Morbidelli et al.: Origin and Evolution of Near-Earth Objects
409
409
Origin and Evolution of Near-Earth Objects
A. Morbidelli
Observatoire de la CĂ´te dâAzur, Nice, France
W. F. Bottke Jr.
Southwest Research Institute, Boulder, Colorado
Ch. FroeschlĂŠ
Observatoire de la CĂ´te dâAzur, Nice, France
P. Michel
Observatoire de la CĂ´te dâAzur, Nice, France
Asteroids and comets on orbits with perihelion distance q < 1.3 AU and aphelion distance
Q > 0.983 AU are usually called near-Earth objects (NEOs). It has long been debated whether
the NEOs are mostly of asteroidal or cometary origin. With improved knowledge of resonant
dynamics, it is now clear that the asteroid belt is capable of supplying most of the observed
NEOs. Particular zones in the main belt provide NEOs via powerful and diffusive resonances.
Through the numerical integration of a large number of test asteroids in these zones, the pos-
sible evolutionary paths of NEOs have been identified and the statistical properties of NEOs
dynamics have been quantified. This work has allowed the construction of a steady-state model
of the orbital and magnitude distribution of the NEO population, dependent on parameters that
are quantified by calibration with the available observations. The model accounts for the exist-
ence of ~1000 NEOs with absolute magnitude H < 18 (roughly 1 km in size). These bodies
carry a probability of one collision with the Earth every 0.5 m.y. Only 6% of the NEO popu-
lation should be of Kuiper Belt origin. Finally, it has been generally believed that collisional
activity in the main belt, which continuously breaks up large asteroids, injects a large quantity
of fresh material into the NEO source regions. In this manner, the NEO population is kept in
steady state. The steep size distribution associated with fresh collisonal debris, however, is not
observed among the NEO population. This paradox might suggest that Yarkovsky thermal drag,
rather than collisional injection, plays the dominant role in delivering material to the NEO source
resonances.
1.
INTRODUCTION
The discovery of 433 Eros in 1898 established the ex-
istence of a population of asteroid-like bodies on orbits
intersecting those of the inner planets. It was not until the
Apollo program in the 1960s and 1970s, however, that lu-
nar craters were shown to be derived from impacts rather
than volcanism. With this evidence in hand, it was finally
recognized that the Earth-Moon system has been incessantly
bombarded by asteroids and comets over the last 4.5 G.y.
In 1980, Alvarez et al. presented convincing arguments that
the numerous species extinction at the Cretaceous-Tertiary
transition were caused by the impact of a massive asteroid
(
Alvarez et al.,
1980).
These results brought increasing attention to the objects
on Earth-crossing orbits and, more generally, to those hav-
ing perihelion distances q
â¤
1.3 AU and aphelion distances
Q
âĽ
0.983 AU. The latter constitute what is usually called
the near-Earth-object population (NEOs). Figure 1 shows
the distribution of the known NEOs with respect to their
semimajor axis, eccentricity, and inclination. The NEOs are
by convention subdivided into Apollos (a
âĽ
1.0 AU; q
â¤
1.0167 AU), Atens (a < 1.0 AU; Q
âĽ
0.983 AU), and Amors
(1.0167 AU < q
â¤
1.3 AU).
It is now generally accepted that the NEOs represent a
hazard of global catastrophe for human civilization. While
the discovery of unknown NEOs is of primary concern, the
theoretical understanding of the origin and evolution of
NEOs is also of great importance. Together, these efforts
can ultimately allow the estimatation of the orbital and size
distributions of the NEO population, which in turn makes
possible the quantification of the collision hazard and the
optimization of NEO search strategies. The purpose of this
chapter is to review our current knowledge of these issues.
We start in section 2 with a brief historical overview, fo-
cused on the many important advances that have contrib-
uted to the understanding of the NEO population. In sec-
tion 3 we discuss how asteroids can escape from the main
410
Asteroids III
belt and become NEOs, but we also mention the cometary
contribution to the NEO population. Section 4 will be de-
voted to a description of the typical evolutions of NEOs. In
these two sections, emphasis will be given to NEO dynami-
cal lifetimes and possible end states. Section 5 will discuss
how the current knowledge on the origin and evolution of
NEOs can be utilized to construct a quantitative model of
the NEO population. Section 6 will detail the debiased NEO
orbital and magnitude distribution resulting from this model-
ing effort. It will also discuss the implications of this model
1
1
0.2
0.4
0.6
0.8
0
10
20
30
40
Apollos
Amors
Mars-crossers
Atens
Main-belt asteroids
2
Semimajor Axis (AU)
ν
6
5:2
3:1
2:1
5:2
3:1
2:1
Eccentr
icity
Inclination
3
ν
6
Fig. 1.
The distribution of NEOs, Mars-crossers and main-belt asteroids with respect to semimajor axis, eccentricity, and inclination.
The first 10,000 main-belt asteroids in are shown in gray. The dots represent the Mars-crossers, according to
Migliorini et al.
âs (1998)
definition and identification: bodies with 1.3 < q < 1.8 that intersect the orbit of Mars within the next 300,000 yr. The Amors, Apollos,
and Atens are shown as circles, squares, and asterisks respectively. In boldface, the solid curve bounds the Earth-crossing region; the
dashed curve delimits the Amor region at q = 1.3 AU, and the dashed vertical line denotes the boundary between the Aten and Apollo
populations. The dotted curve corresponds to Tisserand parameter (1) with respect to Jupiter = 3, at i = 0: Jupiter-family comets re-
side predominantly beyond the curve T = 3. The locations of the 3:1, 5:2, and 2:1 mean motion resonances with Jupiter are shown by
vertical dashed lines. The semimajor axis location of the
ν
6
resonance is roughly independent of the eccentricity but is a function of
the inclination: It is shown by the dashed curve on the top panel, while in the bottom panel it is represented for i = 0.
Morbidelli et al.: Origin and Evolution of Near-Earth Objects
411
for the collision probability of NEOs with the Earth, and
the collisional and dynamical mechanisms that continuously
supply new bodies to the transportation resonances of the
asteroid belt. Finally, we discuss open problems and future
perspectives in section 7.
2.
HISTORICAL OVERVIEW
The asteroid vs. comet origin of the NEO population has
been debated throughout the last 40 years. With calcula-
tions based on a theory of Earth encounter probabilities,
Ăpik
(1961, 1963) claimed that the Mars-crossing asteroid
population was not large enough to keep the known Apollo
population in steady state. Based on this result,
Ăpik con-
cluded that about 80% of the Apollos are of cometary ori-
gin. The existence of meteor streams associated with some
Apollos seemed to provide some support for this hypoth-
esis. Conversely,
Anders
(1964) proposed that most Apollo
objects are small main-belt asteroids that became Earth-
crossers as a result of multiple close encounters with Mars.
