PLEASE NOTE:
*
CCNet ESSAY, 18 April 2002
--------------------------
DREADNOUGHTS, DREADNAUTS & EXCALIBUR-II: SPECIFICATION OF
CRITERIA FOR
OPTIMAL DETECTION OF MAXIMALLY HAZARDOUS NEOs
By Drake A. Mitchell, PlanetaryDefence@Netscape.Net
"The search strategy should evolve synergistically as
knowledge of
the NEO population accrues."
-- Edward Bowell, Karri Muinonen, 1994, in "Hazards Due to
Comets & Asteroids"
I: THE CURRENT STRATEGIC PARADIGM: FLAIL
Current efforts to detect potentially hazardous NEOs depend on
ground-based
optical telescopes to sample regions of space, primarily cones
extending
from the Earth towards the Main Belt. These efforts to find
asteroids and
comets in the many orbits of concern rely on the fact that these
NEOs appear
to these telescopes to be most brightly illuminated at
solar-opposition from
the Earth, i.e. in the antisolar direction of the night sky. Thus
a
searchlight-like zone slowly swings along with the Earth in its
perennial
orbit of the Sun. This data-collection strategy has yielded an
optimization
for search-cost and viable political compromise, in the form of
the goal
proposed to and then mandated by the U.S. Congress, i.e. for NASA
to detect
90% of NEOs 1 km and larger within the ten-year period ending in
2008. This
strategy, however, does not appear to be globally optimal when
time
parameters, hazard metrics, true costs, best effort, and
alternate
strategies are taken into account. We are the inheritors of bad
news: God
apparently does play dice, terribly sorry about that; but the bad
news
really must all be collected, and the sooner the better, chin up,
chop-chop!
The best features of these current survey efforts have been
twofold: their
inexpensive, highly-probable useful warning for the largest
asteroidal
objects; and the consciousness-raising effects on the world
population,
thanks to the more distinguished of the many discoveries. It is
currently
estimated that nearly all "extinction-level" NEAs,
those with H<15.5
(diameter >2-5km), have been detected [1] - hurrah! However,
even with the
inclusion of the other known NEOs that are 1km and larger, a
rather large
~82% of the risk from "global killers" remains [2].
Worse, according to the
results of the latest NEO population model of Morbidelli,
Jedicke, and
Bottke, the existing program to arrive at the 2008 goal does
indeed appear
to be doomed, and the best that can be achieved by then - even
with an
enhanced LINEAR survey focused only on the most hazardous NEOs -
would be
about 60-70% completion [3].
The beneficial detection feature of the current telescopic
surveys degrades
rapidly for the vastly more numerous NEAs with diameters near and
below the
poorly understood threshold for catastrophic global effects [4].
One of the
greatest liabilities of the current strategic regime is that
known
indicators of greatest hazard potential have been so badly
neglected that
valuable time and strategic focus have been lost. The
underutilized leverage
of these indicators leaves Earth vulnerable to a tragic loss of
warning for
the next several predestined NEO impactors, should these
predictable and
avoidable impact events occur within the next few decades of
greatest risk -
whether they are "global killers" or of a smaller size
that could devastate
either civilization or truly Pythonesque "vast tracts of
land."
So what are the prospects for better strategies? Also included in
Morbidelli
et al's assessment, the proposed dual-mission NEO/Dark Matter
8m-class
Large-aperture Synoptic Survey Telescope (LSST) familiar to
CCNet, which
would reach 24th magnitude within 20-second exposures, could be
expected to
be dramatically more effective than LINEAR [3], especially for
smaller NEOs
(~90% of 300m NEOs in 10yrs), though probably not towards
achieving the 2008
goal on time. Furthermore, despite the heroically artistic
attempts to
justify this wondrous ground-based telescope by pointing out the
disadvantageous limits on integration times for smaller
telescopes, and the
unprecedented telemetry bandwidth that would be required for a
comparable
space-based telescope, these arguments appear to suffer from a
conflation of
the two missions: Dark Matter science could benefit from the
unique
capability on the ground, and Planetary Defence could indeed
benefit from
the capacity, but it is not yet clear that the LSST would
necessarily offer
performance superior to alternate NEO detection technology [5].
Indeed,
Morbidelli et al find that a dedicated satellite near Mercury's
orbit could
be more effective towards the standing 2008 goal, although as is
shown in
this essay it may be possible to trump even this option.
