Longitude-dependent effects of fragmentation events in the geosynchronous orbit regime

The effects of on-orbit fragmentation events on localized debris congestion in each of the longitude slots of the geosynchronous orbit (GEO) regime are evaluated by simulating explosions and collisions of uncontrolled rocket bodies in multiple orbit configurations, including libration about one or both of the gravitational wells located at 75°E and 105°W. Fragmentation distributions are generated with the NASA Standard Breakup Model, which samples fragment area-to-mass ratio and delta-velocity as a function of effective diameter. Simulation results indicate that the long-term severity and consequence of a GEO fragmentation event is strongly dependent upon parent body longitude at the epoch of fragmentation, which can spawn bi-annual “fragment storms” in high-risk longitude slots, driven by lower-energy fragments that have been captured and have started librating around the nearby gravitational well.     

Stochastic motion of geosynchronous satellites

Long-period evolution of the orbital elements of geosynchronous objects moving in the neighborhood of separatrices of the region of libration resonance is studied. At the phase plane “the longitude of the subsatellite point-semi-major axis” the regions of migration of separatrices where the separatrices can move due to the influence of perturbations are isolated. The dimensions of these regions and the distances between them have the same order of magnitude, several kilometers along the semi-major axis. The regions of migration do not overlap at the initial value of the orbit inclination 0°. When inclination increases, gradual overlapping of these regions takes place. On average, the width of the zones of stochasticity increases when the area to mass ratio increases and decreases when inclination of the orbit increases. The zones of stochasticity corresponding to different separatrices are separated from each other. A catalog of the passive geosynchronous objects moving in the neighborhood of separatrices is compiled. The evolution of the objects of the catalog is studied.     

Longitudinal dependence of the H<Superscript>+</Superscript> concentration distribution in the plasmasphere according to <Emphasis Type="Italic">INTERBALL-1</Emphasis> satellite data

The paper has presented a study of the dependence of the H⁺ ions concentration in the plasmasphere on geographic longitude. A vast database of measurements of the cold plasma density by the Alpha-3 instrument on board the INTERBALL-1 satellite has been used for the study. Based on these measurements, a dependence of the H⁺ ions concentration in the filled magnetic flux tube in the plasmasphere in the equatorial plane under quiet geomagnetic conditions has been obtained as a function of geographic longitude. Studies have been performed for two seasons, summer and winter. It has been shown that, during the summer in the near-midnight sector, the minimum in the H⁺ concentration falls within geographic longitudes of 270°–315°. The ratio of the concentration of H⁺ ions at various longitudes could reach a factor of three. During the winter, in the near-noon sector, the maximum of the H⁺ ions concentration falls within longitudes of 180°–225°, whereas the concentration ratio could reach a factor of 2.2.     

基于迭代修正方法的严格回归轨道设计

通过分析太阳同步回归轨道的轨道根数和星下点经度/纬度的关系,推导了一组轨道根数的修正公式。基于高精度轨道动力学模型和升交点位置确定方法,构造了关于轨道半长轴和轨道倾角的迭代修正方法。针对偏心率矢量的动力学系统所具有的极限环特性,构造了平均法求其解析近似,从而实现冻结轨道特性对偏心率和近地点幅角的迭代修正。结合迭代修正,得到一组严格回归的轨道根数。该轨道能够重访空间目标点,具有较高的回归精度。     

Solution of the flyby problem for large space debris at sun-synchronous orbits

the paper considers the flyby problem related to large space debris (LSD) objects at low earth orbits. The data on the overall dimensions of known last and upper stages of launch vehicles makes it possible to single out five compact groups of such objects from the NORAD catalog in the 500–2000 km altitude interval. The orbits of objects of each group have approximately the same inclinations. The features of the mutual distribution of the orbital planes of LSD objects in the group are shown in a portrait of the evolution of deviations of the right ascension of ascending nodes (RAAN). In the case of the first three groups (inclinations of 71°, 74°, and 81°), the straight lines of relative RAAN deviations of object orbits barely intersect each other. The fourth (83°) and fifth (97°–100°) LSD groups include a considerable number of objects whose orbits are described by straight lines (diagonals), which intersect other lines many times. The use of diagonals makes it possible to significantly reduce the temporal and total characteristic velocity expenditures required for object flybys, but it complicates determination of the flyby sequence. Diagonal solutions can be obtained using elements of graph theory. A solution to the flyby problem is presented for the case of group 5, formed of LSD objects at sun-synchronous orbits.     