Anders and Arnold
(1965) concluded that some Apollos
with high eccentricities or inclinations (like 1566 Icarus and
2101 Adonis) might be extinct cometary nuclei, whereas the
other Apollos (six known at the time!) should have been of
asteroidal origin. Possible asteroidal and cometary sources
of Apollo and Amor objects were reviewed in
Wetherill
(1976). The author considered several mechanisms (includ-
ing close encounters with Mars, mean motion resonances,
and secular resonances) to produce NEOs from the aster-
oid belt. Ultimately, he concluded that, although qualita-
tively acceptable, these mechanisms were unable to supply
the required number of NEOs by at least an order of mag-
nitude. Thus, Wetherill concluded that most Apollo objects
were cores of comets that had lost their volatile material by
repeated evaporation.
The problem at the time was that resonant dynamics was
poorly understood and computation speed was extremely
limited. Thus, direct numerical integration of asteroid or-
bits could not be used to determine the evolutionary paths
of NEOs. With the underestimatation of the effect of reso-
nant dynamics, NEO modelers were left with collision as
the only viable mechanism for moving asteroids from the
main belt directly into the NEO region. The typical ejec-
tion velocities of asteroid fragments generated in collisions,
however, is ~100 m/s, far too small in most cases to achieve
planet-crossing orbits (
Wetherill,
1976).
The first indication that resonances could force main-
belt bodies to cross the orbits of the planets came from the
Ph.D. thesis work of J. G. Williams. In a diagram reported
by
Wetherill
(1979), Williams showed that bodies close to
the
ν
6
resonance have secular eccentricity oscillations with
amplitude exceeding 0.25, and therefore they must periodi-
cally cross the orbit of Mars. Shortly afterwards,
Wisdom
(1983, 1985a,b) showed that the 3:1 mean motion resonance
has a similar effect: The eccentricity of resonant bodies can
have, at irregular time intervals, rapid and large oscillations
whose amplitudes exceed 0.3, the threshold value to become
a Mars-crosser at the 3:1 location. Following these pioneer-
ing works, attention was focused on the 3:1 and
ν
6
reso-
nances as primary sources of NEOs from the asteroid belt.
The dynamical structure of the 3:1 resonance was further
explored by
Yoshikawa
(1989, 1990),
Henrard and Cara-
nicolas
(1990), and
Ferraz-Mello and Klafke
(1991) in the
framework of the three-body problem. In a more realistic
multiplanet solar system model, numerical integrations by
Farinella et al.
(1993) showed that in the 3:1 resonance
the eccentricity evolves much more chaotically than in the
three-body problem â a phenomenon later explained by
Moons and Morbidelli
(1995) â and typically it reaches
not only Mars-, but also Earth- and Venus-crossing values
(see
Moons,
1997, for a review). Concerning the
ν
6
reso-
nance, the first quantitative numerical results were obtained
by
FroeschlĂŠ and Scholl
(1987), who confirmed the role that
this resonance has in increasing asteroid eccentricities to
Mars-crossing or Earth-crossing values. A first analytic
theory of the dynamics in this resonance was developed by
Yoshikawa
(1987), and later improved by
Morbidelli and
Henrard
(1991) and
Morbidelli
(1993) (see
FroeschlĂŠ and
Morbidelli,
1994, for a review).
Using these advances,
Wetherill
(1979, 1985, 1987,
1988) developed Monte Carlo models of the orbital evolu-
tion of NEOs coming from the
ν
6
and 3:1 resonances. In
these resonances the dynamics were simulated through
simple algorithms designed to mimic the results of analytic
theories or direct integrations, while elsewhere reduced to
the sole effects of close encounters, calculated using two-
body scattering formulae (
Ăpik,
1976). As the Monte Carlo
models were refined over time, the cometary origin hypoth-
esis was progressively abandoned as a potential source of
NEOs in the inner solar system. Wetherill hypothesized that
the
ν
6
and 3:1 resonances are continuously resupplied via
catastrophic collisions and/or cratering events in the main
belt, and that enough material is injected into the resonances
to keep the NEO population in steady state. Wetherillâs work
was later extended by
Rabinowitz
(1997a,b), who predicted
the existence of 875 NEOs larger than 1 km, in remarkable
agreement with current estimates.
In the 1990s, the availability of cheap and fast worksta-
tions allowed the first direct simulations of the dynamical
evolution of test particles, initially placed in the NEO re-
gion or in the transport resonances, over million-year time-
scales. Using a Bulirsch-Stoer integrator, a breakthrough
result was obtained by
Farinella et al.
(1994), who showed
that NEOs with a < 2.5 AU can easily collide with the Sun,
which limits their typical dynamical lifetime to a few mil-
lion years. It became thus rapidly evident that Monte Carlo
codes do not adequately treat the inherently chaotic behav-
ior of bodies in NEO space (see
Dones et al.,
1999, for a
discussion). The introduction of a new numerical integra-
tion code (
Levison and Duncan,
1994), which extended a
numerical symplectic algorithm proposed by
Wisdom and
Holman
(1991), introduced the possibility of numerically
412
Asteroids III
integrating a much larger number of particles, to quantify
the statistical properties of NEO dynamics. The subsequent
studies have contributed to our current understanding of the
origin, evolution, and orbital distribution of NEOs, reviewed
in the next sections.
3.
DYNAMICAL ORIGIN OF NEOs
Asteroids become planet crossers by increasing their
orbital eccentricity under the action of a variety of reso-
nant phenomena. It is suitable to separately consider âpow-
erful resonancesâ and âdiffusive resonances.â The former
can be effectively distinguished from the latter by the ex-
istence of associated gaps in the main-belt asteroid distri-
bution. The most notable resonances in the âpowerfulâ class
are the
ν
6
secular resonance at inner edge of the asteroid
belt, and the mean motion resonances with Jupiter 3:1, 5:2,
and 2:1 at 2.5, 2.8, and 3.2 AU respectively. Their properties
are detailed below. The diffusive resonances are so numer-
ous that they cannot be effectively enumerated. Therefore,
we will discuss only their generic dynamical effects. The
reader can refer to
NesvornĂ˝ et al.
