. DOTTO<sup>5</sup>, E. MAZZOTTA EPIFANI<sup>5</sup>, S. IEVA<sup>5</sup>, M. A. BARUCCI<sup>6</sup>, and D. PERNA<sup>6</sup>

*(Received 04 March 2016; revision accepted 12 November 2016)*

**Abstract**—The present near-Earth asteroids (NEA) discovery rate has surpassed 1500 objects per year, thus calling for extensive observation campaigns devoted to physical characterization in order to define successful mitigation strategies in case of possible impactors. A tool is presented which, through a prioritization algorithm, aims to optimize the planning and the execution of NEA physical observations. Two ranking criteria are introduced, Importance and Urgency, accounting for the need of satisfying the two basic observational modes for physical characterization, that is, rapid response and large observing programs, aimed at selecting targets for exploration and mitigation space missions. The resulting tool generates a daily table of observable targets and it can also be run as a stand-alone tool in order to provide future observing opportunities at a specific date of interest. It has been developed and implemented within the framework of the NEOShield-2 EU/HORIZON 2020 Project; the output of the prioritization algorithm is publicly available, in tabular format, on the NEOShield-2 NEO Properties Portal (http://www.neoshield.net/the-neoshield-project/project-activities/neo-properties-portal), reachable from the main page of the Project website (http://www.neoshield.eu).

## INTRODUCTION

Near-Earth asteroids (NEA) are attracting an increasing audience because of scientific, technological, civil protection, and commercial implications. The interest in their compositional nature as dynamically evolved primitive solar system bodies (Bottke et al. 2004) was at the basis of the realization of dedicated rendezvous missions, such as NEAR (Cheng 2002), and sample return missions such as Hayabusa (Fujiwara et al. 2006). This paved the way to the presently ongoing follow-on sample return missions Hayabusa-2 (Hasegawa et al. 2008) and OSIRIS-REx (Connolly and Lauretta 2014) missions. The possible exploitation of NEAs for extraterrestrial mining (Lewis 1996; Sonter 1997) requires the development of advanced space technologies for returning to Earth large asteroidal

samples (Brophy et al. 2011; Michel et al. 2015). The impact monitoring activities carried out worldwide (Milani et al. 2000; Chamberlin et al. 2001; Chesley et al. 2002; see also Perna et al. [2013] and Farnocchia et al. [2015] for a review) have fostered the need for more efficient discovery and follow-up systems as well as for the development of mitigation techniques in space, for example, deflecting an asteroid by means of a kinetic impactor (Ahrens and Harris 1992; Carusi et al. 2002, 2005; Cheng et al. 2016). Human spaceflight also considers NEAs as an intermediate step before undertaking the much more demanding journey to Mars (Cassady et al. 2015), in particular within the framework of the ARM (Asteroid Redirect Mission) scenario (Mazanek et al. 2016). As a consequence, efficiently browsing the NEA population in search of an object satisfying at best different mission goals, either of

<footnote n="1"><sup>1</sup>Deimos Space, Ronda de Poniente 19, 28760 Tres Cantos, Madrid, Spain</footnote>

<footnote n="2"><sup>2</sup>Serco SpA, Via Sciadonna 24, 00044 Frascati, Roma, Italy</footnote>

<footnote n="3"><sup>3</sup>ESA SSA-NEO Coordination Centre, ESRIN, Via Galileo Galilei 64, 00044 Frascati, Roma, Italy</footnote>

<footnote n="4"><sup>4</sup>INAF—IAPS, Via del Fosso del Cavaliere 100, 00133 Roma, Italy</footnote>

<footnote n="5"><sup>5</sup>INAF—Osservatorio Astronomico di Roma, Via Frascati 33, 00040 Monte Porzio Catone, Roma, Italy</footnote>

<footnote n="6"><sup>6</sup>LESIA Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris Diderot, Sorbonne Paris Cité, 5 place Jules Janssen, 92195 Meudon, France</footnote>

<footnote>*Corresponding author. E-mail: matteo.cortese@serco.com</footnote>
scientific or technological nature, is an essential process
in asteroid mission design.

The NEA population has undergone two major
sharp increases in the discovery rate: a first one at the
turn of the millennium when wide-field high-sensitivity
sky surveys begun operations, and a second one more
recently, since when the US Pan-STARRS1 telescope
time allocation had been devoted mainly to NEAs
(Jedicke et al. 2006; Wainscoat et al. 2014, 2015). At
present, more than 1500 objects are discovered each
year (Fig. 1). Such an increase has also contributed to
alter the properties of typical discoveries, which are now
mostly represented by small-sized asteroids passing close
to the Earth, thus calling for immediate follow-up
observations in order to secure their orbits and prevent
them from being lost.

Another significant consequence of the fast-
growing NEO population is that observing campaigns
devoted to physical characterization must become more
efficient in order to keep pace. At present, only about
15% of the known NEAs have some basic physical
properties determined, such as size (not derived from
the absolute magnitude), shape and/or spectral type.
These data have been collected and organized in
tabular form after Binzel et al. (2002) and made
publicly available at the EARN (European Asteroid
Research Node) web site (http://earn.dlr.de). A
Physical Properties database relying on the EARN
original data and regularly updated, including an
advanced search functionality allowing filtering on
both physical and orbital properties, is presently
available at the ESA SSA-NEO Coordination Centre
website (http://neo.ssa.esa.int). On analyzing these
data, Binzel et al. (2004) have shown that, by
introducing a basic NEO accessibility criterion, it is
possible to focus physical observations on objects for
which the computation of realistic mission profiles can
be attempted.

