A quantitative NEO hazard mitigation scale

A quantitative NEO hazard mitigation scale

Available online at www.sciencedirect.com Acta Astronautica 54 (2004) 755 – 762 www.elsevier.com/locate/actaastro A quantitative NEO hazard mitigati...

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Available online at www.sciencedirect.com

Acta Astronautica 54 (2004) 755 – 762 www.elsevier.com/locate/actaastro

A quantitative NEO hazard mitigation scale John L. Remo1 Harvard-Smithsonian Center for Astrophysics, Mail Stop 18, Cambridge, MA 02138, USA Received 20 June 2003; accepted 3 November 2003

Abstract A hazard mitigation scale is presented that quanti+es the danger from a potential near-Earth object (NEO) impact with Earth in terms of the energy required to perturb the threatening NEO’s orbit to avoid collision in the foreseeable future. The required energy is based on NEO mass, anticipated velocity change to avoid collision, and momentum coupling coe3cient for the particular interaction. The momentum coe3cient can be empirically determined and depends on the type, intensity, placement of the interaction energy, and target materials. Reliable experimental values for momentum coupling coe3cients are provided. c 2003 Elsevier Ltd. All rights reserved. 

1. Introduction It is generally understood among scientists that sooner or later a near-Earth object (NEO) will impact with Earth. The odds may be that this event will occur later rather than sooner, but there is no way to know. To somehow deal with the perception of this threat in a quantitative manner hazard scales based on the severity of the possible impact have been put forth. Since 1997 two related near-Earth object (NEO) impact hazard scales, the so-called Torino and Palermo scales have been proposed [1–3]. Much discussion on the relative merits of these putative scales has ensued since their publication. The former is intended as a means to communicate the potential NEO hazard risk to the public, while the latter is intended for use by specialists. Discussion of these

1 Current address: Quantum Resonance Inc., 1 Brackenwood Path/ Head of the Harbor, St. James, NY 11780, USA. E-mail address: [email protected] (J.L. Remo).

scales can be obtained from the NASA, JPL website (neo.jpl.nasa.gov/risk/doc/pale...). Both scales utilize numbers based on impact probability, impact energy, and (for the Palermo scale) the time to impact to convey a threat associated with the expected damage. These scales discuss potential catastrophic damage to planet Earth rather than addressing the issue of impact mitigation. Neither addresses energy levels required for remediation of the threat. The proposed hazard mitigation scale, within a context of simplifying assumptions, is designed to be more practical in so far as it quanti+es energy requirements for removal of a potential NEO threat by means of orbit changing momentum coupling. In this manner the proposed scale provides enlightenment regarding the scale of the threat in terms of the energy required for mitigation based on NED orbit calculations and experimental data on what is thought to be putative NED materials, i.e. meteorites and comet-like ices. However, the analytical framework presented for the proposed NEO hazard mitigation index, while related to orbital mechanics, in no way should be construed as solving an orbital mechanics problem whose solution

c 2003 Elsevier Ltd. All rights reserved. 0094-5765/$ - see front matter  doi:10.1016/j.actaastro.2003.11.001


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requires a careful, step-by-step numerical integration over extended and distinct time intervals. The impact risk, associated hazards, and mitigation indices and scales change over time, as is well demonstrated by observation. Rather, the objective of the proposed scale is to provide in general terms a physically and quantitatively meaningful NEO hazard mitigation scale. 2. The hazard awareness level and hazard mitigation index In this communication a previously de+ned hazard awareness level (HAL) and hazard mitigation index (HMI) are used as a basis for a proposed hazard mitigation scale that provides operational estimates of NEO hazard reduction in terms of energy requirements for mitigation [4,5]. The HMI is an estimate of the energy required to perturb the orbit of a NEO that could potentially impact Earth such that the threat of Earth impact is mitigated in the immediate future. This approach infers the energy requirements to remove threats rather than to describe some eHects of terrestrial impact, an associated result may be to create alarm. Since it is generally agreed that a catastrophic Earth impact is a totally unacceptable outcome, it is far better to emphasize mitigation eHorts than provide disaster relief, although disaster relief should be part of the contingency plan. Generally speaking, deJection is preferable to demolition, which requires greater energy and generates greater outcome uncertainty. Demolition, is not included in this analysis. The HAL is based on reliable observations and computations over an extended period of time. It determines the required (perturbation) “eHective orbital velocity” change, dv(t), required to avoid impact [4], dv(t) = ( − )R=;