(2002) for a more techni-
cal discussion of the dynamical structure of the main aster-
oid belt.
3.1.
ννννν
6
Resonance
The
ν
6
secular resonance occurs when the precession
frequency of the asteroidâs longitude of perihelion is equal
to the sixth secular frequency of the planetary system. The
latter can be identified with the mean precession frequency
of Saturnâs longitude of perihelion, but it is also relevant
in the secular oscillation of the eccentricity of Jupiter (see
chapter 7 of
Morbidelli,
2002). As shown in the top panel
of Fig. 1, the
ν
6
resonance marks the inner edge of the main
belt. The effect of the resonance rapidly decays with the
distance from the shown curve. To schematize, we divide
the ~0.08-AU-wide neighborhood on the righthand side of
the curve into a âpowerful regionâ and a âborder region,â
roughly of equal size (about 0.04 AU each).
In the powerful region the resonance causes a regular
but large increase of the eccentricity of the asteroids. As a
consequence, the asteroids reach Earth- (or Venus-) cross-
ing orbits, and in several cases they collide with the Sun,
with their perihelion distance becoming smaller than the
solar radius. The median time required to become an Earth-
crosser, starting from a quasicircular orbit, is about 0.5 m.y.
Accounting also for the subsequent evolution in the NEO
region (discussed in section 4), the median lifetime of bod-
ies initially in the
ν
6
resonance is 2 m.y., the typical end
states being collision with the Sun (80% of the cases) and
ejection on hyperbolic orbit (12%) (
Gladman et al.,
1997).
The mean time spent in the NEO region is 6.5 m.y. (
Bottke
et al.,
2002a), and the mean collision probability with Earth,
integrated over the lifetime in the Earth-crossing region, is
~10
â2
(
Morbidelli and Gladman,
1998).
In the border region, the effect of the
ν
6
resonance is less
powerful, but is still capable of forcing the asteroids to cross
the orbit of Mars at the top of the secular oscillation cycle
of their eccentricity. To enter the NEO region, these aster-
oids must evolve under the effect of martian encounters,
and the required time increases sharply with the distance
from the resonance (
Morbidelli and Gladman,
1998). The
dynamics in this region are complicated by the dense pres-
ence of mean motion resonances with Mars, and we will
revisit this in section 3.5.
3.2.
3:1 Resonance
The 3:1 mean-motion resonance with Jupiter occurs at
~2.5 AU. Inside the resonance, one can distinguish two
regions: a narrow central region where the asteroid eccen-
tricity has regular oscillations that cause them to periodi-
cally cross the orbit of Mars, and a larger border region
where the evolution of the eccentricity is wildly chaotic and
unbounded, so that the bodies can rapidly reach Earth-cross-
ing and even Sun-grazing orbits. Under the effect of mar-
tian encounters, bodies in the central region can easily travel
to the border region and be rapidly boosted into NEO space
(see chapter 11 of
Morbidelli,
2002). For a population ini-
tially uniformly distributed inside the resonance, the median
time required to cross the orbit of the Earth is ~1 m.y., the
median lifetime is ~2 m.y., and the typical end states are
the collision with the Sun (70%) and the ejection on hyper-
bolic orbit (28%) (
Gladman et al.,
1997). The mean time
spent in the NEO region is 2.2 m.y. (
Bottke et al.,
2002a),
and the mean collision probability with Earth, integrated
over the lifetime in the Earth-crossing region, is 2 Ă 10
â3
(
Morbidelli and Gladman,
1998).
3.3.
5:2 Resonance
The 5:2 mean-motion resonance with Jupiter is located
at 2.8 AU. The mechanisms that allow the rapid and cha-
otic eccentricity evolution in the border region of the 3:1
resonance in this case extend to the entire resonance (
Moons
and Morbidelli,
1995). As a consequence, this resonance is
the one that pumps the orbital eccentricities on the shortest
timescale. The median time required to reach Earth-crossing
orbit is ~0.3 m.y., and the median lifetime is 0.5 m.y. Be-
cause the resonance is closer to Jupiter than the previous
ones, the ejection on hyperbolic orbit is the most typical
end state (92%), while the collision with the Sun accounts
only for 8% of the losses (
Gladman et al.,
1997). The mean
time spent in the NEO region is 0.4 m.y. and the mean colli-
sion probability with Earth, integrated over the lifetime in
the Earth-crossing region, is 2.5 Ă 10
â4
.
3.4.
2:1 Resonance
Despite the fact that this resonance, located at 3.28 AU,
is associated with a deep gap in the asteroid distribution,
Morbidelli et al.: Origin and Evolution of Near-Earth Objects
413
there are no mechanisms capable of destabilizing the reso-
nant asteroid motion on the short timescales typical of the
other resonances. In fact, the dynamical structure of the 2:1
resonance is very complicated (
NesvornĂ˝ and Ferraz-Mello,
1997;
Moons et al.,
1998). At the center of the resonance
and at moderate eccentricity, there are large regions where
the dynamical lifetime is on the order of the age of the solar
system. Some asteroids are presently located in these re-
gions (the so-called Zhongguo group), but it is still not
completely understood why their number is so small (see
NesvornĂ˝ and Ferraz-Mello,
1997, for a discussion on a
possible cosmogonic mechanism). The regions close to the
borders of the resonance are unstable, but several million
years are required before an Earth-crossing orbit can be
achieved (
Moons et al.,
1998). Once in NEO space, the
dynamical lifetime is only on the order of 0.1 m.y., because
the bodies are rapidly ejected by Jupiter onto hyperbolic
orbit. The mean collision probability with the Earth, inte-
grated over the lifetime in the Earth-crossing region, is
about 5 Ă 10
â5
.
3.5.
Diffusive Resonances
In addition to the few wide mean-motion resonances
with Jupiter described above, the main belt is densely
crossed by hundreds of thin resonances: high-order mean-
motion resonances with Jupiter (where the orbital frequen-
cies are in a ratio of large integer numbers), three-body
resonances with Jupiter and Saturn (where an integer com-
bination of the orbital frequencies of the asteroid, Jupiter,
and Saturn is equal to zero;
Murray et al.,
1998;
NesvornĂ˝
and Morbidelli
, 1998, 1999), and mean motion resonances
with Mars (
Morbidelli and NesvornĂ˝,
1999). Because of
these resonances, many â if not most â main-belt aster-
oids are chaotic (see
NesvornĂ˝ et al.,
2002, for discussion).
