Introduction

Newtonian mechanics is a mathematical model whose purpose is to account for the motions of the various objects in the universe. The general principles of this model were first enunciated by Sir Isaac Newton in a work titled Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). This work, which was published in 1687, is nowadays more commonly referred to as the Principia.

Until the beginning of the twentieth century, Newtonian mechanics was thought to constitute a complete description of all types of motion occurring in the universe. We now know that this is not the case. The modern view is that Newton's model is only an approximation that is valid under certain circumstances. The model breaks down when the velocities of the objects under investigation approach the speed of light in a vacuum, and must be modified in accordance with Einstein's special theory of relativity. The model also fails in regions of space that are sufficiently curved that the propositions of Euclidean geometry do not hold to a good approximation, and must be augmented by Einstein's general theory of relativity. Finally, the model breaks down on atomic and subatomic length scales, and must be replaced by quantum mechanics. In this book, we shall (almost entirely) neglect relativistic and quantum effects. It follows that we must restrict our investigations to the motions of large (compared with an atom), slow (compared with the speed of light) objects moving in Euclidean space. Fortunately, virtually all the motions encountered in conventional celestial mechanics fall into this category.