Book contents
- Frontmatter
- Contents
- Preface
- 1 Newtonian mechanics
- 2 Newtonian gravity
- 3 Keplerian orbits
- 4 Orbits in central force fields
- 5 Rotating reference frames
- 6 Lagrangian mechanics
- 7 Rigid body rotation
- 8 Three-body problem
- 9 Secular perturbation theory
- 10 Lunar motion
- Appendix A Useful mathematics
- Appendix B Derivation of Lagrange planetary equations
- Appendix C Expansion of orbital evolution equations
- Bibliography
- Index
1 - Newtonian mechanics
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- Contents
- Preface
- 1 Newtonian mechanics
- 2 Newtonian gravity
- 3 Keplerian orbits
- 4 Orbits in central force fields
- 5 Rotating reference frames
- 6 Lagrangian mechanics
- 7 Rigid body rotation
- 8 Three-body problem
- 9 Secular perturbation theory
- 10 Lunar motion
- Appendix A Useful mathematics
- Appendix B Derivation of Lagrange planetary equations
- Appendix C Expansion of orbital evolution equations
- Bibliography
- Index
Summary
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.
- Type
- Chapter
- Information
- An Introduction to Celestial Mechanics , pp. 1 - 21Publisher: Cambridge University PressPrint publication year: 2012