A Retrospective Geometric Analysis of the Long-Term Evolution of Orbits and the Ballistic Lifetime for Satellites of the Prognoz Series

We consider the applied aspects of the geometrical analysis of solutions in a restricted circular double-averaged three-body problem that are concerned with the design of high-apogee satellite orbits. Based on the analysis of the long-term evolution and the ballistic lifetime for orbit families of the Prognoz satellites launched into their orbits in the period 1972–1995, we suggest some practical suggestions for choosing long-lived high-apogee orbits with taking into account various requirements for the domain of evolution of the orbital elements.     

Analysis of Ballistic Structures of Multichannel Communication Satellite Systems on Precessing Elliptic Orbits

Two models of intersatellite communication channels in satellite systems on precessing elliptic orbits are considered. By assuming that these systems provide for a continuous survey of the Earth of the necessary multiplicity, algorithms of the analysis of ballistic system structures are constructed for these models in order to maintain multichannel global communication and organization of corresponding intersatellite channels. The algorithm operation is illustrated by numerical examples. This paper develops the results from [1–3], where a similar approach was advanced for the analysis of ballistic structures of satellite systems with simplified models of motion.     

A Study of a Possible Method of Observing Solar Eclipses from Satellite Orbits

We study a possibility of observing the eclipses of the Sun by the Moon from satellite orbits. The scientific tasks planned to be solved onboard satellites are considered. The requirements for the observation of eclipses and for the appropriate satellite trajectories are formulated. A technique of the analysis and synthesis of such trajectories is developed, and some results of preliminary ballistic studies are presented. These results confirm the efficiency of observing the eclipses onboard satellites.     

USA-193 decay predictions using public domain trajectory data and assessment of the post-intercept orbital debris cloud

In early 2008, the need arose to predict the orbital decay of the American spacecraft USA-193, whose characteristics, function and orbit were classified information. With no orbit data and independent Italian tracking capability available, we turned our attention on the orbits determined by a worldwide network of about 20 visual satellite observers. The orbits of USA-193 obtained from their visual observations were therefore used as the sole source of orbit information. Contrary to our expectations, this exercise was extremely successful and we learned a lot in the process. The orbits provided by the visual observers were very accurate for such a low satellite (although the minimum and very stable level of solar activity helped considerably); however, data gaps of a few days were sometimes possible, due to unfavorable pass geometry or weather and light conditions. In any case, the orbital period and the semimajor axis were so accurate that it was possible for us to obtain very good decay fits using special perturbation software, including various atmospheric density models together with all the other relevant perturbing accelerations. We were therefore able to estimate accurate values of the ballistic parameter and the resulting decay and reentry predictions were extremely stable. Amateur optical observations and images of USA-193 had also led to a rough estimation of the shape and sizes of the satellite, revealing that the solar arrays had never been deployed. With this information, and taking into account our estimates of the ballistic parameter, we obtained reasonable and consistent values of the spacecraft mass. Based on previous reentry fragmentation analyses, we were then able to guess the expected USA-193 casualty area, casualty expectancy, debris ground footprint and probability of impact in Italy. Lastly, after the decision by the US Government to destroy the satellite, we independently predicted the interception time windows and the post-event ground tracks. Following the successful spacecraft breakup, we analyzed the evolution of the resulting debris cloud and assessed its (very limited) adverse impact on the circumterrestrial environment.     

On the features of long-term evolution of a high-apogee orbit of the SPECTR-R spacecraft

The practical tasks related to qualitative investigation of long-term evolution of high-apogee orbits of artificial Earth satellites (AES), for which the main perturbing factors are gravitational perturbations from the Moon and the Sun, are considered. Attention is given to the problem of the ballistic lifetime of similar orbits, and the issues associated with possibilities of the correction of orbits for ensuring the required duration of their ballistic lifetime are considered. The orbit of the SPECTR-R spacecraft launched in July of 2011 is considered as an example.     

通信卫星灵活载荷技术综述

通信卫星逐步由高轨地球同步轨道卫星向高、中、低轨结合的全球覆盖卫星方向发展,多业务和多重覆盖的发展趋势对通信卫星的灵活性提出了更高的要求。通信卫星配备灵活载荷已经成为重要发展方向,对面向个人用户的高通量通信卫星及高、中、低轨结合的组网通信卫星来说尤为重要。配备灵活载荷的通信卫星能实现端到端业务,能灵活调整覆盖区,实现灵活组网,并提升资源利用率。分析了国内外通信卫星灵活载荷的发展动态,介绍了通信卫星灵活载荷的技术特点,并给出了有效载荷方案,最后阐述了通信卫星灵活载荷发展的关键技术及发展思路。     

一类适用于各种轨道类型的导航卫星广播星历研究

导航卫星广播星历是卫星导航定位的基础,要求有较高的精度和实时性。GPS和GLONASS广播星历形式适合于某一类卫星轨道,但存在一定局限性。利用切比雪夫多项式拟合导航卫星轨道,拟合系数作为广播星历的参数发布,这是一种新的广播星历形式,可作为各种轨道类型的导航卫星的广播星历参数,而且具有精度高、计算速度快等特点。     

