Periodic orbits based on geometric structure of center manifold around Lagrange points

This study proposes an analytical method that determines the center manifold and identifies the reduced system on the center manifold. The proposed method expresses the center manifold through general equations containing only state variables, and not functions with respect to time. This is the so-called geometric structure of the center manifold. The location of periodic or quasi-periodic orbits is identified after the geometric structure of the center manifold is determined. The reduced system on the center manifold is described using ordinary differential equations, so that periodic or quasi-periodic orbits can be computed by numerically integrating the reduced system. The results indicate that the analytical method proposed in this study has higher precision compared with the Lindstedt-Poincaré method of the same order.     

Holocene environmental change according to lake core in Fildes Peninsula of King George Island,Antarctica

Lake core sampled from Xihu in Fildes Peninsula of King Gorge Island, Antarctica could reveal the environmental change of the district. The lake core( GA7) , 9.28 meters long , was sectioned at an interval of 2 cm. Through measuring the organic carbon, magnetic susceptibility, granularity and organic carbon isotope of GA7, by use of 14C age it was estimated that there were four periods of high temperature in Fildes Peninsula; 4800-4400 aB. P. , 3600-3350 aB. P. ,2100 - 1800 aB. P. and 900 aB. P. - present. Meanwhile, results showed that there was a strikingly positive correlation between the content of organic carbon and that of organic carbon isotope (δC01213 ) which could be the substitute indicators of environmental temperature.     

泥河湾盆地下沙沟动物群的磁性地层学定年及其对泥河湾动物群的年代制约

主要对泥河湾盆地下沙沟动物群（即狭义的泥河湾动物群）所在剖面河湖相沉积物进行了详细的磁性地层学和岩石磁学研究,揭示出下沙沟剖面记录了高斯正极性时（Gauss normal chron）晚期、松山负极性时（Matuyama reverse chron）及布容正极性时（Brunhes normal chron）。下沙沟动物群的层位跨越留尼旺（Reunion normal subchron）和奥杜威（Olduvai normal subchron）正极性亚时,其年代约为2.2~1.7Ma。上新世/更新世界限（高斯/松山（Gauss/Matuyama）地磁极性倒转界限）位于下沙沟剖面底部。结合前人研究结果,将泥河湾盆地已有磁性地层年代数据的动物群标注在地磁极性年表上,获得了泥河湾动物群的年代序列,结果表明泥河湾动物群位于高斯/松山和松山/布容（Matuyama/Brunhes）两个地磁极性倒转界限之间,因此,泥河湾动物群的年代区间为2.6~0.8Ma,这一研究结果完善了泥河湾盆地的生物地层年代学框架。     

Post-earthquake economic resilience and recovery efficiency in the border areas of the Tibetan Plateau: A case study of areas affected by the Wenchuan Ms 8.0 Earthquake in Sichuan,China in 2008

Journal of Geographical Sciences - The border areas of the Tibetan Plateau and the neighboring mountainous areas have a high incidence of earthquakes with a magnitude greater than Ms 5.0, as well...     

Dynamical model of binary asteroid systems using binary octahedrons

We used binary octahedrons to investigate the dynamical behaviors of binary asteroid systems. The mutual potential of the binary polyhedron method is derived from the fourth order to the sixth order. The irregular shapes, relative orbits, attitude angles, as well as the angular velocities of the binary asteroid system are included in the model. We investigated the relative trajectory of the secondary relative to the primary, the total angular momentum and total energy of the system, the three-axis attitude angular velocity of the binary system, as well as the angular momentum of the two components. The relative errors of the total angular momentum and the total energy indicate that the calculation has a high precision. It is found that the influence of the orbital and attitude motion of the primary from the gravitational force of the secondary is obvious. This study is useful in understanding the complicated dynamical behaviors of the binary asteroid systems discovered in our Solar system.     

