|| Implications of the centaurs, Neptune-crossers, and Edgeworth-Kuiper belt for terrestrial catastrophism

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397

The Geological Society of AmericaSpecial Paper 505

2014

Implications of the centaurs, Neptune-crossers, and Edgeworth-Kuiper belt for terrestrial catastrophism

Duncan Steel*Centre for Astrobiology, University of Buckingham, and Armagh Observatory, UK

ABSTRACT

The discovery of many substantial objects in the outer solar system demands a reassessment of extraterrestrial factors putatively implicated in mass extinction events. These bodies, despite their formal classifi cation as minor (or dwarf) planets, actually are physically similar to comets observed passing through the inner solar system. By dint of their sizes (typically 50–100 km and upward), these objects should be considered to be giant comets.

Here, I complement an accompanying paper by Napier, who describes how giant comets should be expected to cause major perturbations of the interplanetary envi-ronment as they disintegrate, leading to fi reball storms, atmospheric dustings, and bursts of impacts by Tunguska- and Chelyabinsk-class bodies into the atmosphere, along with less-frequent arrivals of large (>10 km) objects. I calculate the terrestrial impact probability for all known asteroids and discuss why the old concept of single, random asteroid impacts causing mass extinctions is defi cient, in view of what we now know of the inventory of small bodies in the solar system. Also investigated is how often giant comets might be thrown directly into Earth-crossing orbits, with implica-tions for models of terrestrial catastrophism.

A theme of this paper is an emphasis on the wide disparity of ideas amongst planetary and space scientists regarding how such objects might affect the terres-trial environment, from a purely astronomical perspective. That is, geoscientists and paleontologists should be aware that there is no uniformity of thought in this regard amongst the astronomical community.

*Contact address: P.O. Box 9461, Marion Square, Wellington 6141, New Zealand; e-mail: [email protected].

Steel, D., 2014, Implications of the centaurs, Neptune-crossers, and Edgeworth-Kuiper belt for terrestrial catastrophism, in Keller, G., and Kerr, A.C., eds., Volca-nism, Impacts, and Mass Extinctions: Causes and Effects: Geological Society of America Special Paper 505, p. 397–410, doi:10.1130/2014.2505(21). For permission to copy, contact [email protected]. © 2014 The Geological Society of America. All rights reserved.

PREAMBLE

Papers appearing in this volume result from the international conference on “Volcanism, Impacts and Mass Extinctions.” While that meeting had “impacts” (meaning hypervelocity arriv-als on Earth of extraterrestrial objects) in its title, comparatively

little expertise in that particular area was represented amongst the attendees. That is not, in itself, surprising, and this is also refl ected in the fact that the Geological Society of America (rather than some astronomical society) is publishing these papers.

What I found more surprising was the apparently limited knowledge of the huge advances made in astronomical knowledge

on August 26, 2014specialpapers.gsapubs.orgDownloaded from


398 Steel

and understanding of the smaller bodies in the solar system over the past two decades, with the discovery of myriad asteroids and comets in distinct populations that had hitherto only been sus-pected to exist. That is, in terms of the cosmic environment in which Earth (and therefore, obviously, the biosphere) orbits the Sun, there are now recognized by space scientists to be:

…more things in heaven and earth, Horatio, Than are dreamt of in your philosophy.

—William Shakespeare, Hamlet, Act 1, Scene 5.

In view of this, I have prepared this report in a deliberately chatty manner, contrary to the practice of most researchers, in the hope that it will be more accessible and therefore more useful than most dry, abstruse scientifi c papers.

This report is not intended as a complete review of the fi eld, however, and I have taken very much a personal view. Others in the worldwide astronomical–planetary science community have quite different opinions on substantive matters discussed herein; and so, to the reader: caveat emptor.

Further, as I explain herein, I have benefi ted from the fact that there is also a paper in this volume written by Bill Napier, who has covered much material that otherwise I might have needed to discuss here; thus my paper should be read in conjunc-tion with that of Napier (this volume).

To bring this preamble to a conclusion, I explain that my comment about there being “limited knowledge” of astronomi-cal topics represented at the conference is intended solely as an observation, and not in any way a criticism of either the attendees or the organizers, who come predominantly from the geologi-cal and paleontological fraternities and sororities. For myself, I found the conference extremely interesting and useful specifi -cally because in those geoscience areas I must confess to pro-found ignorance and a lack of solid background. I sat and listened enthralled for three days, trying to understand as best I could what various experts in the fi elds of geology and paleontology were describing in terms of their research outcomes. Very often I found myself thinking: “Yes, that is just what one might expect to result on Earth from a major upset of the inner solar system environment as a big comet breaks apart, spreading its decay products around, rather than the simple (and rather passé) notion of a random single large asteroid strike.”

What I have tried to outline here, then, is a picture of what we now know the outer solar system to contain in terms of giant, comet-like bodies; how and why they are on unstable orbits (on time scales of millions of years); and what this must mean for the inner solar system and therefore the terrestrial environment.

INTRODUCTION

The outer solar system contains a cosmic zoo of large, cold, solid objects variously classifi ed as being centaurs, Edgeworth-Kuiper belt objects (EKBOs), Neptune-crossers, dwarf planets,

minor planets1, and (giant) comets, although other terminology, classifi cations, and subdivisions are also in use amongst the plan-etary science community (e.g., trans-Neptunian objects [TNOs], cis-Neptunian objects, plutinos, cubewanos, scattered disk objects [SDOs], distant detached objects [DDOs], inner Oort [or Oort-Öpik] cloud objects). Considering that the fi rst centaur2 was only discovered in 1977, and the fi rst trans-Neptunian object3 was discovered in 1992, this proliferation of terms is bewildering to the ingénue.

It is lamentable that the reclassifi cation in 2006 of some of the “minor planets” (and one “planet”: Pluto) as “dwarf planets” by the International Astronomical Union (IAU) proceeded as it did, because the opportunity was missed to rectify the anomalous situation whereby many objects that appear stellar to the eye in a small telescope (i.e., literally “asteroidal”) might have been bet-ter defi ned by dint of their physical nature as being “giant com-ets.” That is, many centaurs, Neptune-crossers, and Edgeworth-Kuiper belt objects are actually icy bodies that would certainly be counted as being comets should they have been discovered on paths bringing them suffi ciently close to the Sun (e.g., the water-ice initiation-of-sublimation heliocentric distance of around 2.9 astronomical units [au]) such that cometary emissions of gas and dust would soon have been observed. That is, rather than appear-ing asteroidal, they would be seen to be “hairy stars” (the etymol-ogy of the word “comet”). The revised classifi cation of comet-like bodies suggested by Horner et al. (2003) has, in my opinion, much to recommend it.

A particular example is the centaur (2060) Chiron = 95P/Chiron. The fi rst designation there signifi es Chiron to be a minor planet; the second designation signifi es a periodic comet, number

1The term “minor planet” is that which the International Astronomical Union applies to those objects that most people call “asteroids”; that is, these are broadly synonyms. For this reason, I will use the term “asteroid” in this pa-per to refer to subplanetary rocky/metallic bodies in inner solar system (cis-Jovian) orbits.

