812 Encyclopedia of the Solar System
spin axis does not point in a fixed direction. Therefore the
satellite also undergoes a tumbling motion in addition to its
chaotic rotation.
The dynamics of Hyperion’s motion is complicated by the
fact that it is in a 4:3 orbit–orbit resonance with the larger
Saturnian satellite Titan. Although tides act to decrease the
eccentricities of satellite orbits, Hyperion’s eccentricity is
maintained at 0.104 by means of the resonance. Titan ef-
fectively forces Hyperion to have this large value ofeand so
the apparently regular orbital motion inside the resonance
results, in part, in the extent of the chaos in its rotational
motion. [SeePlanetarySatellites.]
8.3 Other Satellites
Although there is no evidence that other natural satellites
are undergoing chaotic rotation at the present time, it is
possible that several irregularly shaped regular satellites did
experience chaotic rotation at some time in their histories.
In particular, since satellites have to cross chaotic separa-
trices before capture into synchronous rotation can occur,
they must have experienced some episode of chaotic rota-
tion. This may also have occurred if the satellite suffered a
large impact that affected its rotation. Such episodes could
have induced significant internal heating and resurfacing
events in some satellites. The Martian moon Phobos and
the Uranian moon Miranda have been mentioned as pos-
sible candidates for this process. If this happened early in
the history of the solar system, then the evidence may well
have been obliterated by subsequent cratering events. [See
PlanetarySatellites.]
8.4 Chaotic Obliquity
The fact that a planet is not a perfect sphere means that it
experiences additional perturbing effects due to the grav-
itational forces exerted by its satellites and the Sun, and
these can cause long-term evolution in its obliquity (the
angle between the planet’s equator and its orbit plane). Nu-
merical investigations have shown that chaotic changes in
obliquity are particularly common in the inner solar sys-
tem. For example, it is now known that the stabilizing ef-
fect of the Moon results in a variation of±1.3◦in Earth’s
obliquity around a mean value of 23.3◦. Without the Moon,
Earth’s obliquity would undergo large, chaotic variations.
In the case of Mars there is no stabilizing factor and the
obliquity varies chaotically from 0◦to 60◦on a timescale of
50 million years. Therefore an understanding of the long-
term changes in a planet’s climate can be achieved only
by an appreciation of the role of chaos in its dynamical
evolution.
9. Epilog
It is clear that nonlinear dynamics has provided us with a
deeper understanding of the dynamical processes that have
helped to shape the solar system. Chaotic motion is a natural
consequence of even the simplest systems of three or more
interacting bodies. The realization that chaos has played a
fundamental role in the dynamical evolution of the solar
system came about because of contemporary and comple-
mentary advances in mathematical techniques and digital
computers. This coincided with an explosion in our knowl-
edge of the solar system and its major and minor members.
Understanding how a random system of planets, satellites,
ring and dust particles, asteroids, and comets interacts and
evolves under a variety of chaotic processes and timescales,
ultimately means that this knowledge can be used to trace
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