Within this framework, the NEOShield European
Union project (Harris et al. 2012, 2013) has studied the
modeling of asteroid impacts and the design of
mitigation missions, concluding that in both cases
composition and internal structure of an asteroid may
dramatically change the outcome of an impact.
Therefore, a recommendation was issued to specifically
improve the physical characterization of NEAs through
a more systematic approach. As a consequence, one of
the major goals of the NEOShield-2 project, funded
through the Horizon 2020 European Commission
program, focuses on carrying out extensive
observational campaigns devoted to increasing the
percentage of known NEAs for which physical
characterization is available (Dotto et al. 2015; Perna
et al. 2015).

To this end, a network of telescopes capable of
using different techniques such as spectroscopy,
photometry, and polarimetry shall be set up. Large
aperture instruments can be made available through
large programs and dedicated on-demand time; quick
response can be ensured by discretionary time
allocations and/or the availability of smaller telescopes.
Moreover, since this information is also needed for
planning exploration and/or mitigation missions, it
appears desirable to give priority to objects for which
realistic mission profiles can be computed.

These constraints pose a scheduling problem: a
criterion is needed to properly coordinate the
observations in order to ensure that as many as possible
relevant objects are observed, redundant observations
are avoided, and targets needing rapid response are
promptly identified.

Physical Properties Priority List

The problem of efficiently planning and executing
NEA follow-up observations has been first addressed by
Boattini et al. (2007). The goal in that case was to
ensure that the necessary astrometry for improving the
orbit determination accuracy is provided, thus avoiding
that objects are lost. Therefore, a prioritization
algorithm, which ranks objects according to an urgency
criterion, was developed; its output, the so-called
Priority List (PL) was originally made available to
observers at the Spaceguard Central Node website
(http://spaceguard.iaps.inaf.it/SSystem/SSystem.html)
and now it can also be found in different formats on
the ESA SSA-NEO Coordination Centre website.

In this work, a tool is presented which, following
the original PL approach, aims to support and
coordinate observation campaigns devoted to NEA
physical characterization through a prioritization
algorithm, in order to maximize the return from
telescope time allocations.

The Physical Properties Priority List (P3L)
algorithm takes into account:

1. the technical requirements of the NEOShield-2 project, that is, increase the number of NEAs for which physical characterization is available by focusing on objects in the 50 m–300 m size range and which are potentially accessible for a space mission;

2. the need to satisfy the two basic observational modes for physical characterization, that is, rapid response and timely submission of large observing programs, submitted to Time Allocation Committee (TAC) approval.

Therefore, the observing scenario and the
parameters that must be satisfied by the P3L tool are
<figure><img src="image_2.png" /><figcaption>Fig. 1. Discovered NEAs by years from January 1900 to February 2016. (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

undoubtedly more complex than the one characterizing the astrometric PL. Several parameters must be taken into account: the sky uncertainty (i.e., the accuracy of asteroid position on the sky), the visibility period, the phase range and its variation during visibility, the visual magnitude and its behavior during visibility, the object apparent motion, and an estimate of the mission accessibility of each object.

## Algorithm

Two ranking criteria are introduced, Importance and Urgency, which correspond to the different observing requirements described above.

The former is a function of the object size and accessibility, providing the rationale for planning large observing programs. The latter is a function of the number of visibility days and of the magnitude trend and applies especially to newly discovered objects in danger of being observable again only after a long time span, thus calling for rapid response times.

## Ranking by Importance

The Importance parameter is defined as:

$$IMP = DIM \cdot ACC$$

where DIM and ACC take into account the size and the accessibility of the specific object.

The absolute magnitude H of an object is linked to its size through the well-known formula (Chesley et al. 2002):

$$D[\text{km}] = \frac{1329}{\sqrt{p}} 10^{-0.2H}$$

where p is the asteroid albedo.

The DIM parameter is a function of the asteroid absolute magnitude and it is defined as:

$$DIM = \frac{1}{1 + \left| \frac{H-c}{a} \right|^{2b}}$$

where a is a quantity linked to the Full Width Half Maximum, a parameter used to describe the width of a mathematical object when it does not have sharp edges, b is an exponent characterizing the slope of the function and c expresses the function center.

In Fig. 2, it is shown that the DIM function adopted by the P3L algorithm, which has been obtained using the average value for the albedo P = 0.154 (Chesley et al. 2002) translates the NEOShield-2 size range into an interval of magnitudes between 20.26 and 24.15.

In order to fit the DIM function to the NEOShield-2 case study, recommended values for a, b, c parameters are:

a = 2.94

b = 10

c = 22.21.

The DIM function is essentially a filter on asteroid sizes allowing us to maximize, in our case
<figure><img src="image_3.png" /><figcaption>Fig. 2. DIM function adopted by the P3L algorithm for the NEOShield-2 case (a = 2.94, b = 10, c = 22.21) allows us to maximize the importance of objects satisfying the NEOShield-2 constraints on size. (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

study, the importance of objects satisfying the NEOShield-2 requirements. Note that its parameters can be easily tuned to adapt the function behavior to a different case study, thus allowing us to customize the algorithm to different mission and/or observational requirements.

The ACC parameter is a function of the accessibility of an asteroid for a rendez vous mission as described in Perozzi et al. (2001), that is, the total change of velocity (ΔV) for a spacecraft initially on a circular 1 au orbit needed to reach an orbit identical to that of the target asteroid, computed through Hohmann-like formulas.