2Here I have classed (2060) Chiron as the fi rst centaur, in terms of the rec-ognition of such objects constituting a new class of outer solar system body, although (944) Hidalgo was discovered over half a century earlier, in 1920. “Centaurs” are “small” (compared to major planets) outer solar system bodies that are observed mainly in the region between Jupiter and Neptune and cross the orbit of at least one of the Jovian planets: A technical defi nition of centaurs has been discussed recently by Emel’yanenko et al. (2013), and their defi nition would exclude Hidalgo on the basis of its relatively small perihelion distance. The largest-known centaur is (10199) Chariklo, which is about 260 km across; (2060) Chiron is around 200 km in size. Several of the known centaurs display comet-like outgassing and have refl ectance spectra similar to volatile-rich car-bonaceous (C-type) asteroids and cometary nuclei, and so it is not clear whether they should be classed as minor planets (as they generally are), or comets. Be-cause their physical nature appears to be basically cometary, I argue in this paper that they should be classifi ed as being “comets.”

3The fi rst trans-Neptunian object to be discovered was 1992 QB1, hence the peculiar class name “cubewano,” although the existence of such a belt of large bodies had been predicted far earlier, resulting in the term “Edgeworth-Kuiper belt,” containing the names of those who had suggested its unseen existence in the 1940s and 1950s, respectively.



Implications of the centaurs, Neptune-crossers, and Edgeworth-Kuiper belt for terrestrial catastrophism 399

95 in the IAU list of such bodies. This double-designation occurs because it was classifi ed as a minor planet on discovery in 1977 but was later recognized to exhibit comet-like outgassing (and one might argue that it should actually be called “95P/Kowal,” for the discoverer). Many such crossover objects4 are now known to exist, confusing the IAU’s illogical classifi cation scheme.

This mixed bag of distant objects contains bodies that must occasionally be forced to misbehave through long-term gravi-tational perturbations, collisions with each other, and/or close encounters with the gas giant planets. In a small fraction of such contingent events, the intact objects (or perhaps their decay prod-ucts) will be thrown into orbits with small perihelia. Then chaos will reign in the inner solar system as they disintegrate due to thermal stresses and other factors yet to be fully comprehended.

I am indebted to an accompanying paper by my long-time colleague Bill Napier in which he discussed a range of consider-ations with regard to the feasible consequences of a giant comet entering the inner solar system and becoming trapped in a cis-Jovian orbit, especially in terms of what this could mean for the biosphere. Those are largely matters, then, that I do not need to repeat herein, with an adequate prefatory statement regarding the present paper being contained in the next paragraph.

Consider what might happen should a 100 km object (i.e., a giant comet) be diverted fi rst into an orbit with perihelion dis-tance q < 1 au, and then into a cis-Jovian orbit similar to that of 2P/Encke. Such an orbit is dynamically stable for a period of order 105 yr, over which time it would be expected (based on the disparate behavior of observed comets) to undergo a hier-archical disintegration into a vast complex of smaller bodies (which we might classify as minor planets, near-Earth asteroids, comets, meteoroids, and dust). The currently observed Earth-crossing interplanetary dust and meteoroid complex has a total mass equivalent to a comet or asteroid only ~20 km in diameter, so that the infl ux of such small debris to Earth would be hugely enhanced, with substantial environmental effects, in this giant-comet-breakup scenario. A 100 km comet, if subdivided into

neat 1 km fragments, could also result in catastrophic terrestrial impacts on a once-per-century time scale for a million years.

This might be considered to be wildly speculative, but our expanding knowledge and understanding of the outer solar sys-tem should be leading us to an expectation that events such as this—long-lived (105–106 yr) severe perturbations of the inner solar system interplanetary environment with concomitant con-sequences for the biosphere—must have occurred many times over the course of our planet’s history.

In this paper, I examine the likelihood of such events occur-ring. I will start with some calculations and comments regarding the frequency of asteroid impacts on Earth, largely because it is important that a distinction be drawn between the simple idea of stray cosmic rocks upsetting the terrestrial environment for a short interval (1–100 yr?) and the rather more complex sce-nario involving large comets breaking asunder and bombarding our planet over prolonged (105–106 yr) episodes. I then continue with an estimation of the probability per unit time of a Neptune-crosser or a centaur being diverted directly into an Earth-crossing orbit, from there deducing how often episodes like those envi-sioned earlier might have occurred across the Phanerozoic.

The results have implications for the interpretation of Earth’s geological and biological history, and also for our understand-ing of the present and future hazards posed by asteroids, comets, meteoroids, and dust to our contemporary civilizations.

ASTEROIDS VERSUS COMETS

A relatively small contingent of astronomers and space sci-entists attended the conference on “Volcanism, Impacts and Mass Extinctions” held at the Natural History Museum in London in late March of 2013, compared to the number of attendees from the geological and paleontological communities. Just over 2 weeks later, I also attended the Planetary Defense Conference (“Pro-tecting Earth from Asteroids”) in Flagstaff, Arizona, organized by the International Academy of Astronautics; there, the lack of equilibrium between the scientifi c disciplines was reversed.

One thing that these two disparate international conferences did have in common, however, was that the discussions focused squarely on “asteroids” as being the cosmic culprits for extinc-tion events and/or civilization-interrupting catastrophes, rather than “comets.” I believe this is misguided, for both meetings, but for different reasons.

In terms of planetary defense—defending ourselves from the deleterious effects of terrestrial collisions by extraterrestrial bodies of substantial size—for every single mention of comets at the Flagstaff conference, I heard 99 mentions of asteroids. In some ways, this is because comets represented the elephant in the room: Tackling an earthbound asteroid would be diffi cult, but tackling an earthbound comet would be impossible, at least in the foreseeable future, plus we know how to predict aster-oid impacts decades ahead of time, but we might expect only a couple of years’ warning for a new, long-period comet found to be heading our way (Marsden and Steel, 1994). For planetary

4These are not all in the outer solar system. The Earth-crossing object 107P/ Wilson-Harrington (i.e., a periodic comet designation) = (4015) Wilson- Harrington (i.e., a minor planet/asteroid designation) was discovered in 1949, classed then as being a comet due to its nebulous appearance and dust tail, but quickly lost; it was rediscovered in 1979 as an asteroid, and it was not until 1992 that the two discoveries were tied together as being a single object that displayed comet-like activity in 1949 but not in subsequent detections. Based on its absolute magnitude, it is about 2–4 km in size. Whether it is actually an extinct, moribund, or dormant comet is a question that should be answered by future observations, including perhaps by space probes; it is also feasible that Wilson-Harrington might truly be an asteroid (i.e., a rocky/metallic body), which appeared slightly fuzzy in 1949 due to dust and meteoroids having recently been lost from its surface regolith in some way, such as a collision with a smaller but substantial object. There are several other examples: Three crossover asteroid-comet objects were studied in terms of both dynamics and physical properties by Di Martino et al. (1998). In addition to the above objects in high- and moderate-eccentricity (i.e., comet-like) orbits, there are also now several objects known in the (low-eccentricity) main asteroid belt that exhibit comet-like physical activity, and these have been termed the “Lazarus comets” (Ferrin et al., 2013).