where  is the number of Earth radii, R, to establish a safe distance,  is the estimated distance, also in Earth radii, of closest approach to Earth,  is the estimated available time to execute necessary maneuvers to avoid a NEO impact, and  ¿ . It is important to understand that applied velocity changes are likely to be time dependent. As has been previously discussed [4], this secular dependence places an added burden on any mitigation mission. Orbital rami+cations of this temporal variability have very recently been com-

puted elsewhere for some +ctitious cases similar to real objects [6]. As expected, results from this computational exercise indicate the required dv(t) values imparted to threatening NEOs to avoid Earth impact depend largely on the epoch of interception and orbital properties of that object. This conclusion is also applicable to the analyses presented in reference four of this work. While the information provided by (1) is of academic interest, it does nothing to alleviate potential threats. To achieve Earth threat reduction the HMI (equivalent to energy, E) required to execute the orbital perturbation, must be determined. An appropriate equation [5] is HMI ≡ E = M dv=CM :


The energy, E, required to eHect orbital perturbation depends on NEO mass, M , velocity change, dv, and momentum coupling coe3cient, CM . CM is a function of the type of interactants, intensity method of delivery, and NEO material properties, and as such must be determined empirically, depending on the NEO material properties and physical con+gurations encountered [4,5,7–10]. 3. Determination of parameters Reliable determinations of possible values for M , dv, and CM represent critical factors in any NEO mitigation scheme for whatever the method and energy level of interaction is chosen. First, astronomers will have to tell us the value of the mass M (1012 Kg), estimated from the absolute magnitude H according to M = 1:6D3 ;

(3) 3

where the density is assumed to be 3 g=cm and D is in kilometers, D(km) = 1=[1:585(H −18:0) ]:


Mass is estimated from the size (which depends on an assumed albedo) and material composition. Clearly, there are numerous observational uncertainties and errors in correlating mass with diameter and diameter with H . Ideally, active reconnaissance can assist in estimating this value to within a reasonably small error. Another uncertainty is associated with determining the magnitude and direction of orbital deJection, dv,

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required to remove the impact threat in the foreseeable future. As described in [1], dv is determined by the closeness to Earth and the time available for interaction. But in a real situation, one does not necessarily have to apply the exact value of dv. One can choose or be constrained by the orbital properties of the threatening NEO to apply a somewhat diHerent velocity change earlier or later than required. A factor contributing to this decision could be, for example, the distance (from Earth) of interception. Each NEO mitigation interception is in this sense circumstantial depending on the available time to prepare an interception mission, and the (astronautical, astrodynamic, and political) means at one’s disposal for interception. In such cases the HMI serves as guide rather than arbiter. In any case, the +rst step in determining an operational dv is to reliably characterize the orbit. Ordinarily, this requires a set of orbital coordinates based on several days of observations, and generally speaking, the greater number of orbital data points, the greater the accuracy of the orbit. The availability of recovery and archival data is also desirable if not necessary. Sometimes overlooked, but absolutely necessary are the accurate and reliable orbital computations such as those typically carried out on a regular basis by the Minor Planet Center in Cambridge, Massachusetts and other groups worldwide. It is also important to note that the value of dv is not based on the NEO orbital or impact velocity (energy). This fact is the primary diHerential between the putative hazard mitigation index and the other hazard impact scales. Basing a NEO hazard mitigation scale on the energy required to remove the threat rather than in terms of the magnitude of the threat, provides a scale that is not a “scare index.” 4. Uncertainties in and importance of using CM We have introduced the concept of the momentum coupling coe3cient CM into (2). Since this parameter is not well known to most scientists, an explanation is in order. In terms of the dynamics of the orbital perturbation, CM represents the momentum imparted to a target for a given amount of energy and is sometimes described in mixed units of dyn-s=J = 10−5 s=m. The reason for the mixed units is that the magnitude of