The ACC parameter is given by:

$$ACC = \frac{1}{1 + |\frac{\Delta V}{a}|^{2b}} + \left(\frac{\Delta V_0}{\Delta V}\right)^2$$

where a and b are characteristic parameters with the same meaning as the ones in the DIM function, while the ΔVs are measured in km s⁻¹ and have the following meaning:

1. ΔV is the accessibility of the target asteroid computed by applying a best-case transfer strategy criterion;

2. ΔV₀ is a normalizing factor to enhance the importance of an extremely accessible object.

In Fig. 3, the shape of the ACC function with ΔV₀ = 2 km s⁻¹ is shown, with the choice of a = 6 km s⁻¹ and b = 5 used for our NEOShield-2 case study.

<figure><img src="image_4.png" /><figcaption>Fig. 3. The ACC function with a = 6 and b = 5 is unity for a rendez vous mission budget of 5 km s⁻¹. It accounts for the accessibility of a NEA. (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

<table><caption>Table 1. Importance categories in the P3L: The category is established by the numerical value of IMP parameter.</caption><thead><tr><td>Importance category</td><td>IMP min</td><td>IMP max</td></tr></thead><tbody><tr><td>Very important</td><td>1.5</td><td>&gt;1.5</td></tr><tr><td>Important</td><td>1.0</td><td>1.5</td></tr><tr><td>Useful</td><td>0.5</td><td>1.0</td></tr><tr><td>Routine</td><td>0.0</td><td>0.5</td></tr></tbody></table>

For ΔV < ΔV₀, the ACC function grows quickly toward increasingly large values in order to give proper weight to extremely accessible objects.

Note from Fig. 3 that the behavior of the ACC function is representative of the performances allowed by the present developments of space technologies. The function is unity for a ΔV ref = 5 km s⁻¹, which roughly corresponds to the ΔV budget for a mission to Mars.

When the ΔV value grows beyond 7 km s⁻¹, the function drops down toward zero implying the proximity to the present technological level (the solar system escape velocity is 12.3 km s⁻¹).

The Importance parameter defined at the beginning of this section is thus obtained, and according to its value, it is possible to define four Importance categories: very important, important, useful, routine. See Table 1 for the thresholds chosen for this study.

Note that very important objects are those having ΔV < 2 km s⁻¹ and 50 m < D < 300 m, thus representing the best NEOShield-2 targets, while routine objects will
essentially contribute to increase the number of NEAs for which physical observations are available. The important and useful classes often include small and accessible objects.

Ranking by importance is likely to provide the rationale for motivating the selection of targets within the framework of proposals for obtaining telescope time.

## Ranking by Urgency

The Urgency parameter is defined as follows:

$$URG = VP \cdot DMAG$$

where VP and DMAG account for the visibility period and for the behavior of the visual magnitude, respectively.

VP is given by the following relationship:

$$VP = \frac{1}{\left[1 + \left(\frac{DD}{7}\right)^{n/\frac{1}{n}}\right]}$$

where DD is the number of days until end-of-visibility and n is a normalization parameter which allows us to shape the transition between the two regimes in the function introduced.

As shown in Fig. 4, the VP function varies between 0 and 1, assuming the latter value during the last 7 days of visibility to account for a worst-case scenario when the Moon is interfering with the observations, as specified in Boattini et al. (2007). When DD is >7 days, the VP function decreases as DD⁻¹.

All known NEAs' ephemerides are analyzed in order to determine, for any given date, the observable objects in the sky.

The number of days until end-of-visibility is computed by evaluating how long the visual magnitude of an object remains below a certain threshold which depends upon the solar elongation and is given by:

$$FMAG = V_0 - e^{-\frac{\epsilon-\epsilon_0}{k}}$$

where V₀ is the faintest visual magnitude allowed, ε is the osculating solar elongation, ε₀ fixes the lower limit for solar elongation, and k determines how the magnitude limit drops at low solar elongations. Figure 5 reports the behavior of the FMAG function when realistic values are chosen for V₀ = 23 and ε₀ = 45°. The constraint on visual magnitude is set by the typical limiting magnitude of the largest available telescopes for spectroscopy and photometry. The constraint on solar elongation is a geometric factor ensuring good quality observations not hindered by twilight conditions.

<figure><img src="image_5.png" /><figcaption>Fig. 4. Behavior of the VP function. (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5. The FMAG function describes the visibility region of the Physical Properties Priority List. (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

The DMAG parameter accounts for the behavior of the visual magnitude of an object by determining whether it is becoming fainter or brighter. It is obtained by subtracting the current value of the visual magnitude from that computed in 10 days time. The larger and more positive this difference is, the fainter and quicker the object is becoming, thus raising the urgency ranking. Therefore, indicating with $\dot{V}$ the difference in visual magnitude, the corresponding function is defined as follows:

$$DMAG = \begin{cases} 1 & \dot{V} < 0 \\ 1 + \dot{V} & \dot{V} \ge 0 \end{cases}$$
<figure><img src="image_7.png" /><figcaption>Fig. 6. The DMAG function indicates whether the object is going to be brighter or not. (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

<table><caption>Table 2. Urgency categories in the P3L: The category is established by the numerical value of URG parameter.</caption><thead><tr><td>Urgency category</td><td>URG min</td><td>URG max</td></tr></thead><tbody><tr><td>****</td><td>4.0</td><td>&gt;4.0</td></tr><tr><td>***</td><td>2.0</td><td>4.0</td></tr><tr><td>**</td><td>0.5</td><td>2.0</td></tr><tr><td>*</td><td>0.0</td><td>0.5</td></tr></tbody></table>

The corresponding behavior is shown in Fig. 6: negative values do not affect the Urgency ranking of an object, while the more quickly it is foreseen that it will become fainter, the more urgent its observation becomes.

