The Terrestrial Impact Rate Appears To Be Substantially Higher ...
Observatory, 125, 319–322, 2005
EARTH IN THE COSMIC SHOOTING GALLERY
By D.J. Asher1, Mark Bailey1, Vacheslav Emel’yanenko2 and Bill Napier3
1Armagh Observatory, College Hill, Armagh, BT61 9DG
2South Ural University, Chelyabinsk, 454080, Russia
3Cardiff Centre for Astrobiology, Cardiff University, Cardiff CF10 3DY
The terrestrial impact rate appears to be substantially higher than cur-
rent near-Earth object population models imply, consistent with a signifi-
cant unseen cometary contribution to the terrestrial impact hazard.
Introduction
As a result of a growing number of asteroid and comet discoveries in recent years by dedicated
‘Spaceguard’ survey programmes aimed at finding Near-Earth Objects (NEOs) on potentially
Earth-colliding trajectories, and as a result too of improved dynamical modelling of the NEO
population, the impact rate by NEOs of various sizes is thought to be fairly well constrained.
The problem can be approached in at least three ways. One is simply to model the whole
population of potential impactors, based on objects discovered during large-scale surveys1,2. A
second is to consider the cratered surfaces of the Earth and Moon, and estimate the flux of
different-sized projectiles by counting craters3,4. A third is to focus attention on objects that
happen to pass very close to Earth. Although there are relatively few such objects, this method
has the advantage of constraining the flux of relatively small and/or faint objects. Moreover,
objects that actually collide with Earth, or pass (or are predicted to pass) very close, represent
observational ‘ground truth’ so far as impact statistics are concerned.
It is important also to note that occasional exceptional objects with a small (albeit nonzero)
probability of hitting the Earth on centennial timescales continue to make the news and are
frequently placed on so-called ‘risk’ web-sites by virtue of their rather close approaches. By
applying the third of the methods outlined above, we ask whether observations of such ‘close-
approach’ NEOs, with sizes ranging from large meteorites (i.e. several metres) up to comets
(i.e. tens of kilometres or more), are consistent with NEO impact rates determined by either of
the other two methods. In particular, we highlight four independent sets of data which taken
together suggest a substantially higher impact rate than is implied by the current, generally ac-
cepted NEO population models. We conclude that there is a significant unseen and unmodelled
component of the terrestrial impact hazard, some of which may be attributed to low-activity or
dormant comets.
Statistics of close-approach objects
Consider a heuristic model in which a population of objects has essentially random velocities
with respect to the Earth and the number of close approaches per unit time within some impact
parameter b is proportional to b2. Thus, if the mean interval between terrestrial impacts (i.e.
b < R⊕, where R⊕ = 6, 400 km is the radius of the Earth, neglecting a relatively small correction
for gravitational focusing) for such a population is t⊕, then within any observed time interval
tobs we would expect on average to see one encounter with an impact parameter less than b0,
where
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b0 = (t⊕/tobs)1/2 R⊕
(1)
A priori, the number of passages within a distance b during the time interval tobs is deter-
mined by a Poisson distribution with mean (b/b0)2. The probability of at least one approach
within this distance is
pobs = 1 − exp(−b2/b20)
(2)
When b/b0
1, pobs
(b/b0)2. It is interesting to note that the frequency distribution of
minimum impact parameters bmin during such a time interval is given by
2b
f (b
min
min) =
exp(−b2
b2
min/b2
0)
(3)
0
We note that the real world of close-approach impact statistics is more complicated than this5,
but the model nevertheless provides a realistic basis for the following discussion.
An exceptional close-approach asteroid
On 13th April 2029 a small asteroid in an Earth-like orbit, 2004 MN4 will pass within 5–
6 Earth radii of the Earth6, becoming a naked-eye object crossing the sky at tens of degrees
per hour. 2004 MN4 was recently named (99942) Apophis, after the Egyptian god of evil and
destruction, Apep, and its likely diameter in excess of 300 metres corresponds to a potential
impact energy of 1,000 megatons or more. Recent NEO population models1 predict impacts by
such bodies at 63,000 year intervals, with a probable uncertainty of about 50%.
Here, we have t⊕ = 63, 000 yr, tobs = 20 yr (or perhaps 200 yr, if the whole time since aster-
oids have been known is considered as the observed interval), and bobs = 5–6 R⊕. The a priori
probability of observing an object such as 2004 MN4 is then of order 0.01 or 0.1 (the range
depending on the choice of tobs). The close approach of 2004 MN4 in 2029 is more consistent
with a mean impact interval on the Earth for such objects on the order of 500–5,000 years rather
than 63,000 years. It is noteworthy that a similar result was obtained by Hughes4 by considering
the near-miss distances of known NEOs passing the Earth in 2002. He gave the result (loc. cit.
eqn. 10) ˙
NE
3.4 × 10−4(d/300 m)−3 yr−1, indicating a mean impact interval for such objects
on the order of 3,000 years. Thus, our result is robust. Since the discovery of objects of this size
is likely to be very incomplete, close approaches similar to that of 2004 MN4 would seem to be
much more common than expected from current NEO population models.