400 Steel

defense purposes, however, this neglect of comets is likely to be justifi able: the next signifi cant (e.g., 50–200 m) impactors to strike Earth will most probably be small asteroids, and indeed their arrivals are, in principle, predictable, enabling ameliorative action to be taken (even if that only consists of evacuation of the target area or other civil defense actions).

From the perspective of understanding past mass extinction events, though, a mindset that is fi xated on asteroids is most likely not justifi able. Yes, comets generally have substantially higher impact speeds (and therefore impact energies per unit mass that are around an order of magnitude greater than for asteroids), but this ignores the qualitative differences between the two broad types of interplanetary object in terms of how they might affect the terres-trial environment. The frequencies with which comets are observed to fragment on-orbit, their far higher masses, and the plausible con-sequences of fl ooding the inner solar system with small meteoroids and dust, have all been discussed by Napier (this volume) in his accompanying paper, and so they are not repeated here.

At the Volcanism, Impacts and Mass Extinctions Con-ference, it was apparent that most attendees regarded cosmic impacts onto Earth as being largely the consequence of single, monolithic, stray asteroids. From a knowledgeable astronomical perspective, that might be regarded as being simple to the point of being oversimplistic. On the other hand, with the benefi t of hindsight, it would appear that much of the research published by astronomers on this topic in the 1980s and 1990s (cometary waves; Planet X; the Nemesis star; and so on) may have been sophisticated, but also exhibited sophistry. Simply put, I do not believe that we knew enough about giant comets back then to be able to say much defi nitively about their relevance (or not) with regard to mass extinction events; I have already pointed out that the fi rst trans-Neptunian object was not discovered until late 1992, and only three centaurs were known by then, so how could we say anything defi nitive about the ways and frequencies with which giant comets might affect the biosphere? That is a rhetori-cal question anticipating a negative response, but it does have a partial positive answer, which is: Study the papers by Napier and Clube (1979) and Clube and Napier (1984).

Previously, I wrote that at the Planetary Defense Confer-ence it seemed to me that the subject of comets represented the elephant in the room. Now I will use another pachydermic meta-phor, the well-known tale of the blind men and the elephant. The relevant Wikipedia page concerning this story begins:

“The story of the blind men and an elephant originated in the Indian subcontinent from where it has widely diffused. It has been used to illustrate a range of truths and fallacies. At various times it has provided insight into the relativism, opaqueness or inexpressible nature of truth, the behavior of experts in fi elds where there is a defi cit or inaccessibility of information, the need for communication, and respect for different perspectives.”

In trying to understand the biosphere and its evolution, we blind men and women need to be sure we are feeling around the correct end of the elephant. My experience was that at both the 5http://www.minorplanetcenter.net/iau/lists/MPLists.html

Planetary Defense and the Volcanism, Impacts and Mass Extinc-tions conferences, most participants were thinking of cosmic impacts as being like the currant buns that a miscreant ungulate might occasionally throw our way, using its prehensile proboscis, whereas in fact the things we need to regard as being of most sig-nifi cance in terms of unraveling the history of mass extinctions is the less-cohesive, bigger lumps of stuff that come winging at us from under the elephant’s tail. Metaphorically speaking, of course.

PRESENT-EPOCH ASTEROID INFLUX TO EARTH

In this section, I consider the frequency of impacts on Earth by asteroids, based on the presently observed population, and discuss briefl y what this implies with regard to the understand-ing of how asteroid arrivals may (or may not) contribute to mass extinction events or other biospheric upsets.

The atmospheric entry on 15 February 2013 of a small (~17 m) asteroid just to the south of the city of Chelyabinsk in eastern Russia has led to confl icting reports on the population of Earth-crossing asteroids of such a size, and therefore the frequency with which such minor collisions might be anticipated. Obviously, the total population of Earth-crossing asteroids at some size limit multiplied by the mean impact probability of the ensemble should render the frequency of collisions with Earth. A population of about 10 million Earth-crossing asteroids down to this (15–20 m) size has been argued, and a frequency of impacts of about one per century has been proposed. Those two fi gures may be com-bined to provide a mean impact probability of 1.0 × 10−9 per year, and on realizing this, I recognized that something must be wrong, because my earlier calculations of mean impact probabilities (e.g., Steel, 2002) indicated values signifi cantly larger than this, by a factor of at least three or four. Thus, either the population of small Earth-crossing asteroids is numerically lower than stated above, or the frequency of such minor Earth-crossing asteroid arrivals is higher than once per century, or else something else is affect-ing the sums (e.g., some resonance effect is protecting Earth from being struck as often as one might anticipate).

Whatever the cause of the apparent anomaly, it was clear to me that an updated value for the mean Earth-crossing asteroid col-lision probability with Earth as a function of asteroid size would be of utility, and so I accessed all the Earth-crossing asteroid orbits available from the Minor Planet Center5 on 11 April 2013 and set about calculating the individual—and thence average—impact probabilities, and also speeds (v). The cutoff date has no meaning other than the fact that I was about to depart the National Aeronautics and Space Administration (NASA) Ames Research Center in California for the Planetary Defense Conference (Flag-staff, Arizona, 15–19 April 2013), and I thought it might be use-ful to prepare an impromptu poster on this topic.

Previously I have used the technique of Kessler (1981) to calculate the terrestrial impact probabilities and speeds of




various planet-crossing objects based on the known populations of asteroids and comets (e.g., see Steel and Baggaley, 1985; Olsson-Steel, 1987a; Marsden and Steel, 1994; Steel, 1998, 2002). Because the discovered population of Earth-crossing asteroids has grown markedly over the past 11 yr, a revisit of such calculations seems timely.

Kessler’s method is based on the concept of spatial densi-ties, which might be regarded as likelihoods of particular orbiting objects (e.g., Earth and an asteroid) being present in the same vol-ume of space at the same time, whereupon a collision is possible; the probability of such an event occurring depends also on the intersection velocities and the (speed-dependent) collision cross section of the planet. This method allows for both the objects to be in noncircular orbits, and also for both to have nonzero inclinations (although in the present instance, all Earth-crossing asteroid orbits are referred to the ecliptic, and so regions of space at nonzero ecliptic latitudes are not relevant; that is, any impact on Earth must occur in the ecliptic plane). Kessler’s method is superior to that of Öpik (1976, and many earlier papers) in that it is not limited to circular planetary orbits, and Öpik’s geometrical method also strictly requires the impactors to be deep-crossers of the planet’s orbit (cf. Bottke et al., 1994). This is particularly important because shallow-crossers of Earth’s orbit have intrin-sically elevated impact probabilities, meaning that they should not be neglected in collision rate/probability assessments. A comparison between various statistical-type collision probability techniques has been given by Manley et al. (1998).

A fundamental assumption intrinsic in Kessler’s technique is that the longitude of the node and the argument of periapsis of each orbiting object are taken to be random. In essence, this requires the precession time scales of those angular elements to be briefer than the collisional and dynamical lifetimes. It is fea-sible, however, that some orbiting objects cannot collide, due to mean-motion resonance effects (e.g., the Trojan asteroids in a 1:1 resonance with Jupiter; or Pluto in a 3:2 resonance with Neptune).