According to the value of the Urgency parameter defined at the beginning of this section, it is possible to define four Urgency categories using asterisks: from extremely urgent (****) to not urgent at all (*). See Table 2 for the thresholds chosen for this study.

The ranking by Urgency is best suited for sorting out targets for observation with a rapid response system.

## Output

The P3L algorithm output reports, in tabular format, all quantities needed to help the observer in evaluating the feasibility of an observation, while remaining at the same time independent from the specific observing site and telescope performances. In order to do so, the algorithm needs to access high-precision NEA ephemerides.

<table><caption>Table 3. Synthetic description of some representative P3L output ranking possibilities.</caption><thead><tr><td>Ranking</td><td>Description</td></tr></thead><tbody><tr><td>Very important (****)</td><td>Small (50 m &lt; D &lt;300 m) and extremely accessible targets (ΔV &lt;2 km s<sup>-1</sup>) probably having a close encounter with the Earth. A rapid response for physical characterization should be activated.</td></tr><tr><td>Very Important (*)</td><td>Small (50 m &lt; D &lt;300 m) and extremely accessible targets (ΔV &lt;2 km s<sup>-1</sup>), which will be observable for several days, leaving more time to plan physical observations. Possibility of observing the same object at different phase angles.</td></tr><tr><td>Important (****)</td><td>Small and accessible objects with high observing urgency (number of days until end-of-visibility &lt;7 days).</td></tr><tr><td>Useful (*)</td><td>Small and accessible objects with no observing urgency. Possibility of observing the same object at different phase angles.</td></tr><tr><td>Routine</td><td>Lower priority objects which may still contribute to increase the number of NEAs having known physical characterization.</td></tr></tbody></table>

Initially, the P3L algorithm identifies NEAs that, at a given date, are observable from ground-based telescopes for physical characterization; visibility is computed from geocentric ephemerides in order to be independent from a specific observing site. This sample is then used to compute each individual rating. In Table 3, a synthetic description of some interesting ranking combination is reported, representative of specific applications. As an example, if a very important and urgent object appears in the P3L output (first row in Table 3), it deserves maximum attention since it is likely to be an ideal target for an exploration mission, and it needs to be observed quickly.

The implementation of the P3L output relative to the NEOShield case, publicly available through the NEOShield-2 NEO Properties Portal, allows a twofold utilization:

1. Automatic daily generation of P3L through an automatic script embedded in a Web service which produces an output updated daily;