The ‘Tunguska’ impact rate
The ∼10 megaton 1908 Tunguska impact turns out to be similarly rare. Current NEO models
suggest such impacts occur on Earth every t⊕ = 2000–3000 years2, whereas this Siberian impact
(bobs < 1 R⊕) occurred within the last 100 years. Following the same reasoning, the a priori
probability of a ‘Tunguska’ event within the last tobs
100 yr is about 0.05 or less.
An independent estimate of the frequency at which bodies of this size currently pass within
near-Earth space comes from lunar meteorites. In fact, hydrocode simulations suggest that
the minimum size of impactor needed to eject sufficient material from the Moon to produce
fragments that might be observed on Earth as lunar meteorites is approximately Tunguska size
or larger7,8. A large majority of the currently known 30 or so lunar meteorites attributed to
independent falls originate from different lunar impacts, and most of the dated meteorites have
been ejected from the Moon within the last 100,000 years9. Thus, we conclude that there are
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probably at least 15 independent lunar meteorite source craters with ages less than 100,000
years, and so at least 15 Tunguska-sized impactors on the Moon within this time-scale.
However, this is a lower limit to the ‘Tunguska’ impact rate on the Moon. Suppose that, in
fact, there have been N such impactors within the last 100,000 years. Then if N was close to
15 it would be extremely unlikely that the present sample of lunar meteorites would represent
the whole range of lunar impact events; in effect, one would expect to see multiple source pairs
amongst the observed independent lunar meteorite falls. Combinatorial calculations can be used
to quantify this argument, and yield a 95% confidence interval N ≥ 26 for producing exactly one
or no source pairs among a sample of 15 independent meteorites. (The corresponding figure for
no source pairs is N ≥ 41.)
Moreover, these calculations assume that each event yields equal numbers of detectable
meteorites, whereas in reality — when the highest energy events yield more (cf. ref. 10) — an
absence or near absence of pairs is even less likely for a given number of sources. Thus, even
more sources would be needed to explain the observed scarcity of source pairs. These estimates
therefore suggest that the true number of lunar meteorite producing impacts during the past
100,000 years is rather higher than the lower limit of 15, and in what follows we conservatively
assume a figure of 25 such impacts on the Moon.
A rough estimate of the rate of such meteorite producing impacts on the Moon is therefore
one per 4,000 years. The implied ‘Tunguska’ impact rate on Earth (taking account of the ratio of
13.5 in surface area between the two bodies, and neglecting gravitational focusing) is therefore
one event every 300 years and probably rather more frequent. This conservative estimate of
the mean interval between Tunguska-size impacts on the Earth is much shorter than the cur-
rent preferred value of 2,000–3,000 yr, and again any incompleteness in the discovery of lunar
meteorites (including destruction by terrestrial erosion) acts in the direction of increasing the
estimated rate.
The cometary impact rate
On a longer time-scale, an object (comet or asteroid) with a diameter of 10 km, similar to the
diameter of the active comet C/1983 H1 IRAS-Araki-Alcock11, is estimated to collide with the
Earth every 150 million years12, and active comets larger than 7 km once every 3 billion years13.
Here, we have t⊕ = 3 × 109 yr and tobs = 20 yr (or 200 yr, if the period during which comets have
been scientifically observed is considered). In either case, with bobs = 0.0312 AU = 732 R⊕, we
infer a very low a priori probability of an active comet as large as Comet IRAS-Araki-Alcock
coming so close to the Earth. This comet had unusually low activity, suggesting that current
NEO population models are again underestimating the terrestrial impact rate by such bodies.
Conclusion
Taking these arguments together, an appeal to small number statistics seems unconvincing.
It instead suggests that the terrestrial impact rate is substantially higher than current NEO
population models imply. This is consistent with an unseen cometary contribution to the ter-
restrial impact hazard14,15, questioning the conclusions, in this respect, of the 2003 NASA NEO
Science Definition Report13.
Acknowledgements
We thank David Hughes and Duncan Steel for helpful comments which have improved the
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presentation of this paper. Astronomy at Armagh Observatory is supported by the Northern
Ireland Department of Culture, Arts and Leisure.
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