SwRI's SWUIS ultraviolet telescope, with 30 times the
field-of-view of the
Hubble, demonstrated utility for observing targets inside the
Earth's orbit:
it delivered 400,000 post-perihelion images of Comet Hale-Bopp
onboard
STS-85 (Aug97) when the comet was lost to other telescopes
because of the
Sun, and it searched for Vulcanoid asteroids within Mercury's
orbit onboard
STS-93 (Jul99) [6]. A third flight was planned for the side-hatch
window-mounted telescope's spectrograph. Deployment onboard the
ISS is an
unverified theoretical possibility that could both educate and
occupy
forthcoming celebrity space tourists in need of baby-sitting.
This could
also raise consciousness on the ground about the urgency of
space-based
detection of "blind spot" NEOs, and perhaps even
increase sales of astronomy
paraphernalia to the swelling ranks of amateurs.
More promising than SWUIS, Canada's proposed Near-Earth Space
Surveillance
(NESS) dual-mission micro-satellite builds on its
Microvariability and
Oscillations of Stars (MOST) imaging telescope for stellar
photometry, the
latter due for launch in 2003. The NESS telescope would reach
19th magnitude
within 600- second tracking exposures in a 50kg package in
"dawn/dusk"
sun-synchronous orbit, detecting the neglected asteroids and
comets that are
problematic from the ground due to the Earth's several
blind-spots [22] to
within Mercury's 0.387 AU orbit (20-45 degrees to the Sun) and
also
collecting follow-up astrometry, and possibly polarimetry and
eight-color
photometry [7]. Additionally it will demonstrate the tracking of
higher
Earth-orbit satellites for NORAD, all for ~$5M with shared
launch, a
possible historically unprecedented price-point in the aerospace
industry.
Even more promising is the work by Tedesco, Muinonen, Price and
Egan that
NESS is based on, which showed from the Midcourse Space
Experiment (MSX)
that Earth-orbit observations to 8th magnitude in the infra-red
could detect
500m NEOs close to the Sun (25 degrees) out to 2 AU, which if
performed just
twice a month could find 90% of >500m Atens in 5 years [8].
This standard is
better than the currently proposed performance of the
Bepi-Columbo optical
telescope, which would reach 18th magnitude within ingenious
48-second
orbital-synchronous charge-shifted exposures while in polar-orbit
about
Mercury, aiming to detect >80% of Atens above an unspecified
size-limit.
Images analyzed onboard would generate point-source telemetry,
leaving
moving-object detection of potential NEOs to ground-based
processing. This
could start within 6 years after the proposed launch in 2009,
assuming that
it takes as long to get there as the currently NEO-useless
MESSENGER (two
launch windows in 2004, ~5 year low-delta-V transit), and that
the telescope
is finally included in the reference payload for the next
iteration of
design exercises [9].
To summarize, LSST, SWUIS, NESS, MSX, and Bepi-Columbo each
represent
progress in varying degrees. They are all trailblazing increases
in
telescopic capacity and flexibility. They demonstrate the crucial
advantages
of space-based NEO observation and/or the ability to target
troublesome
subpopulations of the NEO hazard. They are all therefore
consistent with a
greater application of the indicators of greatest NEO hazard
potential.
However, none of them represents an attempt at maximal
application of these
indicators, and as such all of them are products of a suboptimal
strategic
regime. Therefore, while a decision to reconfigure and enhance
the MESSENGER
mission is imperative in the current paradigm, it could also be a
suboptimal
deployment of resources in a new one.
II: BUILDING BLOCKS FOR A NEW STRATEGIC PARADIGM: M.O.I.D.'S
& MANIFOLDS
One key parameter that indicates maximal hazard potential, i.e. a
first-order component of NEO threat, is the Minimum Orbit
Intersection
Distance, MOID, with the Earth. The Earth-MOID of NEOs is an
easily
determined, relatively stable parameter that changes as an
object's orbit
changes. It can be initially computed from a one-week arc of
optical
observations. While this can be done more accurately and one to
three orders
of magnitude faster, currently available radar assets offer a
range limited
to Lunar Distances.
Abrupt changes in MOID due to close approaches with massive
bodies are a
fairly rare eventuality on human timescales for the vast majority
of NEAs.