2. Generation of P3L as a stand-alone tool in order to provide future observing opportunities at a specific date of interest; the output is disseminated via e-mail to the users.
<table><caption>Table 4. P3L sample output produced on 26/12/2015. Full table can be downloaded on NEOShield-2 NEO Properties Portal.</caption><thead><tr><th>NEA Name</th><th>H</th><th>V</th><th>V dot</th><th>Visibility Days</th><th>Phase Range [deg]</th><th>Sky Uncertainty</th><th>DeltaV [km s<sup>-1</sup>]</th><th>Importance</th><th>Urgency</th></tr></thead><tbody><tr><td>2009CV</td><td>24.250</td><td>22.5</td><td>0.3</td><td>13</td><td>29.2-42.9</td><td>0.151"</td><td>2.332014</td><td>Very important</td><td>**</td></tr><tr><td>2004VJ1</td><td>24.237</td><td>22.8</td><td>0.4</td><td>3</td><td>78.7-80.6</td><td>0.291"</td><td>2.555221</td><td>Very important</td><td>***</td></tr><tr><td>2003SM84</td><td>22.738</td><td>21.5</td><td>0.5</td><td>35</td><td>26.1-46.9</td><td>0.115"</td><td>2.703518</td><td>Very important</td><td>*</td></tr><tr><td>2014EK24</td><td>23.270</td><td>21.8</td><td>-0.6</td><td>177</td><td>27.3-108.4</td><td>0.326"</td><td>2.910289</td><td>Important</td><td>*</td></tr><tr><td>2015VO105</td><td>24.039</td><td>22.2</td><td>0.6</td><td>14</td><td>46.4-49.2</td><td>0.249"</td><td>3.288084</td><td>Important</td><td>**</td></tr><tr><td>2011CG2</td><td>21.454</td><td>21.8</td><td>0.3</td><td>49</td><td>37.3-54.9</td><td>0.082"</td><td>3.340296</td><td>Important</td><td>*</td></tr><tr><td>2015VV</td><td>24.476</td><td>21.9</td><td>0.4</td><td>25</td><td>46.0-47.1</td><td>0.257"</td><td>3.399528</td><td>Important</td><td>*</td></tr><tr><td>450237</td><td>22.936</td><td>22.3</td><td>0.4</td><td>18</td><td>58.1-59.9</td><td>0.073"</td><td>3.458467</td><td>Important</td><td>**</td></tr><tr><td>2015TJ1</td><td>22.788</td><td>22.0</td><td>0.0</td><td>155</td><td>34.6-101.7</td><td>0.500"</td><td>3.724905</td><td>Important</td><td>*</td></tr><tr><td>2004EO20</td><td>22.256</td><td>21.6</td><td>0.4</td><td>36</td><td>24.7-43.7</td><td>0.136"</td><td>4.019102</td><td>Important</td><td>*</td></tr><tr><td>253062</td><td>20.758</td><td>21.1</td><td>0.3</td><td>51</td><td>2.1-31.2</td><td>0.237"</td><td>4.382974</td><td>Important</td><td>*</td></tr><tr><td>2015XA352</td><td>21.948</td><td>22.7</td><td>0.4</td><td>7</td><td>23.3-27.4</td><td>4.296"</td><td>4.407326</td><td>Important</td><td>**</td></tr><tr><td>2003GA</td><td>21.083</td><td>22.6</td><td>-0.4</td><td>321</td><td>7.7-77.8</td><td>0.259"</td><td>4.421305</td><td>Important</td><td>*</td></tr><tr><td>2006KV89</td><td>21.279</td><td>21.3</td><td>0.6</td><td>87</td><td>75.0-108.4</td><td>0.223"</td><td>4.471303</td><td>Important</td><td>*</td></tr><tr><td>2005TF45</td><td>23.060</td><td>22.4</td><td>0.4</td><td>16</td><td>34.3-42.9</td><td>1.503d</td><td>4.636720</td><td>Important</td><td>**</td></tr><tr><td>2015LE21</td><td>24.756</td><td>22.1</td><td>0.4</td><td>20</td><td>38.7-41.0</td><td>0.982"</td><td>4.366619</td><td>Important</td><td>*</td></tr><tr><td>2015YA1</td><td>24.569</td><td>20.4</td><td>1.2</td><td>26</td><td>20.0-37.1</td><td>5.553"</td><td>4.677656</td><td>Important</td><td>**</td></tr><tr><td>208023</td><td>20.330</td><td>22.2</td><td>0.1</td><td>69</td><td>50.7-60.8</td><td>0.060"</td><td>4.849432</td><td>Important</td><td>*</td></tr><tr><td>2015YZ</td><td>23.093</td><td>21.7</td><td>0.2</td><td>106</td><td>29.5-62.2</td><td>6.659"</td><td>4.853572</td><td>Important</td><td>*</td></tr><tr><td>2008VA15</td><td>23.478</td><td>21.5</td><td>0.0</td><td>78</td><td>0.6-62.6</td><td>0.164"</td><td>4.857144</td><td>Important</td><td>*</td></tr><tr><td>65717</td><td>20.931</td><td>21.7</td><td>0.0</td><td>152</td><td>47.3-76.2</td><td>0.153"</td><td>4.861691</td><td>Important</td><td>*</td></tr><tr><td>451370</td><td>21.494</td><td>22.9</td><td>0.4</td><td>1</td><td>40.9-40.9</td><td>0.056"</td><td>4.866913</td><td>Important</td><td>**</td></tr><tr><td>2010WT8</td><td>21.863</td><td>22.0</td><td>0.3</td><td>37</td><td>28.3-53.0</td><td>0.657"</td><td>4.866945</td><td>Important</td><td>*</td></tr><tr><td>2013EU9</td><td>21.602</td><td>22.4</td><td>0.3</td><td>19</td><td>21.3-33.4</td><td>0.090"</td><td>4.868039</td><td>Important</td><td>*</td></tr><tr><td>451157</td><td>21.026</td><td>20.7</td><td>0.3</td><td>245</td><td>6.8-91.2</td><td>0.143"</td><td>4.913115</td><td>Important</td><td>*</td></tr><tr><td>2015XP128</td><td>22.984</td><td>20.4</td><td>0.5</td><td>37</td><td>4.9-27.6</td><td>0.844"</td><td>4.948385</td><td>Important</td><td>*</td></tr><tr><td>2011YT62</td><td>22.383</td><td>22.8</td><td>-0.2</td><td>92</td><td>15.3-54.0</td><td>4.511'</td><td>4.952465</td><td>Important</td><td>*</td></tr><tr><td>433953</td><td>20.836</td><td>22.0</td><td>-0.2</td><td>269</td><td>21.9-119.3</td><td>0.163"</td><td>5.020270</td><td>Important</td><td>*</td></tr><tr><td>2003QU5</td><td>24.033</td><td>22.7</td><td>0.6</td><td>5</td><td>34.3-34.3</td><td>26.185d</td><td>5.022056</td><td>Important</td><td>**</td></tr><tr><td>416151</td><td>20.549</td><td>21.8</td><td>0.3</td><td>87</td><td>35.3-53.6</td><td>0.037"</td><td>5.067566</td><td>Useful</td><td>*</td></tr><tr><td>138175</td><td>20.210</td><td>19.8</td><td>-0.4</td><td>200</td><td>16.1-105.2</td><td>0.073"</td><td>5.079332</td><td>Useful</td><td>*</td></tr><tr><td>2012DK61</td><td>21.039</td><td>21.0</td><td>0.0</td><td>72</td><td>11.1-43.7</td><td>0.334"</td><td>5.086472</td><td>Useful</td><td>*</td></tr><tr><td>2015RH2</td><td>21.969</td><td>22.3</td><td>-0.1</td><td>158</td><td>13.9-109.2</td><td>0.761"</td><td>5.108339</td><td>Useful</td><td>*</td></tr><tr><td>2015YU1</td><td>24.719</td><td>20.6</td><td>0.4</td><td>48</td><td>10.2-76.6</td><td>10.526"</td><td>5.000217</td><td>Useful</td><td>*</td></tr><tr><td>2015VX</td><td>23.694</td><td>22.4</td><td>0.4</td><td>14</td><td>35.8-39.0</td><td>0.440"</td><td>5.128112</td><td>Useful</td><td>**</td></tr><tr><td>281375</td><td>20.730</td><td>22.3</td><td>0.1</td><td>67</td><td>58.8-80.5</td><td>0.096"</td><td>5.243808</td><td>Useful</td><td>*</td></tr><tr><td>2009WM105</td><td>23.035</td><td>21.4</td><td>0.3</td><td>37</td><td>75.2-103.9</td><td>3.636d</td><td>5.244699</td><td>Useful</td><td>*</td></tr><tr><td>1994UG</td><td>20.994</td><td>21.9</td><td>-0.5</td><td>94</td><td>21.6-136.7</td><td>0.761"</td><td>5.281670</td><td>Useful</td><td>*</td></tr><tr><td>382745</td><td>20.337</td><td>22.9</td><td>-0.3</td><td>323</td><td>2.7-73.0</td><td>0.058"</td><td>5.285972</td><td>Useful</td><td>*</td></tr><tr><td>2004BE86</td><td>20.873</td><td>21.0</td><td>0.3</td><td>192</td><td>29.1-64.9</td><td>0.074"</td><td>5.317254</td><td>Useful</td><td>*</td></tr><tr><td>85990</td><td>20.057</td><td>20.6</td><td>-5.1</td><td>313</td><td>17.5-137.2</td><td>0.115"</td><td>5.313033</td><td>Useful</td><td>*</td></tr><tr><td>424482</td><td>19.651</td><td>21.9</td><td>0.2</td><td>58</td><td>39.7-51.4</td><td>0.233"</td><td>5.205540</td><td>Useful</td><td>*</td></tr><tr><td>2015XL55</td><td>24.151</td><td>21.5</td><td>0.6</td><td>20</td><td>7.9-16.9</td><td>3.199"</td><td>5.395622</td><td>Useful</td><td>**</td></tr><tr><td>2015GN50</td><td>20.150</td><td>22.6</td><td>0.3</td><td>14</td><td>39.3-39.7</td><td>188.723d</td><td>5.417726</td><td>Useful</td><td>**</td></tr><tr><td>2009JR5</td><td>20.360</td><td>22.3</td><td>0.1</td><td>200</td><td>6.2-62.4</td><td>0.085"</td><td>5.455241</td><td>Useful</td><td>*</td></tr><tr><td>264308</td><td>20.332</td><td>21.2</td><td>0.3</td><td>127</td><td>10.4-50.8</td><td>0.079"</td><td>5.460228</td><td>Useful</td><td>*</td></tr></tbody></table>