momentum coupling for a given mount of energy is extremely low for most materials. In fact, this is the core of the problem in changing an orbit with a limited amount of applied energy. Because CM deals with the response of natural materials to diHerent types of interactants (dynamic means used to change the orbit) at diHerent energy levels, its value will generally be a major uncertainty which must be dealt with in an empirical manner. In general, high-energy density interactions are very di3cult to model and complex hydrocodes are required to obtain accurate predictions. However, as a guide simple plasma energy balance can be used [7,10,11] for pure materials that provides fairly accurate estimates of target coupling coe3cients. For the NEO hazard mitigation index, values associated with CM must be experimentally determined on NEO-like materials. This has also been achieved [5,7–9], providing reliable values in terms of the magnitude of demands of the NEO mitigation mission. Nonetheless, such multi-component objects such as asteroids increase the di3culty in predicting dynamic eHects from an impulsive force. The values of the CM depend on the several interacting parameters which eHect momentum coupling including: (1) NEO material chemical composition (e.g. stony solid, metallic, or comet-like). There are variations within this classi+cation because unlike minerals, natural materials like rocks have neither a de+nite composition nor crystal structure, but are aggregates varying in many respects such as composition, texture, porosity, and association. (2) Large-scale NEO target surface morphology, internal structure (solid or rubble pile, etc.) and NEO physical (rotation) dynamics. The NEO rotation structure will to a large extent depend on its collision history. (3) Type of the interaction. DiHerent types and placement of energy interactants include pulsed or continuous laser, mechanical impact, mechanical pushing or thrusting, X-rays, concentrated solar, simple reJectivity, neutrons, etc.). Different materials will have diHerent interaction cross-sections and yield strengths. (4) The energy density and time scale over which the energy is delivered to the target will determine heating, vaporization, ablation, strain rate,


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and shock wave eHects, all of which strongly inJuence momentum and energy transfer in the immediate region of the impact. (5) Because asteroids typically spin about their axes while orbiting the Sun, the placement of an attached thruster, (requiring NEO de-spinning) or nuclear explosives in either stand-oH, surface, or embedded mode must be taken into account in considerable detail. While energy requirements for NEO mitigation tend to point towards the need for high-energy density sources, it is important to bear in mind that CM is not necessarily associated with any one particular method or level of momentum coupling. In many cases, the lower the energy density of interaction, the higher is the reliability and the magnitude of CM . 5. Radiative transfer processes For processes involving radiative transfer, CM is often conveniently expressed in terms of the Juence, F [11], which is a measure of the total energy content per unit area (often for pulsed or continuous energy deposition) or the net intensity deposited on the target over a period of time such that CM = m dv=F = (impulse=area)=F = 1=velocity;


m, is the areal mass (mass per unit area). However, F may also used for primarily non-radiative processes such as mechanical impact or mass driver processes. In using CM , NEO structural integrity depends on the uncertainty of provenance which must also be taken into account. For example, there is considerable speculation and some indirect evidence as to whether some NEOs are highly porous and/or loose aggregates of material. If this is the case, values of CM must be speci+cally determined for these types of materials interactions. If reliable and accurate values or dv(t), M and CM can be obtained, (2) represents a simple, yet viable relationship to determine the energy, E, required for mitigation, and, therefore, for a reliable HMI. Using CM as derived from laboratory experiments on NEO surrogate materials that simulate eHects of various high-energy density interactions to some extent obviates the need to test deJection methods on

