| Preface | p. ix |
| Astrophysics and the three-body problem | p. 1 |
| About the three-body problem | p. 1 |
| The three-body problem in astrophysics | p. 5 |
| Short period comets | p. 8 |
| Binary stars | p. 12 |
| Groups of galaxies | p. 15 |
| Binary black holes | p. 17 |
| Newtonian mechanics | p. 20 |
| Newton's laws | p. 20 |
| Inertial coordinate system | p. 21 |
| Equations of motion for N bodies | p. 22 |
| Gravitational potential | p. 24 |
| Constants of motion | p. 25 |
| The virial theorem | p. 27 |
| The Lagrange and Jacobi forms of the equations of motion | p. 29 |
| Constants of motion in the three-body problem | p. 31 |
| Moment of inertia | p. 32 |
| Scaling of the three-body problem | p. 34 |
| Integration of orbits | p. 34 |
| Dimensions and units of the three-body problem | p. 38 |
| Chaos in the three-body problem | p. 39 |
| Rotating coordinate system | p. 43 |
| Problems | p. 45 |
| The two-body problem | p. 47 |
| Equations of motion | p. 47 |
| Centre of mass coordinate system | p. 48 |
| Integrals of the equation of motion | p. 49 |
| Equation of the orbit and Kepler's first law | p. 52 |
| Kepler's second law | p. 53 |
| Orbital elements | p. 54 |
| Orbital velocity | p. 57 |
| True and eccentric anomalies | p. 58 |
| Mean anomaly and Kepler's equation | p. 60 |
| Solution of Kepler's equation | p. 61 |
| Kepler's third law | p. 63 |
| Position and speed as functions of eccentric anomaly | p. 64 |
| Hyperbolic orbit | p. 66 |
| Dynamical friction | p. 68 |
| Series expansions | p. 70 |
| Problems | p. 78 |
| Hamiltonian mechanics | p. 80 |
| Generalised coordinates | p. 80 |
| Hamiltonian principle | p. 81 |
| Variational calculus | p. 82 |
| Lagrangian equations of motion | p. 85 |
| Hamiltonian equations of motion | p. 87 |
| Properties of the Hamiltonian | p. 89 |
| Canonical transformations | p. 92 |
| Examples of canonical transformations | p. 95 |
| The Hamilton-Jacobi equation | p. 95 |
| Two-body problem in Hamiltonian mechanics: two dimensions | p. 97 |
| Two-body problem in Hamiltonian mechanics: three dimensions | p. 103 |
| Delaunay's elements | p. 108 |
| Hamiltonian formulation of the three-body problem | p. 109 |
| Elimination of nodes | p. 111 |
| Elimination of mean anomalies | p. 113 |
| Problems | p. 113 |
| The planar restricted circular three-body problem and other special cases | p. 115 |
| Coordinate frames | p. 115 |
| Equations of motion | p. 116 |
| Jacobian integral | p. 119 |
| Lagrangian points | p. 123 |
| Stability of the Lagrangian points | p. 125 |
| Satellite orbits | p. 130 |
| The Lagrangian equilateral triangle | p. 133 |
| One-dimensional three-body problem | p. 136 |
| Problems | p. 139 |
| Three-body scattering | p. 141 |
| Scattering of small fast bodies from a binary | p. 141 |
| Evolution of the semi-major axis and eccentricity | p. 148 |
| Capture of small bodies by a circular binary | p. 152 |
| Orbital changes in encounters with planets | p. 154 |
| Inclination and perihelion distance | p. 157 |
| Large angle scattering | p. 162 |
| Changes in the orbital elements | p. 165 |
| Changes in the relative orbital energy of the binary | p. 169 |
| Problems | p. 170 |
| Escape in the general three-body problem | p. 171 |
| Escapes in a bound three-body system | p. 171 |
| A planar case | p. 179 |
| Escape velocity | p. 180 |
| Escaper mass | p. 183 |
| Angular momentum | p. 184 |
| Escape angle | p. 188 |
| Problems | p. 195 |
| Scattering and capture in the general problem | p. 197 |
| Three-body scattering | p. 197 |
| Capture | p. 203 |
| Ejections and lifetime | p. 207 |
| Exchange and flyby | p. 211 |
| Rates of change of the binding energy | p. 214 |
| Collisions | p. 216 |
| Problems | p. 219 |
| Perturbations in hierarchical systems | p. 221 |
| Osculating elements | p. 221 |
| Lagrangian planetary equations | p. 222 |
| Three-body perturbing function | p. 225 |
| Doubly orbit-averaged perturbing function | p. 227 |
| Motions in the hierarchical three-body problem | p. 231 |
| Problems | p. 239 |
| Perturbations in strong three-body encounters | p. 240 |
| Perturbations of the integrals k and e | p. 240 |
| Binary evolution with a constant perturbing force | p. 243 |
| Slow encounters | p. 246 |
| Inclination dependence | p. 260 |
| Change in eccentricity | p. 264 |
| Stability of triple systems | p. 268 |
| Fast encounters | p. 274 |
| Average energy exchange | p. 281 |
| Problems | p. 285 |
| Some astrophysical problems | p. 288 |
| Binary black holes in centres of galaxies | p. 288 |
| The problem of three black holes | p. 296 |
| Satellite black hole systems | p. 310 |
| Three galaxies | p. 310 |
| Binary stars in the Galaxy | p. 313 |
| Evolution of comet orbits | p. 320 |
| Problems | p. 327 |
| References | p. 329 |
| Author index | p. 341 |
| Subject index | p. 343 |
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