In Table 4, a sample output is shown, produced by running the P3L tool on 2015 December 26 when the known NEO population contained 13496 objects. About 14% of them turned out to be potential observing targets for physical characterization; out of them only

four were accessible at less than 3 km s⁻¹, thus deserving a very important ranking.

The full table can be downloaded on NEOShield-2 NEO Properties Portal into two different formats, plain text (.txt) and Excel (.xlsx), in order to use it
<table><caption>Table 5. The same P3L sample output in Table 4 with lower limit on the objects' size relaxed from 50 m to 5 m.</caption><thead><tr><th>NEA Name</th><th>H</th><th>V</th><th>V Dot</th><th>Visibility Days</th><th>Phase Range [deg]</th><th>Sky Uncertainty</th><th>DeltaV [km s<sup>-1</sup>]</th><th>Importance</th><th>Urgency</th></tr></thead><tbody><tr><td>2015VC2</td><td>27.313</td><td>22.3</td><td>0.2</td><td>17</td><td>87.3-110.8</td><td>1.339"</td><td>1.412667</td><td>Very important</td><td>*</td></tr><tr><td>2015XZ378</td><td>27.402</td><td>21.8</td><td>0.7</td><td>18</td><td>20.1-48.0</td><td>8.790"</td><td>1.712088</td><td>Very important</td><td>**</td></tr><tr><td>2009CV</td><td>24.250</td><td>22.5</td><td>0.3</td><td>13</td><td>29.2-42.9</td><td>0.151"</td><td>2.332014</td><td>Very important</td><td>**</td></tr><tr><td>2004VJ1</td><td>24.237</td><td>22.8</td><td>0.4</td><td>3</td><td>78.7-80.6</td><td>0.291"</td><td>2.555221</td><td>Very important</td><td>***</td></tr><tr><td>2003SM84</td><td>22.738</td><td>21.5</td><td>0.5</td><td>35</td><td>26.1-46.9</td><td>0.115"</td><td>2.703518</td><td>Very important</td><td>*</td></tr><tr><td>2007BB</td><td>27.833</td><td>22.9</td><td>-0.7</td><td>22</td><td>25.0-66.5</td><td>23.093d</td><td>2.846262</td><td>Important</td><td>*</td></tr><tr><td>2014EK24</td><td>23.270</td><td>21.8</td><td>-0.6</td><td>177</td><td>27.3-108.4</td><td>0.326"</td><td>2.910289</td><td>Important</td><td>*</td></tr><tr><td>2015XD169</td><td>26.996</td><td>21.9</td><td>0.9</td><td>13</td><td>36.3-38.1</td><td>0.314"</td><td>3.124120</td><td>Important</td><td>**</td></tr><tr><td>2015VO105</td><td>24.039</td><td>22.2</td><td>0.6</td><td>14</td><td>46.4-49.2</td><td>0.249"</td><td>3.288084</td><td>Important</td><td>**</td></tr><tr><td>2011CG2</td><td>21.454</td><td>21.8</td><td>0.3</td><td>49</td><td>37.3-54.9</td><td>0.082"</td><td>3.340296</td><td>Important</td><td>*</td></tr><tr><td>2015XC352</td><td>25.809</td><td>19.0</td><td>4.4</td><td>9</td><td>51.2-122.5</td><td>1.005"</td><td>3.393700</td><td>Important</td><td>****</td></tr><tr><td>2015VV</td><td>24.476</td><td>21.9</td><td>0.4</td><td>25</td><td>46.0-47.1</td><td>0.257"</td><td>3.399528</td><td>Important</td><td>*</td></tr><tr><td>450237</td><td>22.936</td><td>22.3</td><td>0.4</td><td>18</td><td>58.1-59.9</td><td>0.073"</td><td>3.458467</td><td>Important</td><td>**</td></tr><tr><td>2015YK</td><td>25.905</td><td>20.1</td><td>1.7</td><td>20</td><td>65.1-102.3</td><td>0.437"</td><td>3.574354</td><td>Important</td><td>**</td></tr><tr><td>2015XA379</td><td>25.578</td><td>21.1</td><td>-0.5</td><td>126</td><td>8.8-45.5</td><td>29.582"</td><td>3.621501</td><td>Important</td><td>*</td></tr><tr><td>2015TJ1</td><td>22.788</td><td>22.0</td><td>0.0</td><td>155</td><td>34.6-101.7</td><td>0.500"</td><td>3.724905</td><td>Important</td><td>*</td></tr><tr><td>2015YT</td><td>25.827</td><td>21.8</td><td>1.3</td><td>10</td><td>34.7-37.4</td><td>5.588"</td><td>3.902143</td><td>Important</td><td>**</td></tr><tr><td>2004EO20</td><td>22.256</td><td>21.6</td><td>0.4</td><td>36</td><td>24.7-43.7</td><td>0.136"</td><td>4.019102</td><td>Important</td><td>*</td></tr><tr><td>2015VH2</td><td>27.460</td><td>22.9</td><td>0.4</td><td>1</td><td>31.6-31.6</td><td>0.645"</td><td>4.091183</td><td>Important</td><td>**</td></tr><tr><td>2015XO351</td><td>26.633</td><td>22.9</td><td>0.4</td><td>3</td><td>16.9-17.4</td><td>1.486"</td><td>4.145878</td><td>Important</td><td>**</td></tr><tr><td>2015YA</td