The effect of this chaoticity is very weak. The mean semi-
major axis is bounded within the narrow resonant region;
the proper eccentricity and inclination (see
Kne
z
evi
c
et al.,
2002) slowly change with time, in a chaotic diffusion-like
process. The time required to reach a planet-crossing orbit
(Mars-crossing in the inner belt, Jupiter-crossing in the outer
belt) ranges from several 10
7
yr to billions of years, depend-
ing on the resonances and starting eccentricity (
Murray and
Holman,
1997).
Integrating real objects in the inner belt (2 < a < 2.5 AU)
for 100 m.y.
, Morbidelli and NesvornĂ˝
(1999) estimated that
chaotic diffusion drives about two asteroids larger than 5 km
into the Mars-crossing region every million years. The es-
cape rate is particularly high in the region adjacent to the
ν
6
resonance, because of the effect of the latter, but also
because of the dense presence of mean motion resonances
with Mars. The high rate of diffusion of asteroids from the
inner belt can explain the existence of the conspicuous
population of Mars-crossers. Following
Migliorini et al.
(1998), we define the latter as the population of bodies with
q > 1.3 AU that intersect the orbit of Mars within a secular
cycle of their eccentricity oscillation (in practice within the
next 300,000 yr). The Mars-crossers are about 4Ă more
numerous than the NEOs of equal absolute magnitude (sta-
tistics done on bodies with H
< 15, which constitute an
almost complete sample in both populations). It was be-
lieved in the past that most q > 1.3 AU Mars-crossers were
bodies extracted from the main transportation resonances
(i.e., 3:1 and
ν
6
resonances) by close encounters with Mars.
But, as pointed out by Migliorini et al., the eccentricity of
bodies in these resonances increases so rapidly to Earth-
crossing values that only a few bodies can be extracted by
Mars and emplaced in the Mars-crossing region with q >
1.3 AU. This low probability is only partially compensated
by the fact that, once bodies enter this Mars-crossing re-
gion, their dynamical lifetime becomes about 10Ă longer.
Indeed, work on numerical integrations indicate that if the
3:1 and
ν
6
resonances sustained both the Mars-crossing
population with q > 1.3 AU and the NEO population, the
ratio between these populations would be only 0.25 (i.e.,
16Ă smaller than observed).
Figure 1 shows that the population of Mars-crossers
extends up to a ~ 2.8 AU, suggesting that the phenomenon
of chaotic diffusion from the main belt extends at least up
to this threshold. The (a,i) panel shows that in addition to
the main population situated below the
ν
6
resonance (called
IMC hereafter), there are two groups of Mars-crossers with
orbital elements that mimic those of the Hungaria (1.77 <
a < 2.06 AU and i > 15°) and Phocaea (2.1 < a < 2.5 AU
and i >18°) populations, arguing for the effectiveness of
chaotic diffusion as well in these high-inclination regions.
To reach Earth-crossing orbit, the Mars-crossers random
walk in semimajor axis under the effect of martian encoun-
ters until they enter a resonance that is strong enough to
further decrease their perihelion distance below 1.3 AU. For
the IMC group, the median time required to become an
Earth-crosser is ~60 m.y.; about two bodies larger than 5 km
become NEOs every million years (
Michel et al.,
2000b),
consistent with the supply rate from the main belt estimated
by
Morbidelli and NesvornĂ˝
(1999). The mean time spent
in the NEO region is 3.75 m.y. (
Bottke et al.,
2002a). The
median time to reach Earth-crossing orbits from the two
groups of high inclined Mars-crossers exceeds 100 m.y.
(
Michel et al.,
2000b).
The paucity of Mars-crossers with a > 2.8 AU is not due
to the inefficiency of chaotic diffusion in the outer asteroid
belt. It is simply the consequence of the fact that the dynam-
ical lifetime of bodies in the Mars-crossing region drops
with increasing semimajor axis toward the Jupiter-crossing
limit. In addition, the observational biases for kilometer-
sized asteroids are more severe than in the a < 2.8 AU re-
gion. In fact, the outer belt is densely crossed by high-order
mean-motion resonances with Jupiter and three-body reso-
nances with Jupiter and Saturn, so an important escape rate
into the NEO region should be expected.
Bottke et al.
(2002a) have integrated for 100 m.y. nearly 2000 observed
main-belt asteroids with 2.8 < a < 3.5 AU and i < 15° and
414
Asteroids III
q < 2.6 AU; almost 20% of them entered the NEO region.
About 30,000 bodies with H < 18 can be estimated to exist
in the region covered by Bottke et al.âs initial conditions.
According to Bottke et al. integrations, in a steady-state
scenario this population could provide ~600 new H < 18
NEOs per million years, but the mean time that these bod-
ies spend in the NEO region is only ~0.15 m.y.
3.6.
Cometary Contribution
Despite the fact that asteroids dominate the NEO popu-
lation with small semimajor axes, comets are also expected
to be important contributors to the overall NEO population.
Comets can be subdivided into two groups: those coming
from the Kuiper Belt (or, more likely, the scattered disk)
and those coming from the Oort Cloud. The first group in-
cludes the Jupiter-family comets (JFCs). Their orbital distri-
bution has been well-characterized with numerical integra-
tions by
Levison and Duncan
(1997). Their cometary test
bodies, however, remained confined to a > 2.5 AU orbits,
probably because terrestrial planet perturbations and non-
gravitational forces were not included in the simulations.
The population of comets of Oort Cloud origin includes
the long periodic and Halley-type groups. To explain the
orbital distribution of the observed population, several re-
searchers have postulated that the comets from the Oort
Cloud rapidly âfadeâ away, either becoming inactive or
splitting into small components (
Wiegert and Tremaine,
1999;
Levison et al.,
2001). Since the number of faded
comets to new comets has yet to be determined, calculat-
ing the population on NEO orbits is problematic. Despite
this, best-guess estimates suggest that impacts from Oort
Cloud comets may be responsible for 10â30% of the cra-
ters on Earth (see
Weissman et al.,
2002). However, recent
unpublished work (Levison et al., personal communication,
2001) reduces this estimate to only ~1%.
4.
EVOLUTION IN NEO SPACE
The dynamics of the bodies in NEO space is strongly
influenced by close encounters with the planets. Each en-
counter provides an impulse velocity to the bodyâs trajec-
tory, causing the semimajor axis to âjumpâ by a quantity
depending on the geometry of the encounter and the mass
of the planet. The change in semimajor axis is correlated
with the change in eccentricity (and inclination) by the
quasiconservation of the so-called Tisserand parameter
T
a
a
a
e
a
i
p
p
=
+
â
2
1
2
cos
(1)
relative to the encountered planet with semimajor axis a
p
(
Ăpik,
1976). An encounter with Jupiter can easily eject the
body from the solar system (a
=
â
or negative), while this
is virtually impossible in encounters with the terrestrial
planets.