Another possible defi ciency of Kessler’s technique (and similar statistical methods, such as that of Öpik) is that the pre-cession of the argument of perihelion (ω) does not occur at a uni-form rate, but rather is dependent upon the value of ω, whereas collisions can only occur with a planet for specifi c values of ω given a potential impactor’s values of semimajor axis and eccen-tricity, as discussed by Shoemaker et al. (1979). For example, 2P/Encke’s rate of apsidal precession is higher when ω is close to 90° and 270° than when it is near 0° or 180°, and both the eccentricity and inclination also vary with the phase in the apsi-dal precession cycle (i.e., the value of ω): See fi gure A2 in Asher and Clube (1993).

In total, 5633 Earth-crossing asteroids were available for use in the calculations presented here, their orbits being down-loaded from the Minor Planet Center Web site as noted above. Of these, 762 are Atens and 4871 are Apollos (differentiated by the former having semimajor axes smaller than 1 au, and the lat-ter having larger semimajor axes and thus orbital periods longer than one year), based on them crossing the osculating terrestrial

orbit (defi ned by a semimajor axis a = 1 au and eccentricity e = 0.0167). There are also 12 known asteroids with orbits entirely interior to Earth’s present orbit (i.e., their aphelion distances are less than the current terrestrial perihelion distance of 0.9833 au), and these were not included in the calculations because they can-not collide with Earth in the present epoch.

Of these 5633 Earth-crossing asteroids, there are 13 with abso-lute magnitude H > 30, implying sizes (equivalent diameters) of below 2.6–5.9 m (for albedos of 0.25 and 0.05 respectively6), and these I have neglected. This leaves 5620 Earth-crossing asteroids with H ≤ 30 that were used in the calculations discussed in the following.

All “impact speeds” discussed here are the speeds with which an asteroid would strike the terrestrial surface in the absence of any atmospheric deceleration. That is, these impact speeds are the orbital intersection velocities added in quadrature with Earth’s escape speed (~11.2 km/s).

For each of the 5620 Earth-crossing asteroids, the collision probability with Earth was calculated and the individual results stored for later analysis. In addition, the software used was adjusted such that a tally was kept, in working on each Earth-crossing asteroid, of the probability distribution of different impact speeds; the impact speeds for individual Earth-crossing asteroids vary, for example, dependent upon whether the putative collision occurs near Earth’s perihelion, or aphelion. This means that values of the ranges of impact speeds were accumulated in the analysis with allowance for weighting by the impact prob-abilities, so that a properly weighted mean impact speed could be derived based on all Earth-crossing asteroids brighter than whichever limiting absolute magnitude H

lim was selected. The

resulting mean values are shown in Table 1; they are also plotted in Figure 1.

It is also possible to weight the collision probabilities by some other power of the impact speed than unity: For example, if a weighting according to values of v2 were used, then the derived collision probability distribution might be interpreted in terms of the likelihoods of different impact kinetic energies. Such weight-ings (for powers on v from 0.1 to 4.0) were used for both asteroi-dal and parabolic comet orbits that might impact Earth or Mars by Steel (1998).

It is apparent from Table 1 and Figure 1 that the calculated mean terrestrial impact probability, based on the presently known Earth-crossing asteroid population, grows markedly as one admits ever-fainter/smaller asteroids into the sample, while the weighted mean impact speed reduces. Going out from (say) H

lim =

15 to Hlim

= 30 results in the calculated mean impact probability increasing by more than an order of magnitude, while the derived average impact speed tumbles by 40%.

These trends should not be thought to refl ect reality pre-cisely, but rather are most likely affected by discovery selection effects. For the larger Earth-crossing asteroids (size > 1 km, H < 18), the discovery is believed to be almost complete, with over

6http://www.minorplanetcenter.net/iau/lists/Sizes.html



402 Steel

90% of Earth-crossing asteroids in cis-Jovian orbits now being known. For smaller/fainter Earth-crossing asteroids, however, a far smaller fraction of the entire population has so far been identifi ed, with that fraction diminishing as the asteroids in ques-tion get fainter/smaller. The small Earth-crossing asteroids that have been discovered will tend to be those that pass relatively close by Earth, and are therefore preferentially discovered by the telescopic search techniques because they have orbits mak-ing more frequent near-Earth passages. Broadly, these will have low- inclination (i), low-eccentricity (e) orbits, and thus exhibit higher-than-normal collision probabilities, and the collisions would occur at lower-than-normal speeds. This presumed pref-erential discovery of small Earth-crossing asteroids in such near-Earth orbits is most evident in the abrupt upturn at H

lim = 24 in the

impact probability curve in Figure 1.There is an alternative, additional, consideration that might

be worthy of investigation. Earlier, I noted that Earth may be pro-tected from collisions by some Earth-crossing asteroids due to them being in some form of orbital resonance (e.g., Trojan orbits,

or horseshoe orbits such as those occupied by [3753] Cruithne and 2010 SO16), but this would seem likely to be a minor reducer of the overall terrestrial collision rate. A physical effect that could signifi cantly enhance the collision rate by smaller Earth-crossing asteroids might be this: Any large but weak (i.e., “rubble pile”) Earth-crossing asteroid that migrates into a low-e, low-i orbit near 1 au will generally make many close approaches past Earth before any collision occurs. During these close approaches, the tidal force, especially on a spinning or tumbling Earth-crossing asteroid of low tensile strength, may disrupt that object into several/many smaller bodies, each of which would then follow its own trajectory in terms of its future orbital evolution (Richard-son et al., 1998; Michel and Holsapple, 2007). Thus, it is feasible that at least part of the small Earth-crossing asteroid population might derive from larger Earth-crossing asteroids that have split apart after reaching low-e, low-i orbits; this would imply that we should not expect the orbital distribution of small Earth-crossing asteroids (sub–100 m, say) to mimic precisely the large Earth-crossing asteroid orbital distribution. There are also reasons to

Figure 1. The solid curve indicates (on the ordinate) the mean collision prob-ability per billion years for all discov-ered Earth-crossing asteroids (ECAs) that are brighter than some limiting magnitude H

lim (abscissa); the dashed

line shows the mean impact speeds (km/s), weighted by the individual col-lision probabilities; and the dotted line indicates the number (divided by 100) of Earth-crossing asteroids contributing to the calculations at each limiting mag-nitude (cf. Table 1).

TABLE 1. MEAN TERRESTRIAL IMPACT PROBABILITIES AND SPEEDS

Limiting absolute magnitude H lim

Typical size (km)

Number of known Earth-crossing asteroids

Mean impact probability per 109 yr Weighted mean impact speed(km/s)

7.72 79.0 1 5 31 7.72 91.1 5 4 41 1.12 41.2 62 6.2 51 6.02 75.2 101 7.1 61 4.91 10.3 442 0.1 71 5.91 00.3 945 76.0 81 0.91 84.3 7701 24.0 91 3.81 34.4 7771 62.0 02 5.71 76.5 7992 11.0 22 0.61 24.8 9193 40.0 42 0.41 46.81 1494 710.0 62 4.31 29.72 3055 700.0 82 0.31 10.63 0265 300.0 03




believe that radiative effects, and in particular the Yarkovsky pseudo-force, might deliver smaller asteroids more effi ciently than larger ones from the main asteroid belt into Earth-crossing trajectories (Michel et al., 2005).

