You are invited to join in on one of the most remarkable detective stories
of all time—the search for order and chaos in the solar system.
In Newton’s Clock, best-selling author Ivars Peterson
examines a mystery that has fascinated and tormented astronomers and mathematicians for centuries:
are the orbits of planets and other bodies stable and predictable,
or are there elements affecting the dynamics of the solar system that defy calculation?
Weaving together some of the most influential moments of scientific discovery,
Peterson offers a fascinating look at the intimate relationship between
mathematics, astronomy, and our desire to understand the solar system.
Newton’s Laws of Motion, and the workings of our solar system that
they describe, are often held up as examples of the clockwork
precision of classical physics. Actual brass clockwork models of the
solar system, orreries, bolstered this world view. But that never was
the entire story…
A solar system
simple enough to allow — and even encourage — us to search for
patterns and deduce grand universal laws; a solar system just
complicated enough to keep us wondering without stopping us in our
tracks.
This excellent book explodes the clockwork myth, with an historical
account of the mathematics of celestial mechanics, from the ancient
Greeks’ insistence on circles within circles, via
Tycho, Kepler and Newton’s
ellipses, through the early chaos
results of Poincaré, to current day computational results and
Digital Orreries. Newton’s elegant laws, as well as having simple
clockwork-like solutions of planets moving in ellipses, also have
totally chaotic solutions, and our solar system does indeed appear to
be chaotic in the long term.
The story is well told, as a complex dance of observation and theory
complementing each other – new theories simplify some observation,
but then more precise observations show weaknesses in the theories.
This is interspersed with wonderful little morsels – such as the fact
that after Uranus was discovered in 1781, 22 observations of it in the
preceding century, including one by Flamsteed in 1690, were discovered
in the astronomical records; and that Neptune since
its discovery in 1846 has
yet to complete one full orbit of the sun.
I found the later chapters – on the slow discovery of chaos in the
solar system – more interesting, possibly because I am less familiar
with this end of the story. We get a slow build-up: our moon’s
peculiar orbit (because the sun’s influence on it is so large); chaos
in some asteroid orbits possibly explaining the Kirkwood gaps (Jupiter
may make their eccentricity chaotic, but it is then Mars and the Earth
which disrupt them completely); the tumbling motion of Hyperion, one
of the moons of Saturn; the realisation that all moon systems seem to
be chaotic; that Venus and Mars’ rotation axes may tumble chaotically,
and our moon is all that saves our own from doing the same; finally
the realisation that the solar system itself has chaotic behaviour.
All this is told in an exciting, but not sensationalist, style.
Thankfully, we find no tabloid-style “we’re all going to fall
into the sun tomorrow!”, but rather an interesting discussion of
how chaos and stability seem to coexist.
The story is by no means complete. There is obviously still a lot of
research to be done: each time more reality is added to the models –
precise details of planetary masses, non-spherical bodies, General
Relativistic corrections – more interesting and subtle behaviour is
found. And there’s still more to add, such as frictional dissipative
forces and the effect of the solar wind.
What is also made clear is the profound effect that computers have
had on the discipline. The equations of motion might look simple in
the abstract, but there is no closed-form solution even for three
bodies, and numerical solutions are amazingly complicated. By using
computers, and very cunning algorithms, planetary motions can now be
calculated millions of years into the future, enabling long term
quasi-periodic and chaotic behaviour to be discovered. In addition,
ways of visualising the resulting mass of data have been developed. I
would dearly love to see the video that shows how the planetary orbits
change, when viewed at 60000 years per second:
The rings
representing the orbits of Jupiter, Saturn, Uranus, Neptune, and Pluto
seemed to be in continuous motion, restlessly jiggling to jittery,
complex rhythms. Though the rings never quite crashed together, they
seemed to knock one another around
...
Earth certainly wobbled and wandered in its orbit, but its mildly
erratic motion paled in comparison with the wild gyrations and
vibrations of Mars. It was also easy to see the rotation of Mercury’s
elliptical obit, along with a host of more subtle changes. The entire
solar system seemed to vibrate with a mesmerizing energy...