The Spaceguard Survey Report assumed that most MOIDs will not
change by more
than a flat 10 Lunar Distances over a few centuries [10]. Still,
1953 EA
Quetzalcoatl's perihelion is reported to have changed by "a
whopping 7%" in
only 60 years due to Jupiter [11], which substantially perturbs
NEOs that
approach within a 1 AU radius and also has several powerful
resonances by
itself and in conjunction with 3+body interactions with Mars and
Saturn.
This Quetzalcoatl data point is even more unnerving when it is
compared to
the current analytical understanding of this Alinda-class of NEOs
in rapidly
changing orbits. While "synergic resonances" and
"supercrossers" are
mentioned in Milani's lucid discussion of Alindas, the
time-scales examined
in typical solar system integrator experiments are almost
geologic, and in
the face of decadal-scale transitions share the same
consternation that
geology suffered in the previous century with regard to the
severity of the
impact hazard: the shortest time-scale indicated for
"rapid" transitions is
"a few hundred years", and typically ten millennia
[12]. The heavens run
amok, damn truly sorry.
CCNet participants may recall that the Minor Planet Center's
Brian Marsden
examined in depth the MOID variations of 1997 X-Ray Foxtrot 11 in
his
classic discourse [13]. Romania's Berinde presents an analysis of
the MOID
of 1999 Alpha November 10 with his underappreciated SolSyIn
integrator
software package (far more interesting than a SETI screen-saver
for the PC).
Assuming no Earth eccentricity, he shows how the MOID may
decrease by an
order of magnitude to less than 1 LD within 500 years, while its
semimajor
axis decreases by more than 1% in the same period, about half of
that by
2050 [14]. He also indicates the object's Lyapunov time of 20-30
years,
which means that its motions past a few centuries into the future
will
remain behind a quasiperpetual fog of chaos, rendering it and
similar NEOs a
rather interesting bunch; apparently we are somewhat lucky with
1950
District Attorney's 2880 A.D. horizon.
Pisa's Bonnano presents an analytical treatment of stealthy MOID
variances
and applies it to specific NEOs [15]. Ross is building on the
truly
revolutionary work on manifolds by a Caltech/JPL astrodynamics
team, by
aiming to investigate the instabilities of typical NEO resonances
within the
context of an almost surreal labyrinth of enormous mobile
tunnels, which
permeate the solar system in a gargantuan network that has nodes
at the
Lagrangian points of massive bodies [16]. Paffenroth's open ODE
software on
Sourceforge [17] demonstrates how this mathematical paradigm is
on the verge
of revolutionizing at least four decades of work on NEOs, as it
is already
doing with libration-point space mission design.
Ross will be presenting at the University of Warwick's year-long
Geometric
Mechanics Symposium while storming the UK and Germany for the
next month
[18]. Not to be outdone, a celestial mechanics group at the
University of
Vienna has published investigations on orbital resonances in an
outstanding
series of books [19], and even a NATO conference recognized the
importance
of relativistic effects in Marchal's investigation of Einstein's
General
Relativity applied directly to the context of NEOs (recall
Mercury's
precession) [20]. Also noteworthy is the CELMEC series of
European
conferences [21].
At Los Alamos Richard Feynman is said to have described Hans
Bethe as a
battleship at full steam. Some of the most impressive battleships
were known
as Dreadnoughts, and we hope that our world's scholars can rise
to such a
standard, converging, nay aligning, into an unprecedented
astrodynamical
armada, with artillery pointed in the right directions. Given the
pathetic
straits of American academia in the last few decades, we can
perhaps hope
for an increase in scholarships "across the pond" and
elsewhere (just ask
Christopher J. Lucas, "Crisis in the Academy: Rethinking
Higher Education in
America"; for the hardcore disbelievers, dig out an old copy
of Ernest
Boyer's "Scholarship Reconsidered: Priorities of the
Professoriate", which
spoon-feeds the ABC's for PhDs and other typical victims of
stove-pipe
thinking).
III: A NEW STRATEGIC PARADIGM: TOROIDS
MOIDs and manifolds represent a potential strategic "end
run" around many
difficult obstacles. This is true in spite of the variations in
MOID over
decades and centuries to which NEOs are generally subject, and
the
computationally intensive manifold algorithms. Bamberga, in the
darkest,
low-albedo C-class of carbonaceous chondrites, has an albedo of
less than
0.05. Also, NEOs in various zones can be badly illuminated for
ground-based
observations due to poor angles of solar phase or elongation.
