804 Encyclopedia of the Solar System
5.2 Meteorites
Most meteorites are thought to be the fragments of mate-
rial produced from collisions in the asteroid belt, and the
reflectance properties of certain meteorites are known to
be similar to those of common types of asteroids. Since
most collisions take place in the asteroid belt, the fragments
have to evolve into Earth-crossing orbits before they can hit
Earth and be collected as samples.
An estimate of the time taken for a given meteorite to
reach Earth after the collisional event that produced it can
be obtained from a measure of its cosmic ray exposure age.
Prior to the collisions, the fragment may have been well
below the surface of a much larger body, and as such it would
have been shielded from all but the most energetic cosmic
rays. However, after a collision the exposed fragment would
be subjected to cosmic ray bombardment in interplanetary
space. A detailed analysis of meteorite samples allows these
exposure ages to be measured.
In the case of one common class of meteorites called
the ordinary chondrites, the cosmic ray exposure ages are
typically less than 20 million years and the samples show
little evidence of having been exposed to high pressure, or
“shocking.” Prior to the application of chaos theory to the
origin of the Kirkwood gaps, there was no plausible mech-
anism that could explain delivery to Earth within the expo-
sure age constraints and without shocking. However, small
increments in the velocity of the fragments as a result of the
initial collision could easily cause them to enter a chaotic
zone near a given resonance. Numerical integrations of such
orbits near the 3:1 resonance showed that it was possible
for them to achieve eccentricities large enough for them to
cross the orbit of Earth. This result complemented previ-
ous research that had established that this part of the as-
teroid belt was a source region for the ordinary chondrites.
Another effect that must be considered to obtain agree-
ment between theory and observations is the Yarkovski ef-
fect which is discussed below. [SeeMeteorites.]
5.3 Comets
Typical cometary orbits have large eccentricities and there-
fore planet-crossing trajectories are commonplace. Many
comets are thought to originate in the Oort cloud at several
tens of thousands of AU from the Sun; another reservoir of
comets, known as the Kuiper belt, exists just beyond the or-
bit of Neptune. Those that have been detected from Earth
are classified as either long period (most of which have made
single apparitions and have periods>200 yr) or Halley-type
(with orbital periods of 20 – 200 yr) or Jupiter-family, which
have orbital periods<20 yr. All comets with orbital peri-
ods of less than∼ 103 yr have experienced a close approach
to Jupiter or one of the other giant planets. By their very
nature, the orbits of comets are chaotic, since the outcome
of any planetary encounter will be sensitively dependent on
the initial conditions.
Studies of the orbital evolution of the short-period comet
P/Lexell highlight the possible effects of close approaches.
A numerical integration has shown that prior to 1767 it was
a short-period comet with a semimajor axis of 4.4 AU and
an eccentricity of 0.35. In 1767 and 1779, it suffered close
approaches to Jupiter. The first encounter placed it on a
trajectory which brought it into the inner solar system and
close (0.0146 AU) to the Earth, leading to its discovery and
its only apparition in 1770, whereas the second was at a
distance of∼3 Jovian radii. This changed its semimajor axis
to 45 AU with an eccentricity of 0.88.
A more recent example is the orbital history of comet
Shoemaker-Levy 9 prior to its spectacular collision with
Jupiter in 1994. Orbit computations suggest that the comet
was first captured by Jupiter at some time during a 9-year
interval centered on 1929. Prior to its capture, it is likely that
it was orbiting in the outer part of the asteroid belt close
to the 3:2 resonance with Jupiter or between Jupiter and
Saturn close to the 2:3 resonance with Jupiter. However,
the chaotic nature of its orbit means that it is impossible to
derive a more accurate history unless prediscovery images
of the comet are obtained. [SeePhysics andChemistry
ofComets;CometaryDynamics.]5.4 Small Satellites and Rings
Chaos is also involved in the dynamics of a satellite em-
bedded in a planetary ring system. The processes differ
from those discussed in Section 3.1, A because there is a
near-continuous supply of ring material and direct scatter-
ing by the perturber is now important. In this case, the key
quantity is the Hill’s sphere of the satellite. Ring particles
on near-circular orbits passing close to the satellite exhibit
chaotic behavior due to the significant perturbations they
receive at close approach. This causes them to collide with
surrounding ring material, thereby forming a gap. Studies
have shown that for small satellites, the expression for the
width of the cleared gap isW≈ 0. 44(
m 2
m 1) 2 / 7
a (45)wherem 2 andaare the mass and semimajor axis of the
satellite andm 1 is the mass of the planet. Thus, an icy satel-
lite with a radius of 10 km and a density of 1 g cm−^3 orbiting
in Saturn’s A ring at a radial distance of 135,000 km would
create a gap approximately 140 km wide.
Since such a gap is wider than the satellite that creates it,
this provides an indirect method for the detection of small
satellites in ring systems. There are two prominent gaps in
Saturn’s A ring: the∼35-km-wide Keeler gap at 135,800 km