Bearing in mind the near-completeness of discovery of cis-Jovian Earth-crossing asteroids at H < 18, the recommended outcome from this analysis is that a mean terrestrial impact probability of 3 × 10−9 per year should be used for large Earth-crossing asteroids, with a weighted mean impact speed of ~20 km/s. These values might also be applicable to the popu-lation of smaller Earth-crossing asteroids, but as suggested in the preceding paragraph, it could be that the larger mean impact probabilities and smaller impact speeds calculated herein for the discovered smaller/fainter Earth-crossing asteroids, especially at H > 23–24, actually refl ect not only discovery selection effects but perhaps also some real differences in the orbital distributions of large-versus-small Earth-crossing asteroids, with a greater fraction of small Earth-crossing asteroids occupying low-e, low-i orbits near Earth, these having intrinsically higher collision prob-abilities and lower impact speeds.

If there are indeed 10 million small asteroids of the type that arrived near Chelyabinsk on 15 February 2013 (size ~17 m, hence H ≈ 26), and a mean collision probability of ~3 × 10−9 per year applies to them, then such events would occur some-where on Earth about once every 30–35 yr on average. However, the calculations presented herein (cf. Table 1) indicate a mean terrestrial impact probability of almost 2 × 10−8 per year for the discovered Earth-crossing asteroids with H ≤ 26. If, after allow-ing for discovery probabilities, it were found that at H = 26 a mean impact probability of as much as 1 × 10−8 per year were applicable, then if there are 10 million Earth- crossing asteroids similar in size to the Chelyabinsk object, then the impact rate on Earth would be about once per decade; this does not appear to be in accord with what is known of impact events within the past century, but on the other hand, global surveillance (i.e., cov-ering unpopulated regions) using space-based infrared systems has only been conducted for the past 20 yr or so, so this is a fi eld in which comparatively little defi nitive knowledge exists. This remains an open question deserving further investigation.

VERY LARGE ASTEROID IMPACTS IN OTHER EPOCHS?

Might the infl ux of asteroids to Earth have been different in other epochs during the Phanerozoic? The answer to that ques-tion would appear to be “obviously, yes,” if one assumes that at least some of the larger terrestrial craters formed during the last 600 m.y. were due to asteroid (rather than comet) impacts, because there are no cis-Jovian Earth-crossing asteroids as large as 10 km in size at present, and so no asteroids large enough to form craters substantially larger than ~100 km diameters.

The previous calculations and analysis were based on the presently observed population of near-Earth asteroids, and spe-cifi cally those that have osculating orbits crossing that of our

planet, and that population might not refl ect a long-term aver-age situation, then. The largest current Earth-crossing asteroid is (1866) Sisyphus, which has an absolute magnitude H = 12.4 (i.e., it is the sole asteroid at H

lim < 13 in Table 1), which is indic-

ative of a size of 8–9 km given its moderate albedo of 0.16.Larger near-Earth asteroids are known, with perihelia just

outside Earth’s orbit. Amor-type asteroid (1036) Ganymed has q = 1.24 au, and its magnitude H = 9.45 and albedo 0.29 indicate a size/diameter just above 30 km; it may become an Earth-crosser on a time scale of 10 m.y. (Michel et al., 1999). The prime tar-get of the NEAR-Shoemaker spacecraft mission was (433) Eros, which has a measured size of around 34 × 11 × 11 km and q = 1.13 au, bringing it closer by Earth than Ganymed at present.

How such larger asteroids may arrive in Earth-crossing orbits, and so become potential impactors, has been extensively studied (e.g., Michel et al., 1996, 1998, 2005; Gladman et al., 1997, 2000; Migliorini et al., 1998). The time scales involved (for evolution into potential Earth-impacting paths) are brief, compared to geological time frames, typically being measured in millions of years. It follows that over the Phanerozoic, it should be anticipated that the population of potential Earth-impacting asteroids has varied substantially.

Quite apart from the population of Earth-crossing asteroids being different in other epochs, also the eccentricity (e) of Earth’s heliocentric orbit oscillates with a period of only ~105 yr, at times reducing to e ≈ 0.0 (i.e., a circular orbit), while at others a value as high as e = 0.0579 may be attained, i.e., more than three times the current e = 0.0167. This alters the individual impact proba-bilities of asteroids (or comets) with Earth, but more importantly when e is near its upper limit, there would be larger populations of asteroids with perihelion distances (q) near 1.02–1.06, which then become potential impactors despite the fact that, assuming (invalidly) unchanging asteroid orbits, they do not cross Earth’s path when our planet has a lower value of e. The way in which the overall and mean impact probability by asteroids varies with Earth’s orbital eccentricity was discussed by Steel (2002).

In view of these issues, one should not imagine that the cur-rently observed Earth-crossing asteroid population is diagnostic of the long-term population of potential Earth-impacting aster-oids. There are reservoirs of asteroids from which large impac-tors might be delivered into Earth-approaching orbits on time scales less than 10 m.y. (see Fig. 2 for the observed asteroid population larger than 50 km in size). The populations of impac-tors in the inner solar system have been reviewed by Michel and Morbidelli (2007), although as I will indicate later, I believe that any analysis that neglects the distant solar system as a source of Earth-impacting bodies is short-sighted, given what we now know of the host of large objects amongst and beyond the Uranus and Neptune region.

ENTER THE COMETS

In the preceding section I have outlined how, while in the present epoch no Earth-crossing asteroids exist that have



404 Steel

diameters as large as 10 km, in the longer term (1–10 m.y. time scales), it is feasible, indeed likely, that asteroids of such sizes will arrive in Earth-approaching orbits, having been perturbed in one way or another out of the main belt, or indeed currently hav-ing orbits with perihelia just outside Earth’s distance from the Sun (like Eros). Such asteroids might then represent the sorts of energetic impactors visualized by some as being the root cause of mass extinction events.

There is, though, no reason to wait (proverbially speaking) such an extended period for such large impactors to appear close to our planet. For example, Comet Hale-Bopp, which passed peri-helion inside Earth’s orbit in 1997, had a solid nucleus ~60 km in size, and it will be back in a few thousand years. Before that, we can expect many more giant comets to come winging by.

The notion that comets can impact Earth with calamitous consequences is not a new one, dating back far before the discov-ery of the fi rst main-belt asteroid in 1801, the fi rst Earth-approach-ing asteroid in 1898, and the fi rst Earth-crossing asteroids in the 1930s. Napier (this volume) has mentioned some of the early suggestions regarding mass extinctions being caused by comet

or asteroid impacts. To the early writers that he lists, I might add that Edmond Halley, in 1694, discussed how comet impacts must have occurred in the past and that this was a “strange Catastrophe we may be sure has at least once happened to the earth.”

