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Ivars Peterson
Newton's Clock: Chaos in the solar system
The solar system seems to be the epitome of regularity, but there has always been a doubt about whether it is truly stable in the long term - Newton thought that divine intervention might be required from time to time. This isn't a book about the latest discoveries in astronomy, rather it's a look at the history of how a certain problem has been tackled. Peterson is a skilled author and presents what can be a dry subject in an interesting way, with the use of plenty of illusttrations. For instance although the book is wholly nonmathematical, it gives the reader some understanding of mathematical concepts such as Poincare's maps.
The book follows a more or less chronological path, starting with the early ideas of the Greeks and finishing with the recent use of powerful computers to follow the behaviour of the solar system. However it is possible to read the chapters independently if required. In particular those on the behaviour of the moon, the gaps in the asteroid belt, and the tumbling of Saturn's satellite Hyperion would be useful to a reader requiring information on a particular subject. I think it's better to read the whole book though, as this shows how the problem of the stability of the solar system just refuses to go away.