## An Introduction to Celestial MechanicsThis 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. |

### Contents

Orbits in central force fields | 63 |

Rotating reference frames | 74 |

Lagrangian mechanics | 97 |

Rigid body rotation | 105 |

Free precession of the Earth | 114 |

1 | 147 |

63 | 158 |

Secularperturbationtheory | 172 |

10 | 197 |

39 | 203 |

Appendix A Useful mathematics | 217 |

Appendix B Derivation of Lagrange planetary equations | 234 |

Expansion of orbital evolution equations | 247 |

259 | |

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### Common terms and phrases

According to Equation angle angular momentum angular momentum vector angular velocity angular velocity vector ascending node asteroids axes axis of rotation body frame Cartesian coordinates center of mass circular orbit comet constant coordinate system cos² Demonstrate Earth eccentricity ecliptic longitude ecliptic plane equation of motion equinox Figure force gravitational potential Hence inclination inertia Jupiter Lagrange points libration lunar orbit m₁ major radius mass distribution mass m3 moment of inertia Moon Moon's orbital na² orbital angular velocity orbital eccentricities orbital elements orbital motion orbital period orbital plane osculating orbital particle perigee perturbation planet position vector precession rate respectively rotating reference frame Section sin² solar system spherical spin-orbit resonance subtended surface symmetry axis takes the form tidal elongation Tisserand parameter torque unit mass x-axis Yoder z-axis μι др