Research On The Periodic Orbit Of The Binary Star System HD 191408

With the rapid development of space science and technology and the increasing shortage of natural resources on the earth,it is particularly important to explore deep space.Deep space exploration has become a key area funded by major space administrations in the world.Understanding and mastering the orbital characteristics of probers of restricted N-body systems in deep space is also a key scientific issue in practical exploration mission.This thesis is devoted to the study of the orbital dynamics of the prober under the gravitational force and perturbation factors of the binary system HD 191408,including the following four aspects:(1)The dynamic problem of the prober under the gravitational force of the binary system HD 191408 is regarded as a perturbed restricted three-body problem.Firstly,the dynamic governing equation of the prober in the dimensionless centroid rotating coordinate system is given,and then the relationship between the geometric configuration of its zero-velocity surface(curve)and Jacobi constant is discussed.Three collinear libration points and two triangular libration points of the perturbed system are obtained.(2)For the general restricted three-body problem,because of the non-integrability and high complexity of the dynamic governing equation,we use an a prior estimate and Reissig's theory of higher-order nonlinear differential equation to study the conditions of the prober's periodic motion under the gravitational force of the binary system HD 191408.It is found that the existence conditions of the periodic orbit of the system are closely related to the initial state of the system,the mass ratio between the two stars,the selected control parameters and the auxiliary function matrix.(3)The non-linear dynamic behavior of the prober under the gravitational force of the binary system HD 191408 is extremely complicated,and slight changes may have a great impact on the system.Using the theory of bifurcation and chaos,we analyze the influence of different perturbation parameters on the periodic orbit of the prober.These parameters include the mass ratio of the two main stars in the binary system,the triaxial rate,radiation,Coriolis and centrifugal force.By bifurcation analysis,it is found that the dynamic behavior of the prober varies greatly as the values of these parameters change.(4)Based on the Lindstedt-Poincare perturbation method,we construct the mathematical expressions of the second and third order approximate periodic orbits of the prober under the gravitational force of the binary system HD 191408 in two-dimensional plane and three-dimensional space respectively.By comparing the phase portraits of the orbits corresponding to the approximate solutions,we find that the second and third order approximate periodic orbits obtained in plane are very close to each other.While in the spatial case,the second and third order approximate periodic orbits are quite different,which is caused by the different power series of orbital parameters selected in the process of solving,but these orbits have important reference for our research.In summary,this thesis mainly studies the conditions of the periodic motion of the prober under the gravitational force of the binary system HD 191408,discusses the influence of different perturbation parameters on the dynamic behavior of the prober,and gives the second-order and third-order approximate expressions of the periodic orbit.We hope that the results of this study can provide some theoretical references for the future orbit design.