Thus low
albedos and poor illumination merely compound the difficulties
with NEOs in
orbits with higher angles of inclination and/or greater
osculating distances
from the Earth. Then we must factor in the many blind spots [22],
which also
include a lunar zone and a region of galactic latitudes that
provides
background obscuration due to the high stellar density of our
home, the
Milky Way [23], which may compound the well-known blind-spot for
objects
with low apparent motion, perhaps especially for the fraction of
NECs that
might be KBOs. Additionally, ~16% of NEA's are binary/pairs [24],
and
perhaps ~50% could be rubble-piles [25], both of which are
difficult to
detect and even more problematic for defencive strategies. Not to
be
discounted are the intolerably long completion times of
ground-based
surveys, which will take decades to get near 99.99% for the
"global killers"
and 99.9999% for the ~300m "continent busters" even
with the LSST, and the
already painful bottlenecks from the increasing surge in NEO
detections. In
spite of this medusan heap of doo-doo, the only potentially
hazardous NEOs
are the ones with low MOIDs now and in the future.
A low value for Earth-MOID is necessary but not sufficient for
high hazard
potential, because some NEOs are in protective resonances, e.g.
orbits in
Kozai secular or Toro mean-motion resonances [26], even if these
resonances
are subject to variability and instability. A long time ago,
about half of
known PHAs were found to be in these "presonances"
[27]. Therefore a
strategy designed to focus on the detection of NEOs with only the
lowest
values of Earth-MOID would efficiently eradicate the vast
majority of the
current risk exposure that derives from NEAs. Such a strategy
could
potentially perform much faster than any of the existing or
currently
proposed schemes of ground-based or space-based telescopes, with
a resulting
benefit that likewise would not substantially erode for many
decades if not
centuries. In the parlance of the old Admiralty, back when
"shipshape" meant
something, it may be time to "change tack."
What this species of new search strategy would mean in practice
is a
short-duration intense-coverage methodology for sampling the
relatively
minuscule region of space that is determined by a thin torus
surrounding the
Earth's orbit. The radius of this torus around the Earth's orbit
could be
0.05 AU, the present distance for designating an NEA as a
Potentially
Hazardous Asteroid (PHA), or larger, or smaller. Allowing for
Earth's 0.0167
orbital eccentricity, an effective lower-limit for the radius of
a perfect
torus would be about 0.0134 AU. But this is an arbitrary
standard; in
astrodynamical practice, a toroidal region that follows the
actual curve of
Earth's orbit would be substantially equivalent. The main point
is that
instead of flailing after widely uncooperative targets with
ever-more
powerful artillery within the enormous spherical volume inside
Jupiter's
orbit, say ~600 cubic AU's, we focus instead on say the
PHA-radius torus,
which has a neat volume of 0.05 cubic AU. This gives us a
volumetric
leverage factor of at least 10,000. But does this stick in
practice?
According to the most recent estimates, about 1% of NEOs have an
MOID
smaller than 1 LD, 0.00256 AU; this would amount to 245 of the
newly
estimated 24,500 NEOs larger than H<22 (diameter
>110-240m), of which about
6 are estimated to have an MOID smaller than the Earth's radius
[28]. True,
this lower estimate of smaller NEOs is news in itself, and good
news at
that. However, we must conservatively presume that these six
statistically
predestined impactors are not in presonances, and that they do
not have
properties favorable for their detection, e.g. could be
highly-inclined
long-period under-the-radar 900m, 450m, or 275m carbonaceous
Alindas that
approach from the dayside Southern Hemisphere in effortless
synchrony with
the annual seasons of monsoons, typhoons, Sydney hail, McMurdo
blizzards, or
increased solar flares in a fashion reminiscent of the Coral Sea
in WWII
[29]. Regarding cycles of sun spots, solar flares, and pulsating
expansions
of the atmosphere, note that these appear to correlate with a
variable ~5%
lag in Jupiter's primarily Saturn-modulated perihelion every
~11.86 years
(Jupiter's eccentricity is almost three times the Earth's), which
should be
verifiable in Earth climatological data [30]; we dare current
global warming
scientists to quantify their components of variance that are
Earth-exogeneous.
