600 Encyclopedia of the Solar System
Heliocentric distance (AU)0102030110100FIGURE 8 The surface number density (on the plane of the
ecliptic) of ecliptic comets as determined from numerical
integrations by M. Duncan and H. Levison. There are
approximately 10^6 comets larger than about 1 km in radius in this
population.
comets larger than about 1 km in radius currently in orbits
between the giant planets.
7. The Primordial Sculpting of the
Trans-Neptunian Population
In the previous sections, we have seen that many properties
of the Kuiper Belt cannot be explained in the framework of
the current solar system:
1.The existence of the resonant populations
2.The excitation of the eccentricities in the classical belt
3.The coexistence of a cold and a hot population with
different physical properties
4.The presence of an apparent outer edge at the loca-
tion of the 1:2 mean-motion resonance with Neptune
5.The mass deficit of the Kuiper Belt
6.The existence of the extended scattered disk
population
These puzzling aspects of the trans-Neptunian popula-
tion reveal that it has been sculpted when the solar system
was different, due to mechanisms that are no longer at work.
Like detectives on the scene of a crime, trying to reconstruct
what happened from the available clues, the astronomers
try to reconstruct how the solar system formed and evolved
from the traces left in the structure of the Kuiper Belt.
Planet migration has been the first aspect of the primor-
dial evolution of which the astronomers found a signature
in the Kuiper Belt. Once the planets formed and the gas
disappeared, the planetesimals that failed to be incorpo-
rated in the planets’ cores had to be removed from the
planets’ vicinity by the gravitational scattering action of the
planets themselves. If a planet scatters a planetesimal out-
ward, the latter gains energy. Because of energy conserva-
tion, the planet has to lose energy, moving slightly inward.
The opposite happens if the planet scatters the planetesi-
mal toward the inner solar system. A planet is much more
massive than a planetesimal, thus the displacement of the
planet is infinitesimal. However, if the number of planetes-
imals is large, and their total mass is comparable to that of
the planet, the final effect on the planet is not negligible.
This is a general process. We now come to what should have
happened in our solar system.
Numerical simulations show that only a small fraction of
the planetesimals originally in the vicinity of Neptune was
scattered outward: About 1% ended up in the scattered disk,
and 5%, in the Oort cloud. The remaining 94% of the plan-
etesimals eventually were scattered inward toward Jupiter.
The latter, given its large mass, ejected from the solar sys-
tem almost everything that came to cross its orbit. Thus,
the net effect was that Neptune took energy away from the
planetesimals and moved outward, while Jupiter gave en-
ergy to them and moved inward. Numerical simulations
show that Saturn and Uranus also moved outward. Follow-
ing Neptune’s migration, the mean-motion resonances with
Neptune also migrated outward, sweeping the primordial
Kuiper Belt until they reached their present position. Dur-
ing this process, some of the Kuiper Belt objects swept by a
mean-motion resonance could be captured into resonance.
Once captured, these bodies had to follow the resonance in
its migration, while their eccentricity had to steadily grow.
Thus, the planetesimals that were captured first, ended up
on very eccentric resonant orbits, while those captured last
could preserve a small eccentricity inside the resonance.
Numerical simulations show that this process produces an
important population of resonant bodies inside all the main
mean-motion resonances with Neptune. To reproduce the
observed range of eccentricities of resonant bodies, Nep-
tune had to migrate more than 7 AU, thus starting not fur-
ther than 23 AU (see Fig. 9). The existence of resonant
bodies in the Kuiper Belt thus provides a strong indication
that planet migration really happened.
However, as Fig. 9 also shows, several important prop-
erties of the Kuiper Belt cannot be explained by this simple
model invoking resonance sweeping through a dynamically
cold, radially extended disk. The eccentricity of the classical
belt is only moderately excited, and the inclination remains
very cold. The planetesimals are only relocated, from the