Introduction to Celestial Mechanics

Publication Details

Author:            Richard Fitzpatrick
Publisher: Cambridge University Press
Publication Date: June 28, 2012
ISBN: 978-1107023819


This accessible text on classical celestial mechanics, the principles governing the motions of bodies in the Solar System, provides a clear and concise treatment of virtually all of the major features of solar system dynamics. Building on advanced topics in classical mechanics such as rigid body rotation, Langrangian mechanics, and orbital perturbation theory, this text has been written for advanced undergraduates and beginning graduate students in astronomy, physics, mathematics, and related fields. Specific topics covered include Keplerian orbits, the perihelion precession of the planets, tidal interactions between the Earth, Moon, and Sun, the Roche radius, the stability of Lagrange points in the three-body problem, and lunar motion. More than 100 exercises allow students to gauge their understanding, and a solutions manual is available to instructors. Suitable for a first course in celestial mechanics, this text is the ideal bridge to higher level treatments.

Table of Contents

1. Newtonian mechanics. Introduction; Newton's laws of motion; Newton's first law of motion; Newton's second law of motion; Newton's third law of motion; Non-isolated systems; Motion in one-dimensional potential; Simple harmonic motion; Two-body problem.

2. Newtonian gravity. Introduction; Gravitational potential; Gravitational potential energy; Axially symmetric mass distributions; Potential due to uniform sphere; Potential outside uniform spheroid; Potential due to uniform ring.

3. Keplerian orbits. Introduction; Kepler's laws; Conservation laws; Plane polar coordinates; Kepler's second law; Kepler's first law; Kepler's third law; Orbital parameters; Orbital energies; Transfer orbits; Elliptic orbits; Orbital elements; Planetary orbits; Parabolic orbits; Hyperbolic orbits; Binary star systems.

4. Orbits in central force fields. Introduction; Motion in general central force-field; Motion in nearly circular orbit; Perihelion precession of planets; Perihelion precession of Mercury.

5. Rotating reference frames. Introduction; Rotating reference frames; Centrifugal acceleration; Coriolis force; Rotational flattening; Tidal elongation; Tidal torques; Roche radius.

6. Lagrangian dynamics. Introduction; Generalized coordinates; Generalized forces; Lagrange's equation; Generalized momenta.

7. Rigid body rotation. Introduction; Fundamental equations; Moment of inertia tensor; Rotational kinetic energy; Principal axes of rotation; Euler's equations; Euler angles; Free precession of Earth; MacCullagh's formula; Forced precession and nutation of Earth; Spin-orbit coupling; Cassini's laws.

8. Three-body problem. Introduction; Circular restricted three-body problem; Jacobi integral; Tisserand criterion; Co-rotating frame; Lagrange points; Zero-velocity surfaces; Stability of Lagrange points.

9. Secular perturbation theory. Introduction; Evolution equations for two-planet solar system; Secular evolution of planetary orbits; Secular evolution of asteroid orbits; Secular evolution of artificial satellite orbits.

10. Lunar motion. Introduction; Preliminary analysis; Lunar equations of motion; Unperturbed lunar motion; Perturbed lunar motion; Description of lunar motion.

A. Useful mathematics. Calculus; Series expansions; Trigonometric identities; Vector identities; Conservative fields; Rotational coordinate transformations; Precession; Curvilinear coordinates; Conic sections; Elliptic expansions; Matrix eigenvalue theory.

B. Derivation of Lagrange planetary equations. Introduction; Preliminary analysis; Lagrange brackets; Transformation of Lagrange brackets; Lagrange planetary equations; Alternative forms of Lagrange planetary equations.

C. Expansion of orbital evolution equations. Introduction; Expansion of Lagrange planetary equations; Expansion of planetary disturbing functions.


An errata list can be found here.

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Richard Fitzpatrick
Last modified: Tue Mar 26 12:58:10 CDT 2013