Under the sole effect of close encounters with a unique
planet, and neglecting the effects on the inclination, a body
would randomly walk on a curve of the (a, e) plane defined
by T
= constant. These curves are transverse to all mean-
motion resonances and to most secular resonances, so that
the body can be extracted from a resonance and be trans-
ported into another one. Resonances, on the other hand,
change the eccentricity and/or the inclination of the bod-
ies, keeping the semimajor axis constant. The real dynamics
in the NEO region are therefore the result of a complicated
interplay between resonant dynamics and close encounters
(see
Michel et al.,
1996a). A further complication is that
encounters with several planets can occur at the same time,
thus breaking the Tisserand parameter approximation even
in the absence of resonant effects.
As anticipated in the previous section, most bodies that
become NEOs with a > 2.5 AU are preferentially trans-
ported to the outer solar system or are ejected on hyper-
bolic orbit. In fact, if the eccentricity is sufficiently large,
the NEOs in this region approach the Jupiter-crossing limit
where the giant planet can scatter them outward. At that
point, their dynamics become similar to that of Jupiter-fam-
ily comets. A typical example is given by the rightmost evo-
lution in Fig. 2a. The body penetrates the NEO region by
increasing its orbital eccentricity inside the 5:2 resonance
until e ~ 0.7; the encounters with Jupiter then extract it from
the resonance and transport it to a larger semimajor axis.
Only bodies extracted from the resonance by Mars or Earth
and rapidly transported on a low-eccentricity path to a
smaller semimajor axis could escape the scattering action
of Jupiter. But this evolution is increasingly unlikely as the
initial semimajor axis is set to larger and larger values.
Conversely, the bodies on orbits with a ~ 2.5 AU or
smaller do not approach Jupiter even at e ~ 1, so that they
end their evolution preferentially by impacting the Sun.
Most of the bodies originally in the 3:1 resonance are trans-
ported to e ~ 1 without having a chance of being extracted
from the resonance. For the bodies originally in the
ν
6
reso-
nance, a temporary extraction from the resonance in the
Earth-crossing space is more likely (Fig. 2a). Most of the
IMCs with 2 < a < 2.5 AU eventually enter the 3:1 or the
ν
6
resonance and subsequently behave as resonant particles.
Figures 2b and 2c show evolutionary paths from
ν
6
and
3:1, which are unlikely (they occur in ~10% of the cases),
but extremely important to understanding the observed
NEO orbital distribution. In these cases, encounters with
Earth or Venus extract the body from its original resonance
and transport it into the region with a < 2 AU (hereafter
called the âevolved regionâ). Once in the evolved region,
the dynamical lifetime grows longer (~10 m.y.,
Gladman
et al.,
2000) because there are no statistically significant
dynamical mechanisms that pump the eccentricity up to
Sun-grazing values. To be dynamically eliminated, the bod-
ies in the evolved region must either collide with a terres-
trial planet (rare) or be driven back to a > 2 AU, where
powerful resonances can push them into the Sun. The en-
hanced lifetime partially compensates for the difficulty these
Morbidelli et al.: Origin and Evolution of Near-Earth Objects
415
objects have in reaching the evolved region. Thus, the latter
should host 38% and 70% respectively of all NEOs of 3:1
and
ν
6
origin (
Bottke et al.,
2002a).
The dynamical evolution in the evolved region can be
very tortuous, and does not follow any clear curve of con-
stant Tisserand parameter. The main reason is that first-order
secular resonances are present and effective in this region,
and continuously change the perihelion distance of the body
(see
Michel et al.,
1996b;
Michel and FroeschlĂŠ,
1997;
Michel,
1997a). In some cases the perihelion distance can
be temporarily raised above 1 AU, where, in the absence
of encounters with Earth, the body can reside for several
million years (notice the density of points at a ~ 1.62, e ~
0.3 in Fig. 2b). The Kozai resonance (
Michel and Thomas,
1996;
Gronchi and Milani,
1999) and the mean-motion
resonances with the terrestrial planets (
Milani and Baccili,
1998) can also provide a protection mechanism against
close approaches, thus stabilizing the motion of the bodies
temporarily locked into them. Among mean-motion reso-
nance trapping, of importance is the temporary capture in
a coorbital state, where the body follows horseshoe and/or
tadpole librations about a planet. This phenomenon has
been observed in the numerical simulations by
Michel et al.
(1996b),
Michel
(1997b), and
Christou
(2000), and a de-
tailed theory has been developed by
Namouni
(1999). The
asteroid (3753) 1986 T0 has been shown to currently evolve
on a highly inclined horseshoe orbit around Earth (
Wiegert
et al.,
1997).
Fig. 2.
Orbital evolutions of objects leaving the main asteroid belt. The curves indicate the sets of orbits having aphelion or perihe-
lion at the semimajor axis of one of the planets Venus, Earth, Mars, or Jupiter.
(a)
Common evolution paths from the
ν
6
,
3:1, and 5:2
resonances.
(b)
A long-lived particle from the
ν
6
resonance. The evolution before 20 m.y. is shown in black, and the subsequent one
is illustrated in gray.
(c)
A long-lived particle from 3:1; black dots show the evolutions during the first 15 m.y. Adapted from
Gladman
et al.
(1997).
1
1
1.5
2
ν
6
ν
6
2.5
3:1
5:2
3
1
1.5
2
1
(a)
(b)
(c)
2
2.5
2.5
3
0.8
Eccentr
icity
Eccentr
icity
Eccentr
icity
Semimajor Axis (AU)
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
3:1
416
Asteroids III
We point out a few additional features in the evolution
of Fig. 2b that we find remarkable. The body passes into
the region with a ~ 1 AU and e
< 0.1 twice, where the so-
called small Earth approachers (SEAs) have been observed
(
Rabinowitz et al.,
1993). This shows that the SEAs could
come from the main belt. Also, the evolution penetrates in
the region inside Earthâs orbit (aphelion distance smaller
than 0.983 AU). It is then plausible to conjecture the exist-
ence of a population of âinterior to the Earth objectsâ
(IEOs), despite the fact that observations have not yet dis-
covered any such bodies (
Michel et al.,
2000a).
5.