Halley’s ideas in this regard were picked up by many other intellectuals of the era, not always appreciatively, because they tended to be regarded as contrary to Christian beliefs. It was possibly at the suggestion of Isaac Newton that this cometary impact concept was altered by Halley so as to suggest that this was how a former world was reduced to chaos, with the Bibli-cal Creation story then being regarded as an explanation of how order was produced.

Other authors also incorporated such notions into their writ-ing. In Gulliver’s Travels (1726), Jonathan Swift described “peo-ple under continual disquietudes” because they believed that the next return of Halley’s Comet “one and thirty years hence, will probably destroy us.”

Still on the theme of Halley’s Comet, I turn now to the great American statesman and scientist, Benjamin Franklin. In his Poor Richard’s Almanac for 1757, anticipating the earnestly

Figure 2. (Left) The presently observed population of asteroids in the inner solar system (Jupiter’s orbit sunward) with sizes above ~50 km. There are no cis-Jovian Earth-approaching asteroids of such size in the current epoch, although over time scales above 1 m.y. it is feasible that such objects might be delivered from the main belt between Mars and Jupiter. For an up-to-date graphic of all known asteroids and comets in the inner solar system, see http://www.minorplanetcenter.net/iau/lists/InnerPlot.html. (Right) The orbits of a handful of the known short-period (orbital period < 20 yr) and Halley-type (20 yr < orbital period < 200 yr) comets that pass close by Earth in the present epoch. Many of these would, if they collided with our planet, deliver energy releases of the order of those associated with the formation of the Chicxulub crater, or larger. For example, 1P/Halley has an elongated shape around 15 × 8 × 8 km, a mass estimated to be above 2 × 1014 kg, and it would impact Earth at ~66 km/s based on its present orbit.




awaited return of that comet as foreseen by Halley (and Swift), Franklin wrote that:

“Should a Comet in its Course strike the Earth, it might instantly beat it to Pieces, or carry it off out of the Planetary System. The great Confl agration may also, by Means of a Comet, be easily brought about. All the Disputes between the Powers of Europe would be settled in a Moment; the World, to such a Fire, being no more than a Wasp’s Nest thrown into an Oven. But our Com-fort is, the same great Power that made the Universe, governs it by his Providence. And such terrible Catastrophes will not happen till ‘tis best they should.”

Franklin did not, though, say when he thought this might be.To select one more example of the opinions of well-educated

men prior to the era of modern science, in 1822 we have the poet Byron, fully conversant with the concept of extinction events and terrestrial upheavals in the light of Georges Cuvier’s excavations in Paris, stating the following:

“Who knows whether, when a comet shall approach this globe to destroy it, as it often has been and will be destroyed, men will not tear rocks from their foundations by means of steam, and hurl mountains, as the giants are said to have done, against the fl aming mass?—and then we shall have traditions of Titans again, and of wars with Heaven.”

—Medwin’s Conversations of Lord Byron (1824).

Due to my mention of “modern science” above, the reader may have imagined that during and after the nineteenth century, we must have entered a more-sophisticated and rational era, in which professional scientists made only solid, supportable state-ments based on sound knowledge of the phenomena involved; however, the reality is far from that. After its perihelion passages in 1759 and 1835, the expected return of Halley’s Comet in 1910 was again the cause of widespread concern. As a consequence, the following appeared as part of a calming note to the public from someone who should have been an expert in the subject (and therefore should have known what he did not know):

“For a hundred million years life has been continuous on this earth, though we have been visited by at least fi ve comets every year. If comets could ever have done the earth any harm they would have done it long ago and you and I would not be discuss-ing comets or anything else.”

—Robert Stawell Ball, Lowndean Professor of Astronomy and Geometry, University of Cambridge, in a letter to The Times, published on 10 February 1910.

In my personal experience, things have not changed much in the intervening century, with astrophysicists in the main making false witness to the public (and governments) with regard to the hazard posed to us by comets and asteroids, based on their (the astrophysicists’) ignorance of the reality and also the fear that fund-ing might be diverted from their own esoteric research interests.

POPULATIONS OF COMETS

From the preceding section, it should be clear that the thought that comets might impinge on Earth with signifi cant consequences for the terrestrial environment and therefore the biosphere is not at all new. Edmond Halley realized this when he determined the orbit of his eponymous comet, late in the seven-teenth century.

Over the decades and centuries, growing numbers of peri-odic (i.e., routinely returning) comets have been discovered and their orbits determined. Limited numbers (for clarity) have their paths shown in Figure 2.

While certain fractions of comets are periodic, like these, greater numbers of observed comets are nonperiodic (at least compared to historical time scales), or follow near-parabolic orbits around the Sun; an example is the aforementioned Comet Hale-Bopp. That is, such comets are seen once only and then depart again into the region far beyond Neptune and Pluto. The source of these is broadly believed to be a spherical distribution or cloud that stretches out to a substantial proportion of the dis-tance to the nearest stars. This cometary reservoir is known as the Oort-Öpik cloud, and it has been discussed in more detail in the accompanying paper by Napier (this volume); see also, for example, Bailey et al. (1990) and Emel’yanenko et al. (2013). Simply to provide a time scale for readers not familiar with the history, this cloud was hypothesized by Ernst Öpik in 1932, and independently by Jan Oort in 1950.

For present purposes, I want to concentrate on com-etary reservoirs/populations much closer to (and indeed, to some extent, amongst) the outer planetary region: This is the Edgeworth-Kuiper belt and the centaur objects, as foreshad-owed in the introduction to this paper. My reason for concen-trating on these is that they represent source regions for massive comets. For a more detailed description of how and why these various locations should be considered to be reservoirs from which comet-like (i.e., icy, primordial) objects occasionally entering the inner solar system are derived, see Horner et al. (2003) and Emel’yanenko et al. (2013).

While Comet Hale-Bopp was a behemoth amongst com-ets, at a size estimated at 60 ± 20 km, and other very large near-parabolic comets have been witnessed during recorded history, from the perspective of wreaking havoc in the inner solar system (in the future, and in the geological past), the centaurs and the Edgeworth-Kuiper belt objects must surely be amongst the prime suspects, based on what little we know about them so far.

Centaurs are known to range up to 260 km in size, and so (with some central compression to be anticipated) have masses a hundred times as high as Hale-Bopp. At the periphery of the planetary system, close to Neptune’s orbit, far larger objects are known, all discovered in the past two decades. See Figure 3 to gain an appreciation of just how many big objects are out there, each fi guratively representing a Sword of Damocles hanging over life on Earth.



406 Steel

Napier (this volume) has provided some discussion of orbital evolution studies of centaurs, following on the work of Horner et al. (2004b). Since (2060) Chiron was discovered in 1977, there have been several such orbital evolution studies done (e.g., Hahn and Bailey, 1990), involving clones (i.e., slight initial orbital variants) of this object, and such studies have been reviewed by Horner et al. (2004a, 2004b). Other centaurs have also been investigated in this way.