Design of satellite constellations with continuous coverage on elliptic orbits of <Emphasis Type="Italic">Molniya</Emphasis> type

New methods of choosing the structures of satellite constellations (SC) on elliptical orbits of the Molniya type are presented. The methods, using critical inclination and putting the orbit apogee in the Earth’s hemisphere with an area of continuous coverage, are based on geometrical analysis of two-dimensional representation of the coverage conditions and SC motion in the space of inertial longitude of the orbit ascending node and time. The coverage conditions are represented in the form of a certain region. Dynamics of all satellites in this space is represented by uniform motion along a straight line approximately parallel to the ordinate axis, while the satellite system forms a grid. The problem of choosing a minimal (as far as the number of satellites is concerned) SC configuration can be formulated as a search for the most sparse grid. The contemporary advanced methods of computational geometry serve as an algorithmic basis for the problem solution. Design of SC for continuous coverage of latitude belts with the use of kinematically regular systems is considered. A method of analyzing single-track systems for continuous coverage of arbitrary geographic regions is described, which makes a region at any time instant observable by at least one satellite of the system. As an example, SC on elliptical orbits are considered with periods of ～4, 12, and 24 hours.     

Orbit design for the Spektr-R spacecraft of the ground-space interferometer

In order to carry out tasks of the RadioAstron mission, a high-apogee orbit was designed. On average, the period of its satellite’s orbit around the Earth is 8.5 days with evolution due to gravitational perturbations produced by the Moon and the Sun. The perigee and apogee of this orbit vary within the limits 7500–70000 km and 270000–333000 km, respectively. The basic evolution of the orbit represents a rotation of its plane around the line of apsides. Over 3 years, the plane normal to the orbit draws on the celestial sphere an oval with a semi-major axis of about 150° and semi-minor axis of about 45°.     

A comparison of polarization jet characteristics at the greatly separated stations Yakutsk and Podkamennaya Tunguska

Characteristics of the polarization jet (PJ) are considered on the basis of measurements made in 1989–1992 at the ionospheric stations Yakutsk (L = 3.0, λ = 129.6°) and Podkamennaya Tunguska (L = 3.0, λ = 90.0°) separated in longitude. Using the data of these stations, the result obtained earlier (that the formation of PJ during disturbances in the near-midnight sector occurs at the expansion phase of a substorm) is confirmed. At isolated magnetic disturbances with AE > 500 nT in the 11:00–16:00 UT interval, the PJ band covers an MLT sector of 3 h between the Yakutsk and Podkamennaya Tunguska stations. The time of the PJ beginning at the Podkamennaya Tunguska station for the majority of events is 45–60 min behind the PJ beginning at the Yakutsk station. This corresponds to the westward motion of a PJ source with a velocity of ～3 MLT h per hour.     

Uncontrolled motion of the <Emphasis Type="Italic">Foton M-2</Emphasis> satellite and quasistatic microaccelerations on its board

The results of determining the uncontrolled rotational motion of the Foton M-2 satellite (in orbit from May 31 to June 16, 2005) are presented. The determination was made using the data of onboard measurements of the Earth’s magnetic field strength. Segments 270 min long (three orbits) were selected from these data covering the first two thirds of the flight. On each such segment the data were processed jointly by the least squares method using integration of the equations of attitude motion of the satellite. In processing, the initial conditions of motion and parameters of the used mathematical model were estimated. The thus obtained results gave a complete overview of the satellite motion. This motion, having started with a small angular velocity, gradually accelerated, and in two days became close to the regular Euler precession of an axisymmetric solid body. On June 09, 2005 (the last day of measurements) the angular velocity of the satellite relative to its lengthwise axis was about 1.1 deg/s, while the projection of the angular velocity onto a plane perpendicular to this axis had an absolute value of about 0.11 deg/s. Deviations of the lengthwise axis from a normal to the orbit plane did not exceed 60°. Based on the results of determination of the rotational motion of the satellite, calculations of quasi-static microaccelerations on its board are performed.     

Evolution of motion of two viscoelastic planets in the field of forces of their mutual attraction

Translational-rotational motion of two viscoelastic planets in a gravitational force field is studied. The planets are modeled by homogeneous isotropic viscoelastic bodies. In their natural undeformed state each of the planets represents a sphere. We investigate a specific case when the planet’s centers of mass move in a fixed plane, the axis of rotation for each planet being directed along the normal to this plane. An equation describing the evolution of a slow angular variable (perihelion longitude) is derived. The observed displacement of the perihelion of Mercury is compared with the results obtained in the considered model problem about motion of two viscoelastic planets. Quite important is the fact that the planet of smaller mass (Mercury) moves not in a central Newtonian field of forces, but rather in the gravitational field of a rotating viscoelastic planet (Sun).     