We should also consider the implication that this
"hexapocalypse" may only
be a starting lineup that rotates every 50-year inning in an
ubermatch of
cosmic cricket. Why? Not just due to MOID-drift, but also because
contrary
to some unfathomable "professional" opinions, there has
been no announcement
of an even temporary suspension of Murphy's Law; isn't it
completely
irresponsible to assume that the hexapocalyptic roster of PHAs
doesn't need
to be vetted yesterday?
The trespassing traversals of virtually all of the most
threatening NEAs,
and even some SPCs, all with an MOID within our maximally
hazardous toroid
('hazmaroid'?), could in principle be detected within the
governing upper
limit of one-half of Jupiter's orbital period, nominally 6 years,
a
dramatically short, very reasonable duration. In other words, all
of these
most-hazardous low-MOID NEAs have been slipping across the
borders of
Earth's Donut of Danger mostly undetected at least once every 6
years, just
waiting to eat all our future lunches. About 40% of NEOs have
orbital
periods less than 2 years, 65% <3 yrs, and 88% <4 yrs
[31]. Therefore it
appears that a donut-based strategy has highly attractive
features, but
again, does it stick? Consider as well another question: which
would you
rather have, 70% of all NEAs >1km by 2008, or 90% of all the
hazardous NEAs
>100m by 2008 and 99% by 2010? Or is this a false choice, in
that the
synergy of both options may be economically justified?
IV: APPLICATION OF A NEW STRATEGIC PARADIGM
A sampling methodology based on this strategy could be
implemented quickly
and cheaply with relatively short-lived space-based technology
that would
benefit from a mass-production economy of scale. The total cost
of such a
program, including microsatellites, launches, and operations,
could easily
be only a few percent of the total cumulative cost over just the
next
century of the annualized economic damage represented by the
total exposure
to the NEO hazard, which "century cost" is currently
estimated to be roughly
$150B [4]. Almost any sizeable endeavor requires a substantial
up-front
investment, and in the case of the NEO hazard the returns should
generally
last the millennium. Virtually irrelevant by any rational measure
of other
large government programs or largely underestimated government
waste, is the
cost for proof-of-concept missions like NESS, a veritable
hazard-focused
drop in the Hubble barrel of luxury.
What is sorely needed is a practicing economist to build upon the
partial
accounting and to quantify the comparative hazard analysis
(nuclear safety
standards) that was presented in the United Kingdom's NEO Task
Force Report
of 2000. This observer nominates Molly Macauley, senior fellow
and "space
economist" at WDC's Resources for the Future, to whip off
some simple
figures of merit for the field [32].
Inexpensive, "disposable" small satellite technology is
already in hand, and
merely needs to be deployed as a "necklaced perimeter
tripwire" somewhat
inside the Earth's orbit, with a sufficient number of units in
overlapping
ranges to achieve the desired 6-years of quasi-simultaneous
coverage all
along the Earth's orbit(because the drift rates are relatively
small,
coverage could be phased in with minor penalty). 10 identical
satellites
would each have to observe a ~36-degree tube-segment of the
Maximally
Hazardous Torus, at least 0.628 AU in width. Alternatively, 100
identical
smaller satellites would each only have to observe a ~3.6-degree
tube-segment, at least 0.0628 AU in width, and could do so from
an orbit
closer to the Earth's, an important improvement for minimizing
delta-V
requirements. The optimal number of satellites is a somewhat
complex
function of the robust semiconductor sensor technologies,
economies of
scale, novel engineering design solutions (e.g. a superior
methodology for
post-detection follow-up observations, and a capacity for a wide
distribution of NEO angular rates of motion), and the minimum
size object to
be detected. A potential bonus solution is the possibility of
detecting the
toroidal 1% of low-MOID small iron NEAs, which are hazardous
below 20m in
diameter [33] ; just consider the implications of Tedesco et al's
results,
which are much better than older non-IR estimates of the
distribution of
detectable range by NEO size (0.05 albedo): 125m within
0.25 AU at VM=22
[34], 100m within 0.1 AU at VM=18 [35], and 10m within 0.01 AU at
VM=20
[36].