real, so-called innocuous NEOs as suggested by others 2 [12]. But such large scale testing in space is not completely without peril. NEO orbits are inJuenced by many gravitational bodies and the perturbation of an otherwise harmless object could result its becoming a threatening object. Also, because of the possibility of enormous energies needed over short periods of time, such methods could involve the use of nuclear explosives in space. Furthermore, NEDs appear to diHer considerably in their material properties. Interactions with an arbitrary test asteroid could provide misleading results. At the present time, with no clear and present danger from a threatening NEO, experiments related to planetary defense must be pursued strictly within the framework of international law. This includes conforming to the Comprehensive Test Ban Treaty and the 30 year old Non-Proliferation Treaty. Furthermore, to provide safeguards and ensure international participation, the overall organizational structure of dealing with NEO mitigation should in some way be done as an international eHort within the a United Nations framework [13]. 6. The hazard mitigation index and the Cambridge scale If the proposed hazard mitigation scale is adopted, it is suggested that the HMI scale be called the Cambridge Scale (CS) primarily in recognition of the many years of invaluable service to the astronomical community provided by the Minor Planet Center (MPC) in Cambridge MA, and also from the ongoing services of the (Cambridge, UK) Ccnet to the NEO dialogue. It was the data originally computed from the MPC that allowed the computations of the HALs and HMIs which are required for hazard mitigation. From (2) a HMI scale may be derived based on the energy required for orbital remediation to prevent Earth impact. A previous computation of potential PHOs [4] indicate that 1997 XF11 was thought to 2 The mathematical de+nition of Juence, F, is F(z) = iI (z; t) dt, where I is the intensity. F is a measure of the total energy content deposited on a surface and should not be confused with photon Jux. The Juence integral does not represent any speci+c form of energy.

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have required, before its orbit was better determined (which brings up observation and computation issues beyond the scope of this communication [14]), about 0.9 petajoules of energy to render it no longer a threat to Earth [4]. Because the magnitude of the (HMI) energy can vary from 0 to perhaps tens or even hundreds of petajoules, it is advantageous to use a logarithmic scale to index the energy needed to change the NEO’s orbit, i.e., Cambridge Scale (CS) =log [E=1010 ] = [HMI=1010 ];


where the HMI is equal to the energy, E, required for mitigation. The 1010 baseline divisor for the energy required for mitigation, the logarithm of which provides the CS, is chosen because an impactor that requires only 1010 J for mitigation is likely to be so small and consumed in its entry into Earth’s atmosphere, that mitigation is not necessary. Such a small object would also be di3cult to detect. On the CS such an event would register at 0 or less, indicating a threshold value for which no remediation is required. Of course, this situation could change in time thereby changing the CS. For values greater than zero, CS values are computed in a continuous manner. For the reasons discussed above, CS values have physical meaning. In Table 2 CS values are tabulated for several NEOs that are Earth-crossing asteroids (ECAs). For one reason or another, these asteroids were at one time thought to be potentially hazardous. A value for CM of 0.001 is assumed for the momentum coupling coe3cient. In practice, this number can easily vary by a factor of two or even three in either direction depending on the material response to the interaction. How one determines the values for available time, radius and mass underscore the tenuous nature of the other parameters used in (2). Fortunately, in many if not most cases, these uncertainties can be removed by diligent observation (both discovery and follow-up), vigorous reconnaissance, and careful laboratory experiments. Also, appropriately planned missions can be designed such that back-up systems can provide additional safeguards against uncertainties in the observational and empirical parameters. On the CS scale tabulated the well publicized and somewhat (at that time) controversial event, 1997 XF11, would be about


4.95. A value of 10 on the CS would correspond to a PHO that required 1020 J of energy to change its orbit. This is an immense amount of energy which corresponds to 100; 000 J or the equivalent of about 24; 000 M ton of TNT. Therefore, in practice a CS rating of 10 should serve as a reasonable upper limit, although if the need arises the continuously variable CS can rise. An advantage of this scale is that it shows how immense the required energies must be to realistically consider NEO mitigation for a massive object. Returning to Table 2, where the CS scale ranges from −1:7 for 1991 BA and 1994 GV to 4.95 for 1997 XF11, one can in retrospect discuss the outcomes of these NEO threats. 1991 BA and 1994 GV, had they impacted Earth would likely have been consumed by Earth’s atmosphere. Their negative CS values indicate that action would not have been warranted. 1997 XF11 and 1999 AN10 (which are 4.95 and 4.05 on the CS) after some initial concern were found not to pose an immediate threat following input from archival data. After follow-up observations within the year, 1999 RM45 2000 BF19, and 2000 EH26 were also not found to be an immediate threat. 1998 OX4, because of its size, alone remained a serious threat, with a value 1.89 on the CS, until August 2002 when it was accidentally rediscovered [15]. 1998 OX4 was initially observed for only 9 days in 1998, and the limited data derived in this period were not su3ciently accurate for a longer term orbit prediction. But the additional data derived from the recovery observations allowed a more accurate orbit computation which, happy to say, has placed OX4 out of harms way. That is to say that it not a threat in the foreseeable future. Only 1995 CS remains a potential threat, although it may be small enough to be destroyed by Earth’s atmosphere. 7. Long-term prediction and chaotic orbits If an international search and tracking eHort is established, there is a good chance that Earth-crossing asteroids (ECAs) often with somewhat regular periods will be discovered and their orbits computed with a long-term prediction. Hopefully, this should allow enough time to mount a deJection mission. In such cases the application of a hazard mitigation