Navigation Solution to Maneuver a Spacecraft Relative to a Sphere Centered on a Cooperative Satellite

A differential correction algorithm is presented to deliver an impulsive maneuver to a satellite to place it within a sphere, with a user defined radius, centered around a non-maneuvering satellite within a constrained time. The differential correction algorithm develops and utilizes the State Transition Matrix along with the Equations of Motion and multiple satellite?s state information to determine the optimum trajectory to achieve the desired results. The results from the differential correction algorithm are very accurate for prograde orbits, as presented. The results allow for orbit design trade-offs, including satellites? initial inclinations, semi-major axes, as well as the ballistic coefficients. The results also provide an empirical method to determine the optimum ΔV$\mathrm{\Delta }V$ solution for the provided problem. Understanding that the minimum fuel solution lies with a semi-major axis ratio of 1, a very accurate empirical approximation is presented for semi-major axis ratio values less than and greater than 1. This work ultimately provides the generalized framework for applying the algorithm to a unique user defined maneuvering spacecraft scenario.     

非开普勒轨道下卫星交会变轨决策研究

针对卫星在非开普勒轨道下的运动特征,提出了研究卫星交会变轨决策的方法。首先,在Hill坐标下,采用比例导引方法求解卫星进行变轨机动时所需要的速度增量。然后,再通过Lagrange插值算法解出卫星在任意特征点上变轨机动所需要的速度增量,根据数字仿真得出大量的仿真数据并画出满足变轨决策条件的决策曲面。最后,对决策曲面的涵义做出分析,说明了该方法对于研究非开普勒轨道下卫星变轨决策问题具有一定的意义。     

Mapping orbits with low station keeping costs for constellations of satellites based on the integral over the time of the perturbing forces

The present paper is concerned with the search for orbits that have potential to require low fuel consumption for station-keeping maneuvers for constellations of satellites. The method used to study this problem is based on the integral over the time of the undesired perturbing forces. This integral measures the change of velocity caused by the perturbation forces acting on the satellite, so mapping orbits that are less perturbed, which generates good candidates for orbits that requires low fuel consumption for station-keeping maneuvers. The integral over the time depends only on the orbit of the spacecraft and the dynamical system considered. The type of engine and the control technique applied to the spacecraft are not considered to search for those orbits. It can be a good strategy to be applied for a first mapping of orbits. For this search, it is analyzed the integral of orbits with different values of the Keplerian elements in order to find the best ones with respect to this criterion. The perturbations considered are the ones caused by the third body, which includes the Sun and the Moon, and the J₂ term of the geopotential. The results presented here show numerical simulations to obtain the integral of those perturbing forces for different orbits. The GPS and the Molniya constellations are used as examples for those calculations.     

预警卫星对导弹预警模型的仿真

通过分析研究，建立了预警卫星系统对战术弹道导弹（TBM）弹道进行预警的一种数学模型，其中包括预警卫星系统信息库的信息模型、用预警卫星探测信息确定TBM坐标的模型、确定TBM发射时刻及发射点坐标的模型、确定关机点及对应的关机点弹道参数模型、计算预警弹道及落点的模型等，同时还对信息库中信息模型的精度、计算发射点价值及发射时刻模型的精度、计算关机点时刻及参数的精度进行了分析，得出了有一定理论意义和工程应用价值的结论。     

Biaxial Mode of Rotation of a Satellite in the Orbit Plane

A mode of motion of a satellite with respect to its center of mass is studied, which is called the biaxial rotation in the orbit plane. In this mode of rotation, an elongated and nearly dynamically symmetric satellite rotates around the longitudinal axis, which, in turn, rotates around the normal to the plane of an orbit; the angular velocity of rotation around the longitudinal axis is several times larger than the orbital angular velocity, deviations of this axis from the orbit plane are small. Such a rotation is convenient in the case when it is required to secure a sufficiently uniform illumination of the satellite's surface by the Sun at a comparatively small angular velocity of the satellite. The investigation consists of the numerical integration of equations of the satellite's motion, which take into account gravitational and restoring aerodynamic moments, as well as the evolution of the orbit. At high orbits, the mode of the biaxial rotation is conserved for an appreciable length of time, and at low orbits it is destroyed due to the impact of the aerodynamic moment. The orbit altitudes and the method of constructing the initial conditions of motion that guarantee a sufficiently prolonged period of existence of this mode are specified.     

Choice of high-apogee AES orbits on the basis of the qualitative methods of the theory of perturbations and situational analysis. Part I. Situational studies based on orbital tori

The paper discusses the problems of the choice of high-apogee orbits of artificial Earth satellites (AES), proceeding from the tasks of space experiments aimed at studying near-earth space and taking into account the features of the orbital evolution and ballistic lifetime. The suggested methods of the choice of orbits consist of two components. The first is based on the use of mathematical models of studied regions of near-earth space and various techniques of situation analysis, among which the annual and daily orbital tori developed by the author about 35 years ago are key. The second component is based on qualitative methods of the theory of perturbations of high-apogee AES orbits developed by M.L. Lidov more than 50 years ago.     

