The Sheer Joy of Celestial Mechanics

I. Rotating Coordinates.- 1. Some kinematics.- 2. Dynamics.- 3. Newton's Laws of Motion.- 4. The Laws of Motion and conservation laws.- 5. Simple harmonic motion.- 6. Linear motion in an inverse square field.- 7. Pendulum in a uniform gravitational field.- 8. Foucault's pendulum.- II. Central Forces.- 1. Motion in a central field.- 2. Force and orbit.- 3. The integrable cases of central forces.- 4. Bonnet's Theorem.- 5. Miscellaneous exercises.- 6. Motion on a surface of revolution.- III. Orbits under the Inverse Square Law.- 1. Kepler's three laws and Newton's Law.- 2. The orbit from Newton's Law.- 3. The true, eccentric, and mean anomalies.- 4. Kepler's equation.- 5. Solution of Kepler's equation.- 6. The velocity of a planet in its orbit.- 7. Drifting of the gravitational constant.- IV. Expansions for an Elliptic Orbit.- 1. The general problem.- 2. Lagrange's expansion theorem.- 3. Bessel coefficients.- 4. Fourier series.- 5. Preliminaries for expansions.- 6. Some algebraically-derived expansions.- 7. Expansions in terms of the mean anomaly.- V. Gravitation and Closed Orbits.- 1. Bertrand's characterization of a universal gravitation.- 2. Circular motions.- 3. Neighbors of circular motions.- 4. Higher perturbations; completion of the proof.- 5. From differential geometry in the large.- 6. Ovals described under a central attraction.- VI. Dynamical Properties of Rigid Bodies.- 1. From discrete to continuous distributions of mass.- 2. Moments of inertia.- 3. Particular moments of inertia.- 4. Euler's equations of motion.- 5. Euler free motion of the Earth.- 6. Feynman's wobbling plate.- 7. The gyrocompass.- 8. Euler angles.- VII. Gravitational Properties of Solids.- 1. The gravitational potential of a sphere.- 2. Potential of a distant body; MacCullagh's formula.- 3. Precession of the equinoxes.- 4. Internal potential of a homogeneous ellipsoid.- 5. External potential of a homogeneous ellipsoid.- VIII. Shape of a Self-Gravitating Fluid.- 1. Hydrostatic equilibrium.- 2. Distortion of a liquid sphere by a distant mass.- 3. Tide-raising on a ringed planet.- 4. Clairaut and the variation of gravity.- 5. Poincaré's inequality for rotating fluids.- 6. Liechtenstein's symmetry theorem.- 7. Rotundity of a rotating fluid.- 8. Ellipsoidal figures of rotating fluids.