The System of the World by Sir Isaac Newton

The mathematics of planets, tides, and comets

The System of the World (De mundi systemate, in the original Latin) is the third volume of Sir Isaac Newton’s magnum opus Philosophiae Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy). The Principia, for short, is Western Civilization’s fundamental text on physics, including the mathematics necessary to establish and prove the physical laws that govern nature. Volume I of the Principia is written in the logical structure of mathematical proofs, much like Euclid’s Elements. Volume III: The System of the World, on the other hand, is written in plain prose text, for the most part. This foolishly led me to believe that The System of the World might be like the Principia for Dummies, that is, Newton’s attempt to interpret his findings to a wider readership. Alas, this was not the case. While I was certainly able to get the general gist of Newton’s astronomical conclusions, one really needs a PhD in mathematics or physics to fully appreciate all that the great genius has to say in The System of the World.

In this third book of the Principia, Newton demonstrates how the laws of physics that he defined in the earlier volumes are evident in the movements of astronomical bodies in our solar system. Newton focuses on three main topics. First he discusses planets and moons. Newton explains how gravity determines the movements of astronomical bodies, and how the relationship between such factors as mass, distance, speed, and density dictates the amount of gravitational force that these bodies exert on one another. This section of the book is the most accessible to the general reader, but it’s also the briefest. From here, Newton then moves on to an extensive discussion of tides and how they are affected by the gravitational pull of the moon and sun. At this point, Newton’s still not speaking in logical proofs or hauling out geometrical diagrams, but he does use geometrical and astrophysical terms that are not common knowledge to laymen, such as “syzygies,” “quadratures,” and “librations.”

Newton reserves his longest and most difficult discourse for the third major topic of this book: comets, which occupies roughly the second half of the book. Newton begins by recapping much anecdotal and historical research from comet sightings of the past. He then proceeds into mathematical formulae for how to determine a comet’s speed or distance from the sun. Much consideration is given to the tails of comets, what causes them, and what their size and direction says about the comet from which they sprang. Eventually, Newton outlines the necessary mathematics for calculating the trajectories of comets, which was way beyond my understanding. By the end of the book, Newton has returned to the logical syntax of Euclidian geometry, outlining his arguments in the structure of problem, lemmas, and proof.

The System of the World is no doubt a work of genius, but for non-geniuses it doesn’t make for pleasant reading. I’m sure the knowledge that Newton presents here has proven invaluable to scientists, mathematicians, and astronomers for the past three centuries. I’m very glad he wrote it for them, but this was way more than I ever wanted to know about tides and comets. While I won’t blame Newton for my ignorance, I can’t really recommend his book either since 99 percent of the people reading this review will probably find this as mystifying as I did. If you’re part of that other 1 percent, good for you.
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