Research On Orbital Dynamics In The Gravitational Field Of Small Bodies

The orbital dynamics in the near-regime gravitational field of solar system smallbodies (SSSB) is an important aspect of modern celestial mechanics, which is ofabundant physical phenomenon and may offer a deep insight into the referred dynamics.During last two decades, several deep space probes have been sent to SSSB for in-situexplorations to these small worlds, which highlight the orbital dynamics around SSSBas one of the biggest challenges in space engineering. As an applying basic research, thework advanced in this thesis is about the representative and common issues in theorbital dynamics under mechanical models of high approximation, serving as a bridge tounderstanding the orbital motion in the vicinity of real SSSB.Four types of orbits are discussed: the equilibrium points, periodic orbits,resonant orbits near the equatorial plane, and the free motion close to thesurface. Specific asteroids’ models are employed in these studies, and newalgorithms are developed based on the polyhedral models, i.e., the hierarchicalgrid search method (HGSM) designed for searching the large-scale periodicorbits around SSSB, and the free motion model (FMM) in order to mimic thecomplicated motion of a particle close to the surface of SSSB. FORTRANpackages are developed for numerical implementation of these algorithms.In the studies of equilibrium points and periodic orbits, we focus on thequalitative properties of the system, especially for the general behaviors ofvicinal orbits.4equilibrium points of asteroid216Kleopatra are exposed bychecking the three-dimensional geometries of the Zero Velocity Surfaces, andthen their stabilities and topologies are determined. The general motion aroundthe equilibrium points are decomposed into three types of local invariantmanifolds, sketching out the general behaviors of nearby orbits. Six continuousfamilies of local periodic orbits are obtained in the center manifolds. In thestudy of large-scale periodic orbits,29new families around Kleopatra aregenerated using HGSM. Poincaré mapping is introduced to investigate thestability of the29families, and these families are classified into different typesdue to their topologies. It is noticed that the type transition within the same family follows specific strategies, which characterize the topological evolutionof the periodic orbits. Motions around the orbits of the29families are attributedto five simple patterns, thus the general motion near the periodic orbits isqualitatively determined based on a composition view.In the studies of resonant orbits near the equatorial plane and free motionclose to the surface, we value the role of numerical experiments. The variationof orbital energy is analyzed to understand the dynamical nature of the1:1resonance. Grid search on the parameter space reveals the condition of thisresonance. Noticing1:1resonance is the major cause of ejecting motions, wepresent the distribution of ejecting orbits around Kleopatra on the parameterspace and determine the critical conditions. A high-risk region for the probes isfound near Kleopatra for the rich ejecting orbits in the equatorial plane. FMM isapplied to the study of surface motion on asteroid1620Geographos. The globalsurface environment is evaluated, revealing the connections between the freemotions and the surface local geometries. Monte Carlo simulations areperformed to investigate the trajectories initialized close to the surface. Theresults show that the free motions close to the surface are highly influenced bythe local terrain, and several mechanisms may govern the free motion ofdifferent processes.Noticing that most of this work is based on specific SSSB, we generalizethe results consultative for similar types of issues. Essentially, the topicsinvestigated in this thesis are common and representative for a large group ofSSSB, and the ideas and approaches proposed here are quite generic andportable.