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Chaos theory explains origin of new moons
University of Bristol (United Kingdom)
May 15, 2003

The ability to understand how small bodies such as moons switch from
orbiting the Sun to orbiting a planet has long remained one of the
outstanding problems of planetary science. A paper published in
Nature on 15 May shows how this problem has been resolved using chaos
theory, enabling scientists to predict where astronomers might search
for new moons orbiting the giant planets. 

In the last couple of years many small moons have been found orbiting
the giant planets in our Solar System. For example, Jupiter now has
60 moons in total and Saturn more than 30. Astronomers believe that
understanding the nature of these moons can reveal important clues
about the early history of the planets. Such insights into
understanding our own Solar System will help us understand how other
solar systems came into being, and whether they might be favourable
to life. 

The moons can be divided into two groups - regular and irregular.
Regular moons have a roughly circular orbit around their planet and
are believed to have been formed there during the early history of
the Solar System. Irregular moons have an orbit that is highly
elliptical, orbiting the planet at a distance of many millions of
miles. These are believed to have originally encircled the Sun and to
have been subsequently 'captured' by the planet they now orbit.

The discovery of these new moons has shaken our cherished ways of
understanding our Solar System. In particular, the problem of
satellite capture - the mechanism by which bodies switch from an
orbit around the Sun to an orbit around the planet - remained
outstanding. Secondary to this was the problem of why some moons have
prograde orbits - revolving in the same direction as the planet -
while the vast majority have retrograde orbits. 

Stephen Wiggins and Andrew Burbanks, mathematicians at Bristol
University, along with David Farrelly and Sergey Astakhov,
theoretical chemists at Utah State University, were using chaos
theory to understand the mechanics of chemical reactions. They
realised that the approach they had been using in chemistry might
also be applied to the problem of 'capture'. Furthermore, they
thought that if they could solve the capture problem it might give
them some insight into their chemistry problems.

Stephen Wiggins said: "When we started to look at the capture of
irregular moons what we found was that no-one else was trying to
understand this problem in three dimensions using chaos theory. Most
work was focused on understanding the behaviour of these moons after
they had been captured. So in an attempt to understand how a body
orbiting the Sun could be brought in to an orbit around one of the
giant planets we simulated the 'switching' mechanism. We found that
it was chaos that allowed the capture process to take place."

Using the mathematical equations they developed to explain the
capture mechanism, the Bristol and Utah research groups present an
explanation which not only agrees well with the observed locations of
the known irregular moons, but also predicts new regions where moons
could be located. The ability to predict where new moons might be
found should make life much easier for astronomers who face the
daunting task of searching huge regions of space for them.

The joint UK/US research team also showed that the moons initially
captured into prograde orbits of moons are not only chaotic, but that
they have a tendency to approach the region very close to the planet.
This means that they have a greater chance of being eliminated by
collisions with the inner giant moons or the planet, thereby
explaining the far larger number of retrograde moons, especially
around Jupiter. 

This work shows that chaos-assisted capture may be a necessary, and
quite general, predecessor of certain types of orderly and stable
satellite orbits.

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