Residual hazard potentials, e.g. second-order components of the
NEO threat
deriving from perturbations from close-approaches with planets
and minor
planets, nongravitational perturbations (outgassing, Yarkovsky,
MHD),
relativistic effects, resonance transitions, synergic resonances,
supercrossers, collisional and tidal-disruption fragmentation
events,
periodicities in the NEO flux, and the inherent limits on
forecasting
various orbits far into the future due to the mathematically
chaotic nature
of the orbits in our solar system (Wisdom & Sussman [37]),
can all be
addressed by the careful monitoring of NEOs in categories with
well-defined
parameters.
The proposed strategic application could offer additional
continuing benefit
if the effective lifetime of even a few of the deployed
satellites was
greater than the nominal span of 6 years, e.g. for comet
detection [22] and
preliminary NEO recons. Nevertheless, a revolutionary strategy
for the
detection of the remaining poorly-determined NEO threat-fraction
represented
by the LPCs continues to represent a significant challenge [38],
and remains
in the domain of Sir Clarke's original Excalibur proposal [39],
perhaps with
an apo-ecliptic Kuiper-belt variation that could still be
Sol-disk mediated.
For the uninitiated, it may serve to recall the standard
specified by Niven
and Pournelle in "The Mote in God's Eye": worthy
civilizations might be the
ones that can rake up the debris in their front yard, the remains
of the
ancient solar hurricane that was the birth of their home.
V: CONCLUSION
MOIDs and manifold-based algorithms constitute a new paradigm
that offers an
opportunity of potential strategic transcendence; Planetary
Defence may be
able to rise above the technical complications plaguing current
efforts.
Strategic applications of this new "toroidal" paradigm
appear to meet
practical tests and to offer compelling performance metrics. An
application
is specified that is basically the difference between calling for
artillery
fire on very wide-ranging targets, and having perfectly placed
snipers; just
ask any United States Marine Corps Force Recon sniper [40].
Alternatively,
this application can be viewed as laying a sparse, cheap, and
disposable
line of high-performance "space buoys" along the large
circle that is the
path of the Earth in her perpetual orbit about the Sun.
Upon brief historical study, it is amazing how bureaucracies can
melt like
butter upon such events as the signing of Presidential Executive
Orders
[41]. What is key is verifying and developing a proposal such as
has been
outlined here, to the point that it meets the approval of ranking
officers
exemplified by General Worden. The NEO gauntlet may now primarily
be
political, and infinitely easier to run in 2002 than it was
before 1998; the
end of considerable interfactional strife is within reach, if the
bug-a-boo
spectre haunting space-based NEO activities can be blown away.
Time appears to be ample for an interdisciplinary team to
coalesce before
the upcoming conferences in the Fall. From green-light, no
substantive
reasons are seen by this observer to preclude first launch within
12 months
of RDT&E, provided that a decent Quality Assurance program is
included from
incept date, perhaps 01Jan03. Any weaker goal would be
disgraceful to our
species; we may yet deserve a Darwinian verdict, Nature's shrug.
[1] Bottke, Morbidelli, Jedicke, Petit, Levison, Michel,
Metcalfe, "Debiased
Orbital and Absolute Magnitude Distribution of the Near-Earth
Objects" p.38
http://www.obs-nice.fr/michel/Debiased_NEO.pdf
[2] Morbidelli et al, November 2001: "We estimate that the
Earth should
undergo a 1000 megatons collision every 64,000 years. The NEOs
discovered so
far carry only 18% of this collision probability."
