Kuiper Belt: Dynamics 595
FIGURE 4 The dynamical lifetime for small particles in the Kuiper Belt derived from 4 billion
year integrations by M. Duncan, H. Levison, and M. Budd. Each particle is represented by a
narrow vertical strip of color, the center of which is located at the particle’s initial eccentricity and
semimajor axis (initial orbital inclination for all objects was 1◦). The color of each strip represents
the dynamical lifetime of the particle. Strips colored yellow represent objects that survive for the
length of the integration, 4× 109 years. Dark regions are particularly unstable on these
timescales. For reference, the locations of the important Neptune mean-motion resonances are
shown in blue and two curves of constant perihelion distance,q, are shown in red. The orbital
distribution of the real objects is also plotted. Big dots correspond to objects withi< 4 ◦, and
small dots to objects with larger inclination. Remember that the dynamical lifetime map has been
computed assumingi= 1 ◦.Indeed, secular resonances appear to play a critical role
in ejecting particles from this region of the Kuiper Belt.
This can be better seen in Fig. 5, which is an equivalent
map, but plotted relative to the initial semimajor axis and
inclination for particles with initial eccentricity of 0.01. Also
shown are the locations of the Neptune longitude of perihe-
lion secular resonance (in red) and the Neptune longitude
of the ascending node secular resonance (in yellow). It is
important to note that much of the clearing of the Kuiper
Belt occurs where these two resonances overlap. This in-
cludes the low inclination region between 40 and 42 AU,
which is indeed depleted of bodies (compare with Fig. 2).
The Neptune mean-motion resonances are also shown (in
green).
It is interesting to compare the numerical results to the
current best orbital elements of the known Kuiper Belt
objects. This comparison is also made in Fig. 4, where
the observed objects with good orbital determination are
overplotted with green dots. Big dots refer to bodies with
I< 4 ◦, consistent with the low inclination at which the sta-
bility map has been computed. Small dots refer to objects
with larger inclination and are plotted only for complete-
ness. The conclusion is that most observed objects (with
the exception of scattered disk bodies) are associated with
stable zones. Their orbits do not significantly change over
the age of the solar system. Thus, their current excited ec-
centricities and inclination cannot be obtained from pri-
mordial circular and coplanar orbits in the framework of
the current planetary system orbital configuration. Like-
wise, the region beyond the 1:2 mean-motion resonance
with Neptune is totally stable. Thus, the absence of bodies
beyond 48 AU cannot be explained by current dynamical
instabilities.
Therefore, it is evident that the orbital structure of the
Kuiper Belt has been sculpted by mechanisms that are no
longer at work, but presumably were active when the solar
system formed. The main goal of dynamical astronomers
interested in the Kuiper Belt is to uncover these mecha-
nisms and from them deduce, as far as possible, how the
solar system formed and early evolved.