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scale can be computed in a straightforward manner as shown by the examples in Table 2. Almost any asteroid with a chance of impacting Earth is likely to cross Earth’s orbit a su3cient number of times to permit detection and orbit determination well before a possible impact occurs. Of course, there are always exceptions [16]. Because there is no systematic survey for potentially hazardous comets which can approach Earth at almost any angle, discovering a threatening comet can be statistically problematical. It is quite possible that there would be little no warning time which means few, if any, mitigation options would be available. Another potential problem in orbit prediction is that, especially in the case of comets, minor bodies in the solar system are thought to be capable of very rapidly jumping among resonance orbits [17]. Comets, in particular, perform this dynamic activity about the sun in resonance with Jupiter [18]. This phenomenon is distinct from the chaotic motion derived from the three body problem in which NEOs are susceptible to being shifted into chaotic orbits, especially over the long term. The Kolmogorov, Arnold, Moser Theorem [19,20] provides insight into the manner in which planets orbit the Sun, and indicates that although the planets orbit in a predictable and stable fashion, there can be an element of chaos in this motion. This eHect is small and may take millions to billions of years to manifest itself in a way that would cause an appreciable eHect on the orbital dynamics of NEOs. For the short time scales considered in the hazard mitigation scale this slow chaotic instability could, but is not likely, to present a serious problem. But low-energy (resonance) transfers can rapidly give rise to chaotic dynamics. Under certain conditions weak capture can give rise to a complicated chaotic dynamics due to the existence of so-called hyperbolic invariant sets [21]. Such chaotic motions as discussed above are beyond the scope of this paper, but do indicate how fundamentally complicated and often unpredictable are deterministic orbital dynamics when there are more than two bodies interacting gravitationally [22]. When the gravitational forces are combined with the non-trivial non-gravitational forces, to which (active) comets are often susceptible, the computation of a hazard scale is problematical. For these reasons any scale could only serve as secular estimate of the threat level.

8. Conclusion A quantitative method to assess the hazard level from a potential NEO impact with Earth has been presented. The hazard level is proportional to the Table 1 (a) High-intensity laser radiationa and (b) soft (∼ 1 kev) X-radiationb experimental values for the coupling coe3cients CM to diHerent materials properties classes of meteorites [26,27]. Target material

Fluence (J=cm2 ) CM × 10−5 (s/m)

(a) Laser radiation Pure aluminum Al Al

21.6 21.6

Fe Ni meteorites (NEO 3 material) Og 21.6 Og 21.6 Om


Stony meteorites (NEO 1,2 material) Mesosiderite (NEO 2) 22.4 Mesosiderite 22.4

210 127 107 120 111 74 67

LL6 (NEO 1)



CV3 (NEO 1)



(b) soft (∼ 1 keV ) X -radiation Fe Ni meteorites (NEO 3 material) Og 945


Stony meteorites (NEO 1,2 material) Mesosiderite (NEO 2) 352 LL6 (NEO 1) 453 CV3 (NEO 1) 352 CV3 453

4.0 3.9 2.5 1.6

a The meteorite targets were optically con+ned, thereby enhancing the momentum coupling by a factor of about 10 –30. Details of this experiment are in [9]. Experimental momentum coupling coe3cient values for uncon+ned (untamped) Al are 5.5 –6:0 × 10−5 [10,11]. b The meteorite targets were not optically con+ned, thereby not enhancing the momentum coupling. Details of this experiment are in [8]. Experimental values were measured from the Z-accelerator. Other experimental values of CM for soft X-ray coupling coe3cients from experiments range from 4 to 30 × 10−5 for stand-oH X-rays with energies from 5 to 100 kev. Con+ned nuclear explosive tests give values 20 –900 × 10−5 , depending on the con+ning material [5]. Clearly, a con+ned (buried) nuclear charge can be a hundred times more e3cient in momentum coupling.