QUANTITATIVE MODELING OF
THE NEO POPULATION
The observed orbital distribution of NEOs is not repre-
sentative of the real distribution, because strong biases ex-
ist against the discovery of objects on some types of orbits.
Given the pointing history of a NEO survey, the obser-
vational bias for a body with a given orbit and absolute
magnitude can be computed as the probability of being in
the field of view of the survey, with an apparent magnitude
brighter than the limit of detection (see
Jedicke et al.,
2002).
Assuming random angular orbital elements of NEOs, the
bias is a function B(a, e, i, H), dependent on semimajor axis,
eccentricity, inclination, and absolute magnitude H. Each
NEO survey has its own bias. Once the bias is known, in
principle the real number of objects N can be estimated as
N(a, e, i, H) = n(a, e, i, H)/B(a, e, i, H)
where n
is the number of objects detected by the survey.
The problem, however, is resolution; even a coarse binning
in the four-dimensional orbital-magnitude space of the bias
function and the observed distribution requires the use of
about 10,000 cells. The total number of NEOs detected by
the most efficient surveys is a few hundreds. Thus n is zero
on the vast majority of the cells, and it is equal to 1 in most
other cells; cells with n > 1 are very rare. The debiasing of
the NEO population is therefore severely affected by small
number statistics. To circumvent this problem, one can con-
sider projected distributions of the detected NEOs, such as
n(a, e), n(i), and n(H), and try to debias each of them inde-
pendently, using a mean bias [
B
(a, e),
B
(i), or
B
(H)], com-
puted by summation of B(a, e, i, H) over the hidden dimen-
sions (
Stuart,
2000). However, the study of the dynamics
shows that the inclination distribution is strongly dependent
on a and e: Dynamically young NEOs with large semima-
jor axes roughly preserve their main-belt-like inclination,
while dynamically old NEOs in the evolved region have
a much broader inclination distribution, due to the action
of the multitude of resonances that they crossed during
their lifetime. As a consequence, this simplified debiasing
method can lead to very approximate results.
An alternative way to construct a model of the real dis-
tribution of NEOs heavily relies on the dynamics. In fact,
from numerical integrations, it is possible to estimate the
steady-state orbital distribution of the NEOs coming from
each of the main source regions defined in section 3 (see
below for the method). In this approach, the key assump-
tion is that the NEO population is currently in steady state.
This requires some comments. The analysis of lunar and
terrestrial craters suggests that the impact flux on the Earth-
Moon system has been more or less constant for the last
~3 G.y. (
Grieve and Shoemaker,
1994), thus supporting the
idea of a gross steady state of the NEO population. This
view is challenged, however, by the analysis of the aster-
oid belt, which shows that the formation of several aster-
oid families occurred over the age of the solar system (see
ZappalĂ et al.,
2002).
The formation of asteroid families may have had two
consequences on the time evolution of the NEO population:
1. A large number of asteroids might have been injected
into the resonances at the moment of the parent bodies
breakup, producing a temporary large increase in the NEO
population (
ZappalĂ et al.,
1997). Because the median life-
time of resonant particles is ~2 m.y., the NEO population
should have returned to a normal âsteady-stateâ value in
about 10 m.y. Being short-lived, these temporary spikes in
the total number of NEOs should not have left an easily
detectable trace in the terrestrial planet crater record. How-
ever, evidence that one of these spikes really happened â
at least for meteorite-sized NEOs â comes from the dis-
covery of 17 âfossil meteoritesâ in a 480-m.y.-old limestone
(
Schmitz et al.,
1996, 1997). These discoveries suggest that
the influx of meteorites during that 1â2-m.y. period was 10â
100Ă higher than at present. If the general belief that fami-
lies are several 10
8
â10
9
yr old (
Marzari et al.,
1995) is cor-
rect, the current NEO population should not be affected by
any of these hypothetical spikes.
2. The rate at which bodies have been continuously
supplied to some transporting resonance(s) might have in-
creased after a major family formation event enhanced the
population in the resonance vicinity. In this case the NEO
population would have evolved to a new and different
steady-state situation. Possible evidence for such a transi-
tion comes from
Culler et al.
(2000), who claimed that the
lunar impactor flux has been higher by a factor of 3.7 Âą
1.2 over the last 400 m.y. than over the previous 3 G.y. Even
this case, however, would not invalidate the steady-state
assumption, essential for constructing a model of the NEO
distribution based on statistics of the orbital dynamics. In
fact, being short-lived, the NEO population preserves no
memory of what happened several 10
8
yr ago; what is im-
portant is that the NEO population has been in the same
âsteady stateâ during the last several ~10
7
yr, namely on a
timescale significantly longer than the mean lifetime in the
NEO region.
The recipe to compute the steady-state orbital distribu-
tion of the NEOs for a given source is as follows. First, the
dynamical evolutions of a statistically significant number
of particles, initially placed in the NEO source region(s), are
numerically integrated. The particles that enter the NEO
region are followed through a network of cells in the (a, e, i)
space during their entire dynamical lifetime. The mean time
spent in each cell (called residence time hereafter) is com-
Morbidelli et al.: Origin and Evolution of Near-Earth Objects
417
puted. The resultant residence time distribution shows
where the bodies from the source statistically spend their
time in the NEO region. As is well known in statistical
mechanics, in a steady-state scenario, the residence time
distribution is equal to the relative orbital distribution of the
NEOs that originated from the source.
This dynamical approach was first introduced by
Wetherill
(1979) and was later imitated by
Rabinowitz
(1997a). Unfortunately, these works used Monte Carlo
simulations, which allowed only a very approximate knowl-
edge of the statistical properties of the dynamics.
Bottke et
al.
(2000) have reactualized the approach using modern
numerical integrations. They computed the steady-state
orbital distributions of the NEOs from three sources: the
ν
6
resonance, the 3:1 resonance, and the IMC population.
The latter was considered to be representative of the out-
come of all diffusive resonances in the main belt up to a =
2.8 AU. The overall NEO orbital distribution was then con-
structed as a linear combination of these three distributions,
thus obtaining a two-parameter model. The NEO magni-
tude distribution, assumed to be source-independent, was
constructed so its shape could be manipulated using an
additional parameter. Combining the resulting NEO orbital-
magnitude distribution with the observational biases asso-
ciated with the Spacewatch survey (
Jedicke,
1996),
Bottke
et al.
(2000) obtained a model distribution which could be
fit to the orbits and magnitudes of the NEOs discovered or
accidentally rediscovered by Spacewatch. To have a better
match with the observed population at large a,
Bottke et al.
