Main-Belt Asteroids 353
rubble-pile asteroid spins, the more likely that the centrifu-
gal acceleration of material at the surface will be greater
than the acceleration of the object’s gravity. The result is
that above a critical rotation rate, material would be “spun
off ” the weak gravity of the surface. Observations of as-
teroid rotation rates show a “rotation rate barrier” where
almost every asteroid rotates below this critical rate. The
rotation rate barrier would not strongly affect monolithic
asteroids, so this is evidence that most asteroids are limited
by their coherent strength to rotate slower or shed material
from centrifugal acceleration.
2. Locations and Orbits
2.1 Zones, Orbits, and Distributions
Minor planets can be found in almost any region of the solar
system, but as shown in Fig. 3a, one of the largest concen-
trations of asteroids is located in the “belt” between 1.8 and
4.0 AU. A more detailed analysis of theaveragedistances
of asteroids from the Sun (the asteroids’ semimajor axes) as
shown in Fig. 4 reveals a subtle structure to the Asteroid
Belt. First, there appears to be a sharp inner boundary to
the Asteroid Belt at about 2.2 AU. But note that this bound-
ary curves to higher AU for asteroids with higher orbital
inclinations. Second, there is a sharp gap in the number of
FIGURE3a The location of asteroids in the inner solar system.
The outer circle is the orbit of Jupiter with the location of the
planet shown as a tick mark on the orbital path. The “swarms”
before and after Jupiter are the Trojans and the thick Main
Asteroid Belt is readily visible just outside the orbit of Mars.
FIGURE3b The location of asteroids in the outer solar system.
The outer circle is the orbit of Neptune with the location of the
planet shown as a tick mark on the orbital path. The “swarms”
before and after Jupiter are the Trojans and the thick asteroid
belt outside of Neptune is the Kuiper Belt.asteroids whose average distance from the sun (semimajor
axis) is 3.28 AU. Asteroids orbiting here would have exactly
half the orbital period of Jupiter and are said to be in a
1:2mean-motion resonancewith Jupiter. Similar gaps can
be seen elsewhere in the asteroid population as well, most
notably at the locations of the 1:3 and 2:5 mean-motion res-
onances. The gaps in the distribution of asteroid semimajor
axes are calledKirkwood gapsfor Daniel Kirkwood who
first pointed them out in 1886. Unlike the gaps in Saturn’s
rings, however, these gaps are not directly visible within
the Asteroid Belt in Fig. 3a because asteroid orbits have
a wide range of eccentricities and are constantly crossing
through the region of these gaps. Third, there is a dearth
of asteroids in orbits with semimajor axes beyond 3.5 AU,
with two exceptions: There are clusters of asteroids at 3.97
AU, corresponding to the 2:3 mean-motion resonance with
Jupiter, and at 5.2 AU, where asteroids share the same orbit
as Jupiter.
These boundaries and gaps are formed by the steady in-
fluence of the gravitational attraction of the planets on the
orbits of the asteroids. In general, these interactions occur at
random time intervals and at random locations of the aster-
oid’s orbit, and on average they cancel out without causing
a significant change in the asteroid’s orbit. However, an as-
teroid whose orbital period is a simple fraction of Jupiter’s
11.86 year period will be inresonancewith Jupiter and have