All such work has resulted in indications of the compu-tational clones having nonzero probabilities of evolving into Earth-crossing orbits. A variety of fates awaits the clones, depending on contingent events including (in particular) close passages by a large planet, Jupiter being most effective in this regard. The clones may end their virtual lives by col-liding with a planet; by being subject to temporary satellite capture by a major planet; by becoming sungrazers (includ-ing dipping below the solar surface and so being lost); or, more likely, being ejected from the solar system on hyper-bolic heliocentric orbits.

A shortcoming of such research, of necessity, is that only the dynamical evolution of the clones is followed. Any comet-like body7 may also be expected to undergo physical evolution, for example, the sublimation of different volatile constituents occur-ring at distinct heliocentric distances; thermal-stress–induced splitting; spontaneous or tidally induced fragmentation events; the loss of silicates as meteoroid trails and dust tails; and so on. At our present state of understanding of the physical nature of comets, such combined dynamical and physical evolution studies seem somewhat intractable: One could build a model, and run it, but would the outcomes be useful? In orbital evolution stud-ies of comets (contra asteroid dynamical evolution), it is often necessary to include the jetting effect (“nongravitational force”) imposed by the asymmetric outgassing of sublimating volatiles in order to understand specifi c cometary trajectories, but that is often a matter of fi tting input parameters to observed deviations by a comet from the path indicated by a pure gravitational solu-tion. This can render useful information about the comets (e.g., the observed nongravitational accelerations can give an indica-tion of their masses), but almost the only thing predictable about the physical evolution of any particular comet is the fact that the physical evolution will be unpredictable: Comets are often seen to fall apart in interplanetary space for no apparent reason.

Returning to the purely dynamical orbital evolution stud-ies, I note the following. These involve extensive numerical integrations of orbits in order to delineate dynamical avenues, and they represent a special mathematical art. Also, they require extensive computational power; see Horner et al. (2004a, 2004b), for example. Earlier in this paper, I cited publications involving authors including Farinella, Froeschlé, Gladman, Michel, Mor-bidelli, and others, and their work similarly involves such numer-ical integrations of orbits.

SINGLE-IMPULSE DEFLECTION INTO THE INNER SOLAR SYSTEM

All such research work is useful in developing an under-standing of how comet and asteroid orbits evolve. However, for present purposes, I would like to be able to deduce, using limited computing power, and short execution times, the relative likeli-hoods of centaurs or other planet-crossers being defl ected by sin-gular close encounters with planets into wildly different orbits. For example, for a centaur with a low-eccentricity orbit crossing only the orbit of Uranus, what is the probability that a near miss of that planet will divert it (the centaur) into an orbit with a much-smaller perihelion distance? What is the chance of it attaining a path crossing Saturn? Or Jupiter? Or Mars? Or Earth? To answer such a question would require a vast amount of computing power

Figure 3. The ghost in the machine: This diagram shows the orbits of the planets Jupiter, Saturn, Uranus, Neptune, and Pluto, with their positions as at the start of the year 2000. Also shown are the orbits of the discovered centaurs and trans-Neptunian objects (plus a few of the known short-period and Halley-type comets for comparison with Fig. 2), less than a decade after the fi rst trans-Neptunian object was found. For up-to-date maps of the positions of large outer solar system objects, visit the Minor Planet Center Web site at http://www. minorplanetcenter.net/iau/lists/OuterPlot.html. The obvious vast ring of trans-Neptunian objects in Figure 3 represents a reservoir from which giant comets are occasionally perturbed into Neptune-crossing orbits, a few of those then will likely be diverted into the inner solar system, where they must wreak havoc amongst the terrestrial planets.

7Asteroidal bodies should also be expected to undergo physical evolution dur-ing the course of their dynamical evolution; for example, a close passage by a planet may cause the disruption of a rubble-pile asteroid into discrete aggregations or individual monoliths, or at least rearrange the shape of the overall object.




should the precise-numerical-integration-of-orbits technique be employed, as previously discussed.

Some years ago, when (944) Hidalgo and (2060) Chiron were the only known large objects in short-period orbits cross-ing the Jovian planets, I developed an alternative technique for estimating such gross orbital change probabilities and applied it to these two specifi c objects (Olsson-Steel, 1987b).

The technique in question is an extension of the colli-sion probability method introduced by Kessler (1981) and also described by Steel and Baggaley (1985), except that instead of a collision cross section being used, instead I employ a close encounter cross section, rendering the probability (per year, or per orbit) of a minor body on some arbitrary planet-crossing orbit passing through the sphere of infl uence of that planet. Then, for each possible miss distance of the planet and each possible azimuthal angle around the planet (both suitably sub-divided into bins of impact parameter and position angle), the new heliocentric orbit that would result from passage through that particular planetocentric position is computed on the basis of a defl ection derived using the well-known Rutherford scatter-ing formulae. That is, a two, two-body approximation is used, with the pre-encounter orbit of the minor body (i.e., the centaur, here) being a heliocentric ellipse; the orbit during the encounter being a planetocentric hyperbola; and the postencounter orbit being heliocentric but maybe either elliptical (i.e., a new orbit gravitationally bound to the Sun) or hyperbolic (i.e., the body is ejected from the solar system because it has attained a heliocen-tric speed greater than the escape speed at this solar distance). The defi nition of the dimension of the sphere of infl uence is not greatly important here, because the most-interesting alterations in the minor body’s orbit generally occur as a result of close misses of the planet. More details of the model are given by Olsson-Steel (1987b).

As aforesaid, I developed this technique over a quarter- century ago, largely in order to investigate how likely it might be that small bodies/giant comets in the outer solar system would be diverted directly into orbits entering the inner solar system, a matter connected with terrestrial catastrophism that was also examined using numerical integration techniques by other researchers such as Hahn and Bailey (1990) and in particular Bailey et al. (1994). I have also used the technique, for example, to derive probabilities for near-parabolic comets being defl ected into short-period orbits in single planetary encounters (Olsson-Steel et al., 1989; Olsson-Steel, 1990).

What I have done in the present instance is to access over 370 orbits of centaurs and scattered disk objects (SDOs) from the list-ing maintained by the Minor Planet Center.8 This list begins9 with (2060) Chiron, (5145) Pholus, and (7066) Nessus, discovered in

8http://www.minorplanetcenter.net/iau/lists/Centaurs.html

9Again, it is not clear whether (944) Hidalgo should be classed as a centaur; according to Emel’yanenko et al. (2103), it is not.

1977, 1992, and 1993, respectively, and then continues with the hundreds of such objects that have been discovered over the past two decades. The list10 of trans-Neptunian objects (TNOs) is sub-stantially longer, emphasizing to the reader that there are myriad large comet-like objects orbiting at the periphery of the planetary system, of which just a small subset has been spotted since the fi rst was identifi ed 21 yr ago.

From the 370-odd centaurs and scattered disk objects, I selected four example objects: two that have Neptune-crossing orbits with perihelia near that planet, one object with a low-eccentricity orbit that crosses just Uranus, and one with a high-eccentricity long-period orbit that crosses both Neptune and Uranus. Their relevant orbital parameters and estimated sizes are shown in Table 2.

For each of these four objects, I executed my single-impulse new-orbit probability code, and derived results as also shown in Table 2. Close encounters (i.e., passages through a planet’s sphere of infl uence: for defi nitions, see Olsson-Steel, 1987b) with the outermost two Jovian planets are seen to occur typically once every 100–600 orbits of the objects in question.