Study of notches in the Earth’s plasmasphere based on data of the <Emphasis Type="Italic">MAGION-5</Emphasis> satellite

Depleted narrow (localized in longitude) regions (field tubes) in the plasmasphere, recently discovered in He⁺ radiation measurements on the IMAGE spacecraft, were first directly observed by the Magion-5 satellite. The low-density regions (notches) occupy <～ 10–30° in longitude and extend from L ～ 2–3 to the plasmasphere boundary in neighboring plasmasphere regions with larger densities. The Magion-5 data give evidence that in the low-density regions temperature is enhanced as compared to the neighboring denser plasmasphere regions. Formation of notches in the plasmasphere is, apparently, associated with AE intensification during weak magnetic storms, while strong magnetic storms usually result in the overall reduction of plasmasphere dimensions. However, even a strong magnetic storm on April 6–7, 2000 (max K _p = 9-and min D _st ～ ?290 nT), but accompanied by an isolated AE impulse, resulted in a density decrease only in the longitudinally limited post-midnight sector of the plasmasphere.     

一种大功率圆极化交叉对称阵子天线

为了满足大功率反射面天线的馈源设计要求,文章设计了一种大功率圆极化交叉对称阵子天线,其工作频率在1.19GHz~1.285GHz,天线整体由交叉对称阵子和开槽线巴伦组成。通过开槽线巴伦实现平衡-非平衡馈电。为了实现圆极化,通过改变对称阵子结构,在对称阵子臂相邻90°处增添一对阵子臂,形成交叉对称阵子,并通过调整阵子臂的长度,使其实现90°自相移结构,并最终实现圆极化,由于天线整体均为金属,使得天线可以承受更高的功率。该天线在119GHz~1285GHz频带内电压驻波比(votage standing wave ratio,VSWR)<1.5,圆极化轴比<3dB,实测结果表明,实测和仿真结果基本一致,天线在该频段内实现了较好的圆极化特性。     

Influence of disturbances on the angular motion of a spacecraft in the powered section of its descent

The motion of a variable-mass spacecraft is considered in the powered section of a descending trajectory. Approximate analytical solutions are obtained for the angles of spatial orientation of the spacecraft, which allows one to analyze the nutation motion and to develop recommendations on the spacecraft’s mass configuration, providing the smallest possible deviations of the longitudinal axis and thrust vector from specified directions. The errors of stabilization of the spacecraft’s longitudinal axis are calculated by means of numerical integration of complete models and using the obtained analytical solutions, the results being in good agreement.     

Sporadic structures and small-scale irregularity in the nighttime polar ionosphere in the period of high solar activity according to the data of radio occultation measurements on satellite-to-satellite paths

Results of the analysis of 327 sessions of radio occultation on satellite-to-satellite paths are presented. The data are taken in the nighttime polar ionosphere in the regions with latitudes of 67°–88°, and in the period of high solar activity from October 26, 2003 to November 9, 2003. Typical ionospheric changes in the amplitude and phase of decimeter radio waves on paths GPS satellites-CHAMP satellite are presented. It is demonstrated that these data make it possible to determine characteristics of the sporadic E _s structures in the lower ionosphere at heights of 75–120 km. Histograms of distribution of the lower and upper boundaries, thickness, and intensity of the E _s structures are presented. Dispersion and spectra of amplitude fluctuations of decimeter radio waves caused by small-scale irregularity of the ionospheric plasma are analyzed. The relation of the polar E _s structures and intensity of small-scale plasma irregularity to various manifestations of solar activity is discussed. The efficiency of monitoring the ionospheric disturbances caused by shock waves of the solar wind by the radio occultation method on satellite-to-satellite paths is demonstrated.     