(2002a) extended the model by also considering the steady-
state orbital distributions of the NEOs coming from the
outer asteroid belt (a > 2.8 AU) and from the Transneptu-
nian region. The resulting best-fit model nicely matches the
distribution of the NEOs observed by Spacewatch, without
restriction on the semimajor axis (see Fig. 10 of
Bottke
et al.,
2002a).
Notice that, once the values of the parameters of the
model are computed by best-fitting the observations of
one
survey, the steady-state orbital-magnitude distribution of the
entire
NEO population is determined. This distribution is
valid also in those regions of the orbital space that have
never been sampled by any survey because of extreme
observational biases. For instance, Bottke et al. models
predict the total number of IEOs, despite the fact that none
of these objects has ever been detected. This underlines the
power of the dynamical approach for debiasing the NEO
population.
6.
DEBIASED NEO POPULATION
This section is based strongly on the results of the mod-
eling effort by
Bottke et al.
(2002a). Unless explicitly stated,
all numbers reported below are taken from that work.
The total NEO population contains 960 Âą 120 objects
with absolute magnitude H < 18 (roughly 1 km in diameter)
and a < 7.4 AU. The observational completeness of this pop-
ulation as of July 2001 is ~45%. The NEO absolute mag-
nitude distribution is of type N(<H) = C Ă 10
0.35 Âą 0.02 H
in
the range 13 < H < 22, implying 24,500 Âą 3000 NEOs with
H < 22. Assuming that the albedo distribution is not depen-
dent on H, this magnitude distribution implies a power-law
cumulative size distribution with exponent â1.75 Âą 0.1. This
distribution is in perfect agreement with that obtained by
Rabinowitz et al
. (2000), who directly debiased the mag-
nitude distribution observed by the NEAT survey. Also,
once scaling laws are taken into account, it is in agreement
with the â2 mean exponent of the cumulative crater size
distributions observed on all terrestrial planets and the Moon
(see
Ivanov et al.,
2002).
The debiased orbital-magnitude distribution of the NEOs
with H < 18 is shown in Fig. 3. For comparison, the figure
also reports the distribution of discovered objects, combin-
ing the results of all NEO surveys. Most of the undiscov-
ered NEOs have H > 16, e > 0.4, a = 1â3 AU, and i =
5°â40°. Overall, 32 Âą 1% of the NEOs are Amors, 62 Âą 1%
are Apollos, and 6 Âą 1% are Atens. Of the NEOs, 49 Âą 4%
should be in the evolved region (a < 2 AU), where the dy-
namical lifetime is strongly enhanced. The ratio between
the IEO and the NEO populations is about 2%.
With this orbital distribution, and assuming random val-
ues for the argument of perihelion and the longitude of
node, about 21% of the NEOs turn out to have a minimal
orbital intersection distance (MOID) with the Earth smaller
than 0.05. The MOID is defined as the minimal distance
between the osculating orbits of two objects. NEOs with
MOID < 0.05 AU are classified as potentially hazardous
objects (PHOs), and the accurate orbital determination of
these bodies is considered a top priority.
To estimate the collision probability with the Earth, we
use the collision probability model described by
Bottke et al.
(1994). This model, which is an updated version of similar
models described by
Ăpik
(1951),
Wetherill
(1967), and
Greenberg
(1982), assumes that the values of the mean
anomalies of the Earth and the NEOs are random. The
gravitational attraction exerted by the Earth is also included.
We find that, on average, the Earth collides with an H < 18
NEO once every 0.5 m.y. Figure 4 shows how the collision
probability is distributed as a function of the NEO orbital
elements or, equivalently, which NEOs carry most of the
collisional hazard. For an individual object, the collision
probability with the Earth decreases with increasing semi-
major axis, eccentricity, and/or inclination (
Morbidelli and
Gladman,
1998). For this reason, the histograms in Fig. 4
are very different from those in Fig. 3: The a distribution
peaks at 1 AU instead of 2.2 AU, the e distribution is more
symmetric with respect to the e = 0.5 value, and the i dis-
tribution is much steeper.
The stated goal of the Spaceguard survey, a NEO sur-
vey program proposed in the early 1990s, was to discover
90% of the NEOs with H < 18 (
Morrison,
1992). However,
it would be more appropriate to state the goal in terms of
discovering the NEOs carrying 90% of the total collision
probability. Figures 3 and 4 show that the two goals are not
equivalent. For instance, the Atens, even though they are
only 6% of the total NEO population, carry about 20% of
the total collision probability; thus, their discovery (of sec-
418
Asteroids III
ondary importance for the original Spaceguard goal) be-
comes a top priority, when collisional hazards are taken into
account.
By applying the same collision probability calculations
to the H < 18 NEOs discovered so far, we find that the
known objects carry about 47% of the total collisional haz-
ard. Thus, the current completeness of the population com-
puted in terms of collision probability is about the same of
that computed in terms of number of objects. This seems
to imply that the current surveys discover NEOs more or
less evenly with respect to the collision probability with the
Earth. In Fig. 4 the shaded histogram shows how the colli-
sion probability of the known NEOs is distributed as a func-
tion of the orbital elements.
Finally, we discuss the origin of NEOs. The
Bottke et al.
(2002a) model implies that 37 Âą 8% of the NEOs with 13 <
H < 22 come from the
ν
6
resonance, 25 Âą 3% from the
IMC population, 23 Âą 9% from the 3:1 resonance, 8 Âą 1%
from the outer-belt population, and 6 Âą 4% from the
Transneptunian region. Thus, the long-debated cometary
contribution to the NEO population probably does not ex-
ceed 10%. Note, however, that the Bottke et al. model does
not account for the contribution of comets of Oort Cloud
origin, which is still largely unconstrained for the reasons
explained in section 3.6. These comets should be relegated
to orbits with a > 2.6 AU and/or orbits with large eccen-
tricities and inclinations.
About 800 bodies with H < 18, 70% of which come from
the outer main belt, should escape from the asteroid belt
every million years in order to sustain the NEO population.
These fluxes may seem huge, but they only imply a mass
loss of ~5 Ă 10
16
kg/m.y., or the equivalent of 6% of the
total mass of the asteroid belt over 3.5 G.y. (assuming that
the flux has been constant over this timescale).
