Two Types Of Motions In The Restrict Three Body Problem

The Circular Restricted Three Body Problem (CRTBP) is one of most im-portant model in the Celestial mechanics. Because of the existence of the Jocobi Constant and5libration points, the structure of phase space of CRTBP is rela-tively simple, thus it is used in sorts of scenarios. In this thesis, we focus on two types of orbits, which are the Kozai effect orbits and ballistic capture orbits.If the third body moves around one of the primes, and the orbit plane is tilted by a significant angle (iB) with respect to the orbit plane of the two primes, its eccentricity will be excited to very large value due to the Kozai effect. We investigate the effects of gas-disk gravity on the planetesimal dynamics in inclined binary systems. Using both analytical and numerical methods, we find that, on one hand, the disk gravity generally narrows down the Kozai-on region, i.e., the Kozai effect can be suppressed in certain parts of (or even the whole of) the disk, depending on various parameters. On the other hand, when we include the effects of disk gravity, we find that the Kozai effect can operate even at arbitrarily low inclinations (iB), although lower iB leads to a smaller Kozai-on region. Furthermore, in the Kozai-on region, most planetesimals'eccentricities can be excited to extremely high values (～1). Once a planetesimal reaches very high orbital eccentricity, gas drag damping will shrink the planetesimal orbit, forming a "hot planetesimal" on a near circular orbit very close to the primary star, which may favor the planet formation.This thesis also study the ballistic capture orbit by the Moon in the frame-work of Planar Circle Restrict Three-Body Problem. The Weak Stability Bound-ary (WSB) describes the region where spacecraft can be ballistic captured by the Moon. Five types of boundaries of weak stability set are found which are (1) boundaries related to stable invariant manifold,(2) boundaries because of singular,(3) boundary orbits whose tangent lines are l(θ),(4) boundary orbits with zero Kepler energy,(5)other types of boundaries. Distribution of each type of boundaries is also illustrated. The boundaries of the central stable region of WSB are mainly those related to invariant manifolds. We further find that the first periapsides on the stable invariant manifolds around the Moon provide outer boundaries of the central structure of WSB. Four large arms appears in the WSB set. We find that large extension arm structures of WSB is related to the peri-odic orbits around the Moon, especially the C family, H1family and H2family of periodic orbits. The properties of the periodic orbits decide the position and thickness of the arms.