## Orbital Dynamics in the Gravitational Field of Small BodiesThis prizewinning PhD thesis presents a general discussion of the orbital motion close to solar system small bodies (SSSBs), which induce non-central asymmetric gravitational fields in their neighborhoods. It introduces the methods of qualitative theory in nonlinear dynamics to the study of local/global behaviors around SSSBs. Detailed mechanical models are employed throughout this dissertation, and specific numeric techniques are developed to compensate for the difficulties of directly analyzing. Applying this method, several target systems, like asteroid 216 Kleopatra, are explored in great detail, and the results prove to be both revealing and pervasive for a large group of SSSBs. |

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### Contents

1 | |

2 Modelling Orbital Dynamics in the Potential of Small Bodies | 19 |

3 Stability of Equilibrium Points and Behaviour of Nearby Trajectories | 38 |

4 Topological Classification and Stability of LargeScale Periodic Orbits | 61 |

5 Orbital Resonance Near the Equatorial Plane of Small Bodies | 85 |

6 Natural Motion Near the Surface of Small Bodies | 99 |

7 Conclusions and Future Directions | 120 |

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1:1 resonant orbits 1620 Geographos 216 Kleopatra 29 families analysis asteroid 216 Kleopatra Bézier patches binary asteroid Castalia central saddle centre manifold chapter complex saddle corresponding craters CRTBP defined determined distribution E1 and E2 efficient potential eigenvalues ejecting orbits equatorial plane equilibrium points Eros focus map frame Oxyz global gravitational field Icarus indicates Jacobi integral mass point mechanical mission motion equation multipliers NASA neighbourhoods numerical orbital behaviours orbital dynamics orbital energy orbital motion orbital resonance parameter particle patch ID periodic motion periodic orbit families periodic orbits perturbation planetary Poincaré map polyhedral method polyhedron presents quadrant real saddle regolith rotating saddle type Scheeres DJ shape model shows solar radiation pressure Solar System small solar tide space spacecraft specific asteroid spherical harmonics stability subspace system Eq System small bodies tangent topological trajectories unstable vector velocity voxels Ws and Wu zero-velocity surface Γα Γβ