It is the outcomes from such close encounters that are of most interest here. The two Neptune-crossers 2008 LP17 and 2011 GM27 are found to have nonzero probabilities of being diverted into Saturn-crossing orbits (and, of course, Uranus-crossing orbits) in single-impulse events, whereupon it would be expected that Saturn would dominate their further orbital evo-lution with a high probability of being passed inward to orbits with yet smaller perihelion distances. The probability fi gures for these two Neptune-crossers are quite different (by three orders of magnitude), however, and it was for this reason that I have presented results for both of them, to highlight that contrasting results can eventuate for initial orbits that appear broadly simi-lar. Object 2011 GM27 is much more likely to reach a Saturn-crossing orbit quickly. If there were a thousand such objects (note its size is around 250 km) in similar orbits, then single-impulse defl ections by Neptune would deliver one per 10,000 yr into Saturn-crossing trajectories.

Uranus-crosser 2012 CE17 was selected so as to demonstrate that low-eccentricity orbits near Uranus and Neptune are unlikely to be transformed directly into orbits with substantially smaller perihelion distances: Note the low probability fi gures pertaining to this object quickly entering a substantially reduced perihelion distance orbit, as given in the fi nal two columns in Table 2.

The Uranus- and Neptune-crosser (65489) Ceto is more interesting. Uranus can divert it directly into Jupiter (and indeed Mars) crossing orbits, but Neptune is able to defl ect it directly into an Earth-crossing trajectory, in fact an orbit with perihelion as small as 0.2 au, so that it would in that case be a crosser of all the major planets. The probability of becoming an Earth-crosser may seem small (~8 × 10-13 per year), but with a semimajor axis of just above 100 au, it has an orbital period of over 1000 yr, and

10http://www.minorplanetcenter.net/iau/lists/TNOs.html



408 Steel

so most such objects spend the vast majority of their lifetimes at aphelion far beyond the reach of our telescopes. If there were a million objects in similar orbits, which would seem to be fea-sible, then the rate of delivery into Earth-crossing orbits would be about one per million years.

The previous calculations pertain only to objects being thrown directly into smaller-perihelion orbits, and they would remain (at least for some time) on paths with aphelia in the outer planetary region. However, the results of these computations indi-cate that we should be anticipating that radical alterations in the inner solar system environment will occur on time scales which are at most millions of years, with frequent arrivals of giant com-ets of sizes 100 km and upward, which would then (based on observed comet behavior) undergo hierarchical disintegrations as described by Napier (this volume). Apart from being of interest in themselves, the results for particular centaur and scattered disk object orbits may be useful in making preliminary identifi cations of those objects that are most likely to undergo rapid orbital evo-lution, thus informing the choice of sample orbits in numerical experiments such as those undertaken by Horner et al. (2004a, 2004b), Emel’yanenko et al. (2103), and others.

A fi nal point with regard to my own calculations as pre-sented here: One might anticipate that radical orbital changes through close planetary encounters should be evidenced in the results of such centaur orbit numerical integrations as those mentioned previously. Horner et al. (2004a) followed 23,328 test particles for 3 m.y. both into the past, and into the future. The number of particle-years involved in their experiment was therefore ~2 × 104 particles × 6 × 106 yr ≈ 1011 particle-years. My calculations of the individual probabilities of being plunged directly into Earth-crossing orbits from the outer solar system through a close planetary encounter are of order 10-12 per year. Therefore, it is not surprising that no such events were identi-fi ed in the study by Horner et al. (2004a): They would need to increase the extent of their experiment (the number of particle-years) by a factor of 10 before one might expect to fi nd such an event occurring11. This might be interpreted as evidence of the utility of the probabilistic method I have employed here, which may be regarded as an adjunct to numerical integrations of orbits, rather than a replacement.

CONCLUSIONS

Our understanding of the inventory of the smaller bodies in the solar system is currently undergoing a revolution, and the

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below 36 au, many were not Neptune-crossers; however, many test particles did migrate into small q orbits, including falling into the Sun. A search of their (and others’) integrations for planetary close encounters causing immediate gross changes of heliocentric orbits would be of interest in the present context, and so is to be encouraged.




discovery of many hundreds of large bodies in and around the outer planetary region over the past 20 yr has important repercus-sions for interpretations of Earth’s collisional history.

The old idea of occasional singular asteroid impacts by large rogue rocks escaping from the main belt between Mars and Jupi-ter should be reconsidered in the light of discoveries such as those mentioned herein. Models for terrestrial catastrophism should encompass what we see happening on a yearly basis—comets decaying and disintegrating into smaller debris that persist in the inner solar system for time scales of ~105–106 yr—with research-ers’ imaginations being engaged so as to visualize and under-stand what must happen should a giant (larger than ~100 km) comet enter the inner solar system and become trapped in a cis-Jovian orbit. Such prolonged episodes of interplanetary upset, and concomitant terrestrial chaos, must have occurred many times over geological history.

Earlier in this paper, I stated that I would be giving a personal view, and that other researchers in the planetary and space science community would not necessarily agree with me with regard to the signifi cance of the large outer solar system objects in terms of the supply of Earth impactors and therefore the importance (or otherwise) of cosmic impacts in mass extinction events. In order to illustrate this, I describe here the following.

Michel and Morbidelli (2007) supposedly have reviewed knowledge of “the population of impactors and the impact cratering rate in the inner solar system,” but in doing so, they have made almost no mention of the observed outer solar sys-tem population of minor bodies and the implications of these, despite there having been more than two decades of history of investigations of the dynamics of centaurs using numerical integration techniques essentially the same as Michel and Mor-bidelli themselves used. These investigations of centaurs have shown that they must occasionally enter short-period orbits and indeed Earth-crossing trajectories, and must therefore have contributed to the cratering record of the solid planetary sur-faces from which we obtain ground-truth in terms of cratering rates. The only paper cited by Michel and Morbidelli (2007) that is relevant in this specifi c regard is that by Koeberl (2003), a useful paper in itself, but only one from substantial numbers of publications that have dealt with the question of the con-tribution of presently observed outer solar system minor bod-ies (which are claimed here to be, in essence, gigantic comets) to the Earth-cratering population and terrestrial catastrophism over the history of the solar system.

In view of this situation, which I have identifi ed here simply as an example of how single-minded researchers can be in the astronomical community (and, one might therefore presume, also in the geoscience community), I must repeat my earlier warning of caveat emptor, with regard to this paper of mine and also all others. It would certainly be possible to be marvelously mistook if one were not to adopt a critical stance. We yet have much to learn about the cosmic context of our planet, and the ways in which it may affect the biosphere.

ACKNOWLEDGMENTS

I am grateful to David Asher, Mark Bailey, Victor Clube, and Bill Napier for various discussions over the decades; I also thank Richard Fire stone and an anonymous reviewer for their helpful comments. This paper was partly written while I was a visiting space scientist at National Aeronautics and Space Administration Ames Research Center, Moffett Field, California. This work was not supported by any funding agency, but was personally fi nanced.

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