Celestialhtml

Introduction to Celestial Mechanics

2nd Edition

Richard Fitzpatrick

Professor of Physics

The University of Texas at Austin

Preface
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
- Exercises
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
- Exercises
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
- Exercises
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
- Exercises
Rotating reference frames
- Introduction
- Rotating reference frames
- Centrifugal acceleration
- Coriolis force
- Rotational flattening
- Tidal elongation
- Tidal torques
- Roche radius
- Exercises
Lagrangian mechanics
- Introduction
- Generalized coordinates
- Generalized forces
- Lagrange's equation
- Generalized momenta
- Exercises
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
- Exercises
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
- Exercises
Secular perturbation theory
- Introduction
- Evolution equations for two-planet solar system
- Secular evolution of planetary orbits
- Secular evolution of asteroid orbits
- Effect of terrestrial oblateness on artificial satellite orbits
- Effect of atmospheric drag on artificial satellite orbits
- Effect of solar radiation on interplanetary dust grains
- Exercises
Lunar motion
- Introduction
- Major planetary satellites in solar system
- Earth–Moon–Sun system
- Solar orbit
- Derivation of lunar equations of motion
- Useful definitions
- Solution of lunar equations of motion
- Variation
- Annual equation
- Parallactic inequality
- Evection
- Evection in latitude
- Reduction to ecliptic
- Summary of results
- Precession of lunar perigee
- Regression of lunar ascending node
- Historical note
- Exercises
Useful mathematics
- Calculus
- Series expansions
- Trigonometric identities
- Vector identities
- Conservative fields
- Rotational coordinate transformations
- Precession
- Curvilinear coordinates
- Conic sections
- Elliptic expansions
- Matrix eigenvalue theory
- Spherical harmonics
Perihelion precession of Mercury
- Introduction
- Time evolution of eccentricity vector
- Perihelion precession rate
- Evaluation of disturbing function
- Secular perihelion precession rate
Yielding of an elastic planet to tidal forces
- Introduction
- Surface harmonics and solid harmonics
- Gravitational potential theory
- Elastic response theory
Darwin-Radau equation
- Introduction
- Calculation of gravitational potential
- Derivation and properties of Clairaut equation
- Derivation of Radau equation
- Derivation of Darwin-Radau equation
- Simple application of Darwin-Radau theory
Free precession of Earth
Forced precession and nutation of Earth
Derivation of Lagrange planetary equations
- Introduction
- Preliminary analysis
- Lagrange brackets
- Transformation of Lagrange brackets
- Lagrange planetary equations
- Alternative forms of Lagrange planetary equations
Expansion of orbital evolution equations
- Introduction
- Expansion of Lagrange planetary equations
- Expansion of planetary disturbing functions
Derivation of Gauss planetary equations
- Unperturbed planetary orbit
- Perturbed planetary orbit
- Perturbed orbit in standard reference frame
- Gauss planetary equations
Bibliography
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