><td>27.415</td><td>22.1</td><td>1.8</td><td>4</td><td>18.6-20.7</td><td>0.424"</td><td>4.177655</td><td>Important</td><td>***</td></tr><tr><td>2015YM1</td><td>28.375</td><td>22.4</td><td>1.8</td><td>3</td><td>18.4-20.3</td><td>1.170"</td><td>4.230670</td><td>Important</td><td>***</td></tr><tr><td>2015XX128</td><td>26.054</td><td>21.8</td><td>0.6</td><td>34</td><td>61.6-101.5</td><td>0.689"</td><td>4.243125</td><td>Important</td><td>*</td></tr><tr><td>2015LE21</td><td>24.756</td><td>22.1</td><td>0.4</td><td>20</td><td>38.7-41.0</td><td>0.982"</td><td>4.366619</td><td>Important</td><td>*</td></tr><tr><td>253062</td><td>20.758</td><td>21.1</td><td>0.3</td><td>51</td><td>2.1-31.2</td><td>0.237"</td><td>4.382974</td><td>Important</td><td>*</td></tr><tr><td>2015XA352</td><td>21.948</td><td>22.7</td><td>0.4</td><td>7</td><td>23.3-27.4</td><td>4.296"</td><td>4.407326</td><td>Important</td><td>**</td></tr><tr><td>2003GA</td><td>21.083</td><td>22.6</td><td>-0.4</td><td>321</td><td>7.7-77.8</td><td>0.259"</td><td>4.421305</td><td>Important</td><td>*</td></tr><tr><td>2006KV89</td><td>21.279</td><td>21.3</td><td>0.6</td><td>87</td><td>75.0-108.4</td><td>0.223"</td><td>4.471303</td><td>Important</td><td>*</td></tr><tr><td>2015VG150</td><td>25.636</td><td>22.0</td><td>0.8</td><td>13</td><td>8.1-13.4</td><td>0.569"</td><td>4.584884</td><td>Important</td><td>**</td></tr><tr><td>2005TF45</td><td>23.060</td><td>22.4</td><td>0.4</td><td>16</td><td>34.3-42.9</td><td>1.503d</td><td>4.636720</td><td>Important</td><td>**</td></tr><tr><td>2015YA1</td><td>24.569</td><td>20.4</td><td>1.2</td><td>26</td><td>20.0-37.1</td><td>5.553"</td><td>4.677656</td><td>Important</td><td>**</td></tr><tr><td>208023</td><td>20.330</td><td>22.2</td><td>0.1</td><td>69</td><td>50.7-60.8</td><td>0.060"</td><td>4.849432</td><td>Important</td><td>*</td></tr><tr><td>2015YZ</td><td>23.093</td><td>21.7</td><td>0.2</td><td>106</td><td>29.5-62.2</td><td>6.659"</td><td>4.853572</td><td>Important</td><td>*</td></tr><tr><td>2008VA15</td><td>23.478</td><td>21.5</td><td>0.0</td><td>78</td><td>0.6-62.6</td><td>0.164"</td><td>4.857144</td><td>Important</td><td>*</td></tr><tr><td>65717</td><td>20.931</td><td>21.7</td><td>0.0</td><td>152</td><td>47.3-76.2</td><td>0.153"</td><td>4.861691</td><td>Important</td><td>*</td></tr><tr><td>451370</td><td>21.494</td><td>22.9</td><td>0.4</td><td>1</td><td>40.9-40.9</td><td>0.056"</td><td>4.866913</td><td>Important</td><td>**</td></tr><tr><td>2010WT8</td><td>21.863</td><td>22.0</td><td>0.3</td><td>37</td><td>28.3-53.0</td><td>0.657"</td><td>4.866945</td><td>Important</td><td>*</td></tr><tr><td>2013EU9</td><td>21.602</td><td>22.4</td><td>0.3</td><td>19</td><td>21.3-33.4</td><td>0.090"</td><td>4.868039</td><td>Important</td><td>*</td></tr><tr><td>451157</td><td>21.026</td><td>20.7</td><td>0.3</td><td>245</td><td>6.8-91.2</td><td>0.143"</td><td>4.913115</td><td>Important</td><td>*</td></tr><tr><td>2015XP128</td><td>22.984</td><td>20.4</td><td>0.5</td><td>37</td><td>4.9-27.6</td><td>0.844"</td><td>4.948385</td><td>Important</td><td>*</td></tr><tr><td>2011YT62</td><td>22.383</td><td>22.8</td><td>-0.2</td><td>92</td><td>15.3-54.0</td><td>4.511'</td><td>4.952465</td><td>Important</td><td>*</td></tr><tr><td>2015YU1</td><td>24.719</td><td>20.6</td><td>0.4</td><td>48</td><td>10.2-76.6</td><td>10.526"</td><td>5.000217</td><td>Important</td><td>*</td></tr><tr><td>433953</td><td>20.836</td><td>22.0</td><td>-0.2</td><td>269</td><td>21.9-119.3</td><td>0.163"</td><td>5.020270</td><td>Important</td><td>*</td></tr><tr><td>2003QU5</td><td>24.033</td><td>22.7</td><td>0.6</td><td>5</td><td>34.3-34.3</td><td>26.185d</td><td>5.022056</td><td>Important</td><td>**</td></tr><tr><td>2015YH</td><td>27.891</td><td>22.8</td><td>1.4</td><td>1</td><td>14.7-14.7</td><td>7.062"</td><td>5.025272</td><td>Important</td><td>***</td></tr><tr><td>416151</td><td>20.549</td><td>21.8</td><td>0.3</td><td>87</td><td>35.3-53.6</td><td>0.037"</td><td>5.067566</td><td>Useful</td><td>*</td></tr></tbody></table>