A low-thrust transfer between the Earth–Moon and Sun–Earth systems based on invariant manifolds

A low-energy, low-thrust transfer between two halo orbits associated with two coupled three-body systems is studied in this paper. The transfer is composed of a ballistic departure, a ballistic insertion and a powered phase using low-thrust propulsion to connect these two trajectories. The ballistic departure and insertion are computed by constructing the unstable and stable invariant manifolds of the corresponding halo orbits, and a complete low-energy transfer based on the patched invariant manifolds is optimized using the particle swarm optimization (PSO) algorithm on the criterion of smallest velocity discontinuity and limited position discontinuity (less than 1 km). Then, the result is expropriated as the boundary conditions for the subsequent low-thrust trajectory design. The fuel-optimal problem is formulated using the calculus of variations and Pontryagin's Maximum Principle in a complete four-body dynamical environment. Then, a typical bang–bang control is derived and solved using the indirect method combined with a homotopic technique. The contributions of the present work mainly consist of two points. Firstly, the global search method proposed in this paper is simply handled using the PSO algorithm, a number of feasible solutions in a fairly wide range can be delivered without a priori or perfect knowledge of the transfers. Secondly, the indirect optimization method is used in the low-thrust trajectory design and the derivations of the first-order necessary conditions are simplified with a modified controlled, restricted four-body model.     

一种导航星座星间链路拓扑设计方法

利用星间测距和通信实现卫星自主导航是下一代导航星座的发展方向之一.为了确定星间测距和通信链路的网络拓扑结构,对walker24/3/2星座的卫星之间几何可见性、卫星天线之间的可见性进行了研究,给出了可见性判断条件,并针对三条轨道相互垂直的情况,推导了星间几何距离随时间变化的公式.对天线扫描区域为±60°对地圆锥的情况进...     

Quasioptimal control with feedback for multiorbit low-thrust transfer between noncoplanar elliptic and circular orbits

The problem of synthesizing stable feedback control is considered based on solving the problem of time minimization for a multiorbit transfer between noncoplanar elliptic and circular orbits in a Newtonian gravitational field. The problem is solved using asymptotic properties and symmetries of optimal control in the unperturbed problem. Stability of the obtained control against external perturbations, deviations of initial conditions, and errors in thrust vector realizations is demonstrated. The obtained quasioptimal control with feedback can be used as an onboard algorithm of spacecraft control and when performing design and ballistic analysis.     

Feasibility of using statellites in non-equatorial 24-hour circular orbits for communications

The early sixties witnessed the debate among competing candidate orbits that led to the emergence of perfect geostationary systems as virtually the sole “instruments” for satellite communication. The subsequent problem of overcrowding of geostationary ring on one hand and explosive growth in demand on communication capacity on the other led comsat experts to focus on the alternate routes through various near-earth and medium attitude satellite constellations later proposed for uninterrupted communication. However, the opportunities thrown up by quasi-stationary orbits for augmentation of the space communication capacity have gone abegging. This paper attempts to draw attention of communication satellite designers/planners to the immense potential for utilization of the non-equatorial, 24-hour circular orbits for communication. For the proposed quasi-stationary orbits, the change and/or control of the inclination of the plane is not envisaged in the launch and/or operational phase. The resulting significant payload weight advantage is associated with the problem of periodic as well as secular apparent angular satellite drift relative to the ground terminal. However, the problem may be largely overcome through controlled satellite tilting using solar radiation pressure or through the use of tethered auxiliary mass attachment. Alternatively, it may be possible to overcome the attitude control problem by the use of systems such as on-bard electronically steerable phased array antenna capable of following the line-of-sight to the co-operative ground station.     

基于轨迹特征的预警系统目标识别

文章针对弹道导弹预警系统目标识别任务的特点,通过分析弹道导弹和卫星目标间的运动特性差异,给出了预警雷达基于最小矢径这一特征区分弹道导弹和卫星的流程,并分析了弹道导弹射程、雷达测量精度、观测时间、采样间隔等因素对此流程的影响。仿真结果表明:利用最小矢径实现弹道导弹和卫星的区分是可行的,而且此法对雷达测量精度要求不是特别高。     

Trajectory correction of the Spektr-R spacecraft motion

The results of refining the parameters of the Spektr-R spacecraft (RadioAstron project) motion after it was launched into the orbit of the Earth’s artificial satellite in July 2011 showed that, at the beginning of 2013, the condition of staying in the Earth’s shadow was violated. The duration of shading of the spacecraft exceeds the acceptable value (about 2 h). At the end of 2013 to the beginning of 2014, the ballistic lifetime of the spacecraft completed. Therefore, the question arose of how to correct the trajectory of the motion of the Spektr-R satellite using its onboard propulsion system. In this paper, the ballistic parameters that define the operation of onboard propulsion system when implementing the correction, and the ballistic characteristics of the orbital spacecraft motion before and after correction are presented.     

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.