天问一号环绕器中继轨道受摄共振特性分析

“天问一号”环绕器在环火中继轨道为“祝融”火星车提供中继服务时,星下点出现了过着陆点纬度时的经度先增大再减小的特殊漂移现象,需要对该现象产生的原因进行深入分析。基于摄动理论设计了一系列数值实验,提出了一种星下点过指定纬度时经度的简化计算方法;并结合对田谐项引力场位函数的解析推导发现,由于中继轨道周期与火星自转周期比接近1:3,导致3阶3次田谐项产生了轨道共振,从而使得半长轴长周期运动有着较为显著的振荡,进而与带谐项摄动联合导致了该特殊现象。研究揭示了“天问一号”环绕器的轨道共振现象,发现了高阶田谐项对非同步轨道上的环火卫星仍能产生较为明显的轨道共振现象。研究结果可为后续火星环绕探测任务轨道设计提供重要参考。     

The Effect of Dissipative Moments Caused by Liquid Body Viscosity on the Rotation Stability of a Space Object

The influence of dissipative forces in a viscous liquid that completely fills the cavities of a space object executing a rotational motion is analyzed. The Navier–Stokes equations are solved by expanding them into a series in terms of eigenfunctions of the boundary value problem on involving the resting liquid in rotation around the longitudinal axis of a cavity. The analytical solutions for coaxial cylindrical and concentric spherical cavities are obtained, in particular, for a straight circular cylinder and a sphere. The stability of the single-axis orientation of a space object filled with a viscous liquid is investigated. The dependences of rotation decay processes and drifts of the space object's longitudinal axis from a given direction are shown on the plane of constructive parameters.     

Families of periodic solutions in three-dimensional restricted three-body problem

Planar orbits of three-dimensional restricted circular three-body problem are considered as a special case of three-dimensional orbits, and the second-order monodromy matrices M (in coordinate z and velocity v _z ) are calculated for them. Semi-trace s of matrix M determines vertical stability of an orbit. If |s| ≤ 1, then transformation of the subspace (z, v _z ) in the neighborhood of solution for the period is reduced to deformation and a rotation through angle φ, cosφ = s. If the angle ? can be rationally expressed through 2π,φ = 2π·p/q, where p and q are integer, then a planar orbit generates the families of three-dimensional periodic solutions that have a period larger by a factor of q (second kind Poincareé periodic solutions). Directions of continuation in the subspace (z, v _z ) are determined by matrix M. If |s| < 1, we have two new families, while only one exists at resonances 1: 1 (s = 1) and 2: 1 (s = ?1). In the course of motion along the family of three-dimensional periodic solutions, a transition is possible from one family of planar solutions to another one, sometimes previously unknown family of planar solutions.     

Control of an orbiting flexible square platform in the presence of solar radiation

A mathematical model for the solar radiation forces and moments acting on a square plate (platform) in orbit is obtained by considering the plate mode shapes as combinations of free-free beam shape functions. The moment expressions for a plate of arbitrary reflectivity coefficient are obtained as a function of the solar incidence angle. It is seen that only the first three flexible modes of the plate generate a first order net moment about the center of mass, and that the solar radiation pressure does not influence the flexible modes of the plate for small amplitude vibrations. The solar radiation disturbance model is then included in the dynamic model of a square plate nominally oriented along the local vertical and having the major surface of the plate normal to the orbital plane. The roll angle of the plate is seen to increase steadily due to the solar radiation pressure whereas the pitch and yaw motions oscillate with an amplitude of approximately 0.2° for a 100 m square thin aluminum plate in synchronous orbit. To control the shape and orientation of the plate two point actuators are assumed—one whose force axis is normal to the plane of the plate, the second with a force axis in the plane of the plate. The control law and the feedback gain values are obtained based on linear quadratic Gaussian methods. Transient responses and control requirements are simulated for local vertical and horizontal orientations.     

立式捏合机桨叶结构参数对混合釜流场影响的仿真分析

为揭示立式捏合机桨叶几何结构参数与混合釜流场之间的关系,以1 L两桨立式捏合机为研究对象,采用计算流体力学ANSYS Fluent 14.5软件对立式捏合机进行了三维模型仿真研究,分析了桨叶结构参数(桨桨间隙、桨叶螺旋角)的改变对混合物料挤压应力和剪切应力的影响。结果表明,增大桨桨间隙可减小桨叶对混合物料的挤压应力和剪切应力,空心桨螺旋角分别为40°、45°、50°,桨桨间隙由1.0 mm增加到3.0 mm,挤压应力、剪切应力分别平均减小了82.4%、57.23%;增大桨叶螺旋角可增大桨叶对混合物料的挤压应力和剪切应力,空心桨间隙分别为1.0、2.0 mm,桨叶螺旋角由35°增加到55°,挤压应力、剪切应力分别平均增加了92.8%、55.7%。