354 Encyclopedia of the Solar System
FIGURE 4 Plot of orbital
parameters of numbered
asteroids in semimajor axis vs.
inclination space.a close approach in the same place in its orbit over and over
again. Jupiter’s strongest pull will occur when it is closest;
for an asteroid with a 6 year period (in a 1:2 resonance), this
closest approach will occur at the same place every other
asteroid orbit. (Similarly, asteroids in the 1:3 resonance en-
counter Jupiter at the same place in their orbits, every third
orbit.) Jupiter’s pull at this point, imparting some energy to
the asteroid’s orbit, will then compound itself, rather than
cancel out. The largest effect of this sort of perturbation
is to increase theeccentricityof the asteroid’s orbit. This
does not change its “average” distance from the Sun, but
it makes the perihelion move closer to the Sun, and the
aphelion move farther out. Once its eccentricity reaches a
value of about 0.3, a Main Belt Asteroid’s orbit begins to
approach or even cross the orbit of Mars. Close encounters
with Mars can further alter its orbit, leading to interactions
with the other inner planets or with Jupiter, which eventu-
ally results in a collision with either a planet or the Sun, or
ejection from the solar system. For asteroids, orbital life in
the Kirkwood gaps is (relatively) short, but exciting.
This kind of resonance explains the Kirkwood gaps. But
it does not explain the inner boundary and its dependence
on the inclination of the asteroid orbit, the lack of asteroids
with semimajor axes outside 3.5 AU, or the concentration of
asteroids at the outer resonances. More indirect effects give
rise to these patterns. The shape of the inner boundary is
the result of a subtle but surprisingly powerful effect. Every
asteroid has an orbit that is at least slightly eccentric, and
the orientation of its perihelion slowly drifts with time. This
precessionof the perihelion is caused by the perturbations
of the other planets. Likewise, the orientations of the major
planets’ orbits, which are not perfectly circular, also drift
with time. A subtle interaction arises when the precession
of Saturn’s orbit is in resonance with the precession of an
asteroid’s orbit. Thissecular resonance(so-called because
it builds up over time, regardless of where the asteroid and
Saturn are in their orbits) is called theν 6 resonance;νis
the Greek letter that represents the precession rate, and
the 6 represents Saturn, the sixth planet from the Sun. Its
effect is to increase an asteroid orbit’s eccentricity, as with
the Jupiter mean-motion resonances. The position of this
resonance depends on both the location and the inclination
of the asteroid orbit. For asteroids orbiting in the plane of
the planets, it occurs at around 2.2 AU; as the inclination of
the asteroid orbit increases, the location of this resonance
moves further from the Sun. This resonance sculpts the
inner edge of the Asteroid Belt.
A possible inward migration of Jupiter’s orbit early in
the history of the solar system may have been responsible
for clearing out the outer regions of the Asteroid Belt. If
the solar nebula from which the planets were formed was a
smooth cloud of gas and dust, there should have been nearly
as much material in the region just inside where Jupiter was
formed—the location of the Asteroid Belt today—as there
was in Jupiter itself. But Jupiter’s gravity has its strongest ef-
fect on material closest to it. If Jupiter formed first, its grav-
ity would have stirred up the material nearby and stopped
it from forming another planet. That material would have
been ejected from the inner solar system by Jupiter’s grav-
ity. Some of that material may today be residing in the
far-distantOort cloud.[SeePhysics and Chemistry of
Comets.]