Orbital Dynamics About Asteroids

Asteroids have always been the focus of the study on the formation and evolu-tion of the Solar System.They are believed to be closely related to the genesis and development of life on Earth,and may pose potential threat to the existence of human beings.The observations of asteroids began very early on the ground,which provide a wealth of evidence and constraints to their theoretical research.With the advent of deep space exploration,a new era for asteroid observation and study begins.The in-creasing amount of exploration missions to asteroids entails a good knowledge of the orbital dynamics about such asteroids.Due to their unique characteristics such as low masses,irregular shapes,and inhomogeneous densities,orbital dynamics about aster-oids may have fascinating traits and require novel theoretical approaches on the basis of traditional orbital dynamics about planetary bodies.We have tentatively provide new analyses and results to this field in this thesis.The first chapter provides the necessary background knowledge about asteroids and review the past and ongoing space missions to asteroids as well as those that are planned.The dynamical environment about a typical asteroid is analysed with the con-clusion that the gravitation of the the asteroid and the solar radiation pressure(SRP)are the two dominating forces worth considering when studying the orbital dynamics about asteroids,especially those in the category of the near-Earth asteroids.The second chapter deals with asteroids,gravity models.Available gravity models for both single asteroids and binary asteroids are reviewed.The detailed comparison between the spherical harmonic gravity model and the polyhedron gravity model for single asteroids in terms of both computation speed and accuracy are carried out takingthree real asteroids as examples.Based on this comparative study,general guidance for applying the commonly used spherical harmonic gravity model to asteroids is proposed.A new algorithm for computing the mutual potential of arbitrary order,force and torques between components of a binary asteroid based on inertial integrals are put forward,which is proved to be more efficient than existing models.The third chapter studies the orbital dynamics about single asteroids.For the hov-ering motion about an asteroid,the existing studies and conclusions associated with the equilibrium points in the gravitational field of an asteroid are introduced.Taking into account of the SRP,a novel hovering motion,dynamical substitutes to the equilibrium points,are obtained.Different types of dynamical substitutes are identified and their stability properties are analysed both in the ideal model as well as more realistic sce-nario.For the general circum-asteroid motion,three types of motion together with their stability properties are studied from the approach of periodic orbits of the dynamical systems theory.The connections between these three types of motion as well as their stability properties in relation to the non-spherical terms of the asteroid are investigated.With the addition of the SRP,two special frozen orbits around asteroids available in the literature,i.e.,the heliotropic orbit and terminator orbit,are discussed.The fourth chapter focuses on the orbital dynamics about binary asteroids.The equilibrium states and the associated stability of doubly synchronous binary asteroids are analysed under the influence of high-order mutual potential.Systematic investiga-tion of the role of spin-orbit resonance of the primary in the stability of a synchronous binary asteroid system is carried out from the novel perspective of periodic orbits.Then the first-order analytical solutions to the full planar motion of a binary asteroid are de-rived with mutual potential truncated at the second order and degree.Hovering orbits in terms of the equilibrium points in the binary asteroid systems are studied.In the context of the Restricted Full Three-Body Problem(RFTBP),the geometrical equilib-rium points in the doubly synchronous binary asteroid systems are computed along with the analysis of their stability properties.For the general binary asteroid systems(both asynchronous and synchronous),dynamical substitutes for the corresponding equilib-rium points are obtained both analytically and numerically.Finally,the status quo of the study of circum-asteroidal motions about binary asteroids are briefly discussed.In all,this thesis is the compilation of a series of systematic research work in the field of orbital dynamics about asteroids.The originality of this thesis is summarised as follows:(1)novel efficient expansion of the mutual potential of a binary asteroid system with arbitrary shape and mass distribution to arbitrary order,(2)the computa-tion and stability analysis of hovering orbits about a single asteroid under the influence of SRP,(3)the evolution and stability analysis of families of periodic orbits about a single asteroid,(4)stability analysis of binary asteroid systems,(5)study of hovering orbits about binary asteroid systems,including equilibrium points of the doubly syn-chronous binary asteroid systems and dynamical substitutes of the equilibrium points in the synchronous and asynchronous binary asteroid systems.