By itself, this flux does not constrain the mechanism (or
mechanisms) that resupply the transporting (powerful and
diffusing) resonances with new bodies. The shallow size
distribution of NEOs, however, suggests that collisional
injection probably does not play a dominant role in the
delivery of asteroidal material to resonances. If it did, the
NEOs, being fragments from catastrophic breakups, would
have a much steeper size distribution, at least like that of
60
40
20
0
0
1
2
3
Semimajor Axis a (AU)
Number
4
5
100
60
80
20
40
0
0.0
0.2
0.4
0.6
Eccentricity e
Number
0.8
1.0
150
100
50
0
0
20
40
60
Inclination i (degrees)
Number
80
300
250
100
150
200
50
0
13
15
14
16
17
Absolute Magnitude H
Number
18
Fig. 3.
The steady-state orbital and absolute magnitude distribution of NEOs for H < 18. The predicted NEO distribution (solid line)
is normalized to 960 objects. It is compared with the 426 known NEOs for all surveys (shaded histogram). From
Bottke et al.
(2002a).
Morbidelli et al.: Origin and Evolution of Near-Earth Objects
419
the observed asteroid families (
Tanga et al.,
1999;
Campo
Bagatin et al.,
2000). Recall that the mean lifetime in the
NEO region is only a few million years, too short for colli-
sional erosion to significantly reduce the slope of a size
distribution dominated by fresh debris (bodies with a diam-
eter of about 170 m have a collisional lifetime >100 m.y.;
Bottke et al.,
1994). Moreover, it is unclear how collisional
injection could explain the relative abundance of multi-
kilometer objects in the NEO population. According to stan-
dard collision models, only the largest (and most infrequent)
catastrophic disruption events are capable of throwing
multikilometer objects into the transporting major reso-
nances (
Menichella et al.,
1996;
ZappalĂ and Cellino,
2002). The NEO size distribution shows some interesting
similarities with the main-belt size distribution. At present,
a direct estimate of the latter is available only for D > 2 km
asteroids (
Jedicke and Metcalfe,
1998), but its shape has
been extrapolated to smaller sizes by
Durda et al.
(1998)
using a collisional model. The results suggest the main
beltâs size distribution for 0.2 < D < 5 km asteroids is NEO-
like or possibly shallower. The results of recent surveys
(
Ivezi
c
et al.,
2001;
Yoshida et al.,
2001) seem to confirm
this expectation.
Although more quantitative studies are needed for a
definite conclusion, we suspect that this paradox might be
solved by the Yarkovsky effect. The latter forces kilometer-
sized bodies to drift in semimajor axis by ~10
â4
AU m.y.
â1
(
Farinella and VokrouhlickĂ˝,
1999; see also
Bottke et al.,
2002b), enough to bring into resonance a large â possibly
sufficient â number of bodies. The Yarkovsky drift rate is
slow enough that the size distribution of fresh collisional
debris would have the time to collisionally evolve to a shal-
lower, main-belt-like slope.
7.
CONCLUSIONS AND PERSPECTIVES
The massive use of long-term numerical integrations
have boosted our understanding of the origin, evolution, and
steady-state orbital distribution of NEOs. The âpowerful
resonancesâ of the main belt have been shown to transport
the asteroids into the NEO region on a timescale of only a
few 10
5
yr. On the other hand, we now understand that these
12
4
6
8
10
2
0
0
1
2
3
Semimajor Axis a (AU)
Number of Collisions/100 m.y
.
4
20
15
5
10
0
0.0
0.2
0.4
0.6
Eccentricity e
Number of Collisions/100 m.y
.
0.8
1.0
50
30
40
10
20
0
0
20
40
60
Inclination i (degrees)
Number of Collisions/100 m.y
.
80
Fig. 4.
Number of Earth impacts with H < 18 NEOs as a function of the NEO orbital distribution. The solid histogram shows the
expected distribution, deduced from the
Bottke et al.
(2002a) model; the shaded histogram is obtained applying the collision probabil-
ity calculation to the population of known objects.
420
Asteroids III
resonances eliminate most of these same bodies by forcing
them to collide with the Sun. The âdiffusive resonancesâ
have been shown to be additional important sources of
NEOs. The steady-state orbital distributions of the NEO
subpopulations related to the various sources have been
computed. This work has allowed the construction of a
quantitative model of the debiased orbital and magnitude
distribution of the NEO population, calibrated on available
observations.
Despite the steady progress, the current understanding
of the NEO population is still lacking in several areas. As
more and more NEOs are continuously found, the NEO
model presented here will certainly need to be refined.
Moreover, although it is now clear that the vast majority
of NEOs with semimajor axes inside Jupiterâs orbit are of
asteroidal origin, the contribution of inactive comets com-
ing from the Oort Cloud remains poorly quantified.
The most unclear part of the scenario regarding the ori-
gin and evolution of NEOs concerns the mechanisms that
resupply the transporting resonances with new asteroids. At
the end of the previous section, we discussed several argu-
ments that suggest that the Yarkovsky effect plays the domi-
nant role in moving small asteroids to powerful and diffu-
sive resonances. More definitive conclusions, however, will
require a better knowledge of the orbital and size distribu-
tion of the main-belt population in the kilometer size range,
in order to quantify the availability of material in the neigh-
borhood of the transporting resonances. Our understanding
of asteroidal and cometary collisional physics is also lim-
ited, and additional work will be needed to determine more
accurately the size-frequency and velocity-frequency dis-
tributions of asteroid disruption events. Simulations are also
required to understand the interaction of the Yarkovsky-
drifting bodies with the multitude of diffusive resonances
that they encounter. It is possible that small bodies drift too
fast to be efficiently captured by these thin resonances. If
it turns out that different mechanisms resupply different
NEO source regions, it may be inappropriate to assume that
the NEO subpopulations coming from the various sources
described in this chapter have the same size distribution.
Finally, we need to better understand the changes that
occurred over the last 3.8 G.y. (after the so-called late heavy
bombardment), in terms of the total number of NEOs and
their size or orbital distribution. For this purpose, we need
to understand whether the members of asteroid families
dominate the rest of the main-belt asteroid population. If
they do (as claimed by
ZappalĂ and Cellino,
1996), the
formation of new families should have significantly changed
the main-belt population and consequently altered the feed-
ing rate of the NEO population. If not, the breakup of as-
teroid families can be considered noise in the history of the
NEO population.
We believe that a detailed knowledge of the physical
properties of asteroids close to the transporting resonances
will eventually allow us to indirectly but accurately deduce
the compositional distribution of the NEO population. In
turn, this will enable the conversion of NEO absolute mag-
nitudes into diameters, and better quantify the collisional
hazard (frequency of collisions as a function of the impact
energy) for Earth.
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