either as an input file for further processing or as a spreadsheet.

Table 5 shows the same output in Table 4 with an observational priority extended to objects with smaller sizes; the lower limit on the object size has been relaxed

from 50 m to 5 m producing an output more fitting to rapid response systems or space missions directed toward very small targets. In this case, out of the visible objects two were very small and accessible at less than 2 km s⁻¹ gaining a very high ranking in the resulting table.
CONCLUSIONS

The present NEA discovery rate has surpassed 1500 objects per year, thus calling for extensive observation campaigns devoted not only to improve the orbit determination accuracy, but also our knowledge of their physical properties. Building up on previous successful experiences devoted solely to astrometry, a prioritization tool for driving NEA follow-up physical observations has been developed in order to provide support to observers in optimizing their effort.

The algorithm, in its general formulation, allows generating ranked lists of potential NEA targets (Physical Properties Priority List) and it has been designed to account for a number of external constraints (e.g., visibility, size, accessibility). An application specifically addressing the NEOShield-2 scenario, which focuses on objects in the 50 m–300 m size range that can be visited by space missions, has been implemented and made publicly available on the project website.

Two ranking criteria have been introduced: Importance is linked to both accessibility and size of a target; Urgency takes into account the visibility constraints and most notably the time span left for planning and executing follow-up observations. The priority rankings can be customized by changing the input parameters (e.g., the telescope limiting magnitude, the accessibility estimate, etc.) of the underlying geometrical and dynamical models in order to cover a wide range of different observational and mission-related scenarios.

As an example, in the present deployment the prioritization algorithm has been tuned to the NEOShield-2 requirements, but the shape of the DIM function can be easily changed if one wishes to extend the observational priority to smaller sizes. This could be relevant since an ever increasing share of the present discoveries belong to the sub-50 m size range. Relaxing the lower limit on the object size from 50 m to 5 m, the prioritization algorithm produces an output more fitting to rapid response systems or space missions directed toward very small targets, for example, the original ARM mission scenario (Brophy et al. 2011, 2012; Brophy and Muirhead 2013). By comparing the two prioritizations (Tables 4 and 5) it is possible to see that, as expected, in the latter case a higher number of objects with high ranking on both criteria (i.e., very important and very urgent) are found.

The prioritized lists produced by the P3L software have been proven also useful in helping to resolve conflicting requirements imposed on the same parameter, for example, a long time left to the end-of-visibility would make an observation less urgent but at

the same time very appealing because of the possibility of observing the same object at different phase angles.

Future implementations or upgrades to the algorithm may include either different parameterizations of some functions discussed in the text, or entirely new components. For example, an evaluation of urgency based on future observability at upcoming apparitions is feasible, although technically complex due to the need to carefully evaluate the future ephemeris uncertainty of the object.

Physical Properties Priority Lists are produced either daily or on-demand (i.e., at any future date) for the NEOShield-2 project and are publicly available at the NEOShield-2 NEO Properties Portal. We would like to remark that the P3L tool is intended as an aid to experienced observers, who are ultimately responsible for the actual choice of targets and observation time, which may take into account additional considerations and constraints.

*Acknowledgments*—We acknowledge the financial support from the NEOShield-2 project, funded by the European Commission's HORIZON 2020 program (contract PROTEC-2-2014-640351). This work was also partially funded under ESA contract 4000112366 SSA P2-NEO-I NEO Precursor Services. The postgraduate course in Space Science and Technology of the Department of Mathematics, University of Rome Tor Vergata is gratefully acknowledged. The P3L is available online thanks to the invaluable support of Esther Parrilla, Maria del Mar, Alvaro Ortiz, and Juan-Luis Cano (Deimos Space). Finally, we would like to thank the referees of this paper for their helpful suggestions.

*Editorial Handling*—Dr. Josep Trigo-Rodríguez

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