Trajectory Analysis and Design for A Jupiter Exploration Mission

The trajectory design for a Jupiter exploration mission is investigated in this paper. The differences between the Jupiter exploration trajectory and the Mars or Venus exploration trajectory are mainly concerned about. Firstly, the selection of the Jupiter-centered orbit is analyzed based on the Galileo Jupiter mission. As for the Earth-Jupiter transfer orbit, the fuel consumption of the direct transfer is too large. So the energy-saving technologies such as the planetary gravity assist should be used for the trajectory to the Jupiter. The different sequences of planetary gravity assists are examined by applying the Particle Swarm Optimization (PSO). According to the searched result, the Venus-Earth-Earth sequence (VEEGA) is the most effective one for the Jupiter mission. During the Jupiter mission, the spacecraft will pass though the main asteroid belt between the orbits of Mars and Jupiter, and may encounter multiple asteroids. Therefore the Jupiter mission is able to combine with the main-belt asteroid flyby mission. The design method of the intermediate asteroid flyby trajectory is also considered. At last, an entire trajectory for the Jupiter mission launched in 2023 is presented.     

Periodic orbits in the gravity field of a fixed homogeneous cube

In the current study, the existence of periodic orbits around a fixed homogeneous cube is investigated, and the results have powerful implications for examining periodic orbits around non-spherical celestial bodies. In the two different types of symmetry planes of the fixed cube, periodic orbits are obtained using the method of the Poincaré surface of section. While in general positions, periodic orbits are found by the homotopy method. The results show that periodic orbits exist extensively in symmetry planes of the fixed cube, and also exist near asymmetry planes that contain the regular Hex cross section. The stability of these periodic orbits is determined on the basis of the eigenvalues of the monodromy matrix. This paper proves that the homotopy method is effective to find periodic orbits in the gravity field of the cube, which provides a new thought of searching for periodic orbits around non-spherical celestial bodies. The investigation of orbits around the cube could be considered as the first step of the complicated cases, and helps to understand the dynamics of orbits around bodies with complicated shapes. The work is an extension of the previous research work about the dynamics of orbits around some simple shaped bodies, including a straight segment, a circular ring, an annulus disk, and simple planar plates.     

Approximate analysis for relative motion of satellite formation flying in elliptical orbits

This paper studies the relative motion of satellite formation flying in arbitrary elliptical orbits with no perturbation. The trajectories of the leader and follower satellites are projected onto the celestial sphere. These two projections and celestial equator intersect each other to form a spherical triangle, in which the vertex angles and arc-distances are used to describe the relative motion equations. This method is entitled the reference orbital element approach. Here the dimensionless distance is defined as the ratio of the maximal distance between the leader and follower satellites to the semi-major axis of the leader satellite. In close formations, this dimensionless distance, as well as some vertex angles and arc-distances of this spherical triangle, and the orbital element differences are small quantities. A series of order-of-magnitude analyses about these quantities are conducted. Consequently, the relative motion equations are approximated by expansions truncated to the second order, i.e. square of the dimensionless distance. In order to study the problem of periodicity of relative motion, the semi-major axis of the follower is expanded as Taylor series around that of the leader, by regarding relative position and velocity as small quantities. Using this expansion, it is proved that the periodicity condition derived from Lawden’s equations is equivalent to the condition that the Taylor series of order one is zero. The first-order relative motion equations, simplified from the second-order ones, possess the same forms as the periodic solutions of Lawden’s equations. It is presented that the latter are further first-order approximations to the former; and moreover, compared with the latter more suitable to research spacecraft rendezvous and docking, the former are more suitable to research relative orbit configurations. The first-order relative motion equations are expanded as trigonometric series with eccentric anomaly as the angle variable. Except the terms of order one, the trigonometric series’ amplitudes are geometric series, and corresponding phases are constant both in the radial and in-track directions. When the trajectory of the in-plane relative motion is similar to an ellipse, a method to seek this ellipse is presented. The advantage of this method is shown by an example.     

海洋科学的前沿-“数字海洋”

本文所提出的“数字海洋”,系基于当前世界各国极为关注的“数字地球”发展前景 ,其事关我国海洋科学进入21世纪信息时代所面临的挑战和机遇。对此,从“数字地球”概念及其所涉及的新理论和高新技术 ,到中国“数字地球”中的“数字海洋”有待顺应发展,作了概述。同时 ,重点就“数字海洋”技术与目标和建设的设想等作了探讨。