http://www.aas.org/publications/baas/v33n3/dps2001/134.htm
[3]
http://www.astropa.unipa.it/Asteroids2001/Abstracts/Posters/morbidelli.doc
[4] http://abob.libs.uga.edu/bobk/ccc/cc012602.html
[5] http://www.lssto.org/lssto/index.htm
http://wwwrc.obs-azur.fr/schmidt/general/NEOsurvey.html
http://abob.libs.uga.edu/bobk/ccc/cc032601.html
http://abob.libs.uga.edu/bobk/ccc/cc022801.html
http://abob.libs.uga.edu/bobk/ccc/cc022301.html
http://abob.libs.uga.edu/bobk/ccc/cc052500.html
[6] http://www.boulder.swri.edu/swuis/sts93/
[7] http://www.dynacon.ca/ness_paper_2000.pdf
http://abob.libs.uga.edu/bobk/ccc/cc101600.html
http://abob.libs.uga.edu/bobk/ccc/cc083000.html
[8] http://world.std.com/~terra/DPS98/
http://www.astropa.unipa.it/Asteroids2001/Abstracts/Posters/egan.doc
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[9] http://esapub.esrin.esa.it/br/br165/BEPI.pdf
[10] http://impact.arc.nasa.gov/reports/spaceguard/sg_5.html
[11] http://www.meteors.com/cgibin/cometlinear/wwwboard/messages/234.html
[12] http://copernico.dm.unipi.it/~milani/maratea/node6.html
[13] http://freespace.virgin.net/british.interplanetary/marsden.pdf
http://abob.libs.uga.edu/bobk/ccc/cc071999.html
[14] http://math.ubbcluj.ro/~sberinde/solsyin/examples.html
[15]
http://link.springer.de/link/service/journals/00230/bibs/0360001/2300411/sma
ll.htm
[16] "Potential Earth-impacting asteroids may utilize the
dynamical channels
as a pathway to Earth from nearby, seemingly harmless
heliocentric orbits
which are in resonance with the Earth. The same dynamics which
allows us to
construct libration point space missions such as the Genesis
Discovery
Mission, which is on a natural Earth collision orbit, is also the
dynamics
that could bring unexpected Earth impactors." p.23
http://www.cds.caltech.edu/~shane/papers/report.pdf
[17] http://www.cds.caltech.edu/conferences/2002/smd/talks/paffenroth.pdf
[18] http://www.maths.warwick.ac.uk/~mark/symposium/
[19] http://www.astro.univie.ac.at/~dvorak/download/books/book6.html
[20] http://www.maths.gcal.ac.uk/natoconf/program.html
[21] http://www.mat.uniroma2.it/celmec/abstracts3.html
[22] http://abob.libs.uga.edu/bobk/ccc/cc032502.html
[23] http://www.llnl.gov/planetary/pdfs/Detection/03-Harris.pdf
[24] http://astrosun.tn.cornell.edu/staff/bottke/Abstracts/binary_abs.html
http://www.space.com/scienceastronomy/solarsystem/double_asteroids_020411.html
[25] http://www.lpi.usra.edu/pub/meetings/lpsc2002/pdf/1843.pdf
[26] http://copernico.dm.unipi.it/~milani/maratea/maratea.html
[27] In 1994 about half of known PHA's were in resonances;
Gehrels et al,
"Hazards due to Comets & Asteroids", p. 179.
[28] Op cit, Bottke et al, p.41.
[29] http://www.austehc.unimelb.edu.au/fam/0641.html
[30] http://www.grandunification.com/hypertext/Jupiter.html
[31] As of 05Apr02, out of 1,841 known NEAs, better than 99.5%
have orbital
periods of less than 6 years. This is due to Jupiter's powerful
2:1
resonance. Only 9 known NEAs have orbital periods greater than 6
years, and
all of these are less than 9 years. Of the 28 known NECs, 10 SPCs
(36%) have
orbital periods less than 6 years, 18 (64%) less than 12 years.
N.B.: the population of known NEOs suffers from several flavors
of bias.
http://neo.jpl.nasa.gov/cgi-bin/neo_elem
[32] http://rff.org/about_rff/web_bios/macauley.htm
See "NEOs; Rapporteur", p.15 in:
http://www2.aiaa.org/international/content/PDF/ISCW-6_report.pdf
[33] http://www.aas.org/publications/baas/v33n3/dps2001/538.htm
[34] Gehrels et al, "Hazards due to Comets &
Asteroids", p. 157.
[35]
http://lifesci3.arc.nasa.gov/SpaceSettlement/spaceres/images/figIV-3-3.GIF
[36] http://www.astro.rug.nl/~vermaas/initiative2.html
[37]"Chaotic Evolution of the Solar System,'' Gerald Jay
Sussman and Jack
Wisdom,
Science, 257, 3 July 1992 http://www.swiss.ai.mit.edu/~gjs/gjs.html
[38] http://www.boulder.swri.edu/clark/neowp.html
[39] http://abob.libs.uga.edu/bobk/ccc/ce031902.html
[40] Perhaps John "Goldi-Locks" Bartlett, USMC (Ret.),
Gulf War Veteran,
who was at the very tip of "the tip of the spear."
[41] http://www.fas.org/irp/offdocs/direct.htm
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