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Table 2 Application of the Cambridge Scale (CS) to nine well-documented near-Earth asteroid cases [4] NEO 1991 1994 1995 1997 1998 1999 1999 2000 2000

BA GV CS XF11 OX4 AN10 RM45 BF19 EH26


dv (m=s)

D (km)

M (1012 kg)

E (1015 J)

CS b

7 40 42 28 35 30 38 17 36

0.29 0.05 0.05 0.07 0.06 0.07 0.05 0.12 0.06

0.0008 0.013 0.04 2.0 0.2 1.0 0.6 0.6 0.2

0.000008 0.000005 0.0001 12.8 0.0128 1.6 0.346 0.346 0.128

0.0000002 0.0000002 0.000005 0.896 0.00077 0.112 0.0173 0.0415 0.00077

−1.7 −1.7 −0.3 4.95 1.89 4.05 3.24 3.62 1.89

The mass, M , of the asteroids are assumed, for the purpose of calculation, to have a density of 3:6 g=cm3 . a  represents the time from +rst discovery, o, less 5 years preparation time for the mitigation action to commence. b CS = log (E=1010 J).

logarithm of the amount of energy input into the NEO to deJect the object out of the Earths path. The (payload) amount of energy required is based on the momentum coupling coe3cient. The mitigation energy will depend upon CM for the interactant placement, as shown in Tables 1a and b. Hence, the location of the energy will also play a critical role in determining the magnitude of CM , as shown in Tables 1a and b. For example, diHerences among stand-oH, surface, and embedded explosives can effect the momentum transfer by factors of 100 times or more. Ordinarily, subsurface momentum coupling will provide the highest values for CM [23], but structural properties and rotational dynamics of the target NEO must be carefully taken into account. For a subsurface or embedded explosion, the porous nature of a NEO could work to the mitigation mission’s advantage by localizing the explosive eHects on the NEO while maximizing the amount of (rubble) mass ejected. The ECA case histories underscore that even under ideal circumstances how di3cult it is to de+ne a hazard mitigation scale and to predict the ultimate orbital outcome of a mitigation mission for a potentially hazardous object. For the case of ECAs whose orbits are generally well-understood, Table 2 shows how initial orbital data can be (alarmingly) misleading. For comets, the situation is much more problematical from the observational, orbit prediction, and mitigation perspective. As a +rst step, one cannot overestimate the importance of recovery observations to

provide follow-up data. For mitigation, knowledge of material properties is of paramount importance. Here, knowledge of the material properties is seriously lagging. The CS hazard mitigation index cannot predict orbital outcomes, but the CS can serve as a guide to estimating the amount of energy it would take to deJect a threatening NEO. The CS does not presume or favor any particular method of interaction or time frame for interaction. A potential orbit modi+cation must be evaluated on its own merits. The CS is applicable to gentle continuous tugs; laser, solar or powerful nuclear standoH irradiation or even a sub surface nuclear detonation, or even mass wasting or hypervelocity impact. Approaches to orbit change must convert energy to momentum to eHectively change an orbit. That is the key. The results in Table 2 also suggest that premature public announcements of impending doom based on preliminary orbital data are nugatory and even counterproductive. Such announcements can cause alarm or even mild panic and ultimately undermine credibility which is not in anyone’s best interest. In any case, even with a reliable quantitative NEO hazard mitigation scale, the astrodynamics [24] and astronautics [25] of a NEO interception mission will pose formidable problems in their own right. Acknowledgements I thank B. Marsden and G. Williams at the MPC for providing orbital data used in Table 2, Sandia national


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laboratory for providing the research facilities where experiments could be conducted and E. Belbruno, P. Hammerling, and P. Sforza for helpful comments.

[13] [14]

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