Bifurcation Analysis and Periodic Solutions of the HD 191408 System with Triaxial and Radiative Perturbations

The nonlinear orbital dynamics of a class of the perturbed restricted three-body problem is studied. The two primaries considered here refer to the binary system HD 191408. The third particle moves under the gravity of the binary system, whose triaxial rate and radiation factor are also considered. Based on the dynamic governing equation of the third particle in the binary HD 191408 system, the motion state manifold is given. By plotting bifurcation diagrams of the system, the effects of various perturbation factors on the dynamic behavior of the third particle are discussed in detail. In addition, the relationship between the geometric configuration and the Jacobian constant is discussed by analyzing the zero-velocity surface and zero-velocity curve of the system. Then, using the Poincaré–Lindsted method and numerical simulation, the second- and third-order periodic orbits of the third particle around the collinear libration point in two- and three-dimensional spaces are analytically and numerically presented. This paper complements the results by Singh et al. [Singh et al., AMC, 2018]. It contains not only higher-order analytical periodic solutions in the vicinity of the collinear equilibrium points but also conducts extensive numerical research on the bifurcation of the binary system.

Calculating the periods of radio signal transmission between two spacecrafts through the Venus atmosphere in the problem of studying its composition

The paper considers calculating the periods of radio signal transmission through the atmosphere of Venus between a small spacecraft placed in a limited orbit in the vicinity of the collinear libration point of the Sun-Venus system and a Venus orbiter. The problem arises in the framework of the project under discussion to study the atmosphere of Venus. The possibility of transfers of these spacecrafts to the required orbits under various initial conditions is also studied. The impulses required for transferring to the specified orbits at the selected initial state vector, the most suitable for solving this problem are calculated. The duration and the number of transmission periods depending on the location of one of the spacecrafts in a limited orbit in the vicinity of the libration point L1 or L2 of the Sun-Venus system are analyzed. The influence of the shape of the orbiter near-Venusian orbit on the character and duration of the periods of transmission through the atmosphere of Venus is investigated. It is concluded that the location of a small spacecraft in a limited orbit in the vicinity of the L1 libration point of the Sun-Venus system is more advantageous compared to L2 both in terms of the duration and the number of the transmission periods as well as terms of the necessary energy costs.

Impulse control flight to the invariant manifold near collinear libration point

We consider the special problem of flight from near-Earth orbit to a neighborhood of first collinear libration point of the Sun-Earth system. For such flight the numerical experiments substantiate the adequacy of the model of Hill’s equations, which is the nonlinear approximation of equations of circular limited three-body problem. Otherwise, we would be obliged to use the model of limited three-body problem (or its approximation) in conjunction with the model of two-body problem for modeling of motion. During of approach to the neighborhood of libration point (in space of positions), the series of impulse controls are implemented. Controls are built on the basis of equations in variations. The purpose of implementing presented controls is hitting the manifold, where a spacecraft will be as long as possible in the linear case. This manifold is achieved when the special functions of phase variables is equal to zero. All the presented studies are illustrated in detail.