Large-size space debris flyby in low earth orbits

the analysis of NORAD catalogue of space objects executed with respect to the overall sizes of upper-stages and last stages of carrier rockets allows the classification of 5 groups of large-size space debris (LSSD). These groups are defined according to the proximity of orbital inclinations of the involved objects. The orbits within a group have various values of deviations in the Right Ascension of the Ascending Node (RAAN). It is proposed to use the RAANs deviations' evolution portrait to clarify the orbital planes’ relative spatial distribution in a group so that the RAAN deviations should be calculated with respect to the concrete precessing orbital plane of the concrete object. In case of the first three groups (inclinations i = 71°, i = 74°, i = 81°) the straight lines of the RAAN relative deviations almost do not intersect each other. So the simple, successive flyby of group’s elements is effective, but the significant value of total ΔV is required to form drift orbits. In case of the fifth group (Sun-synchronous orbits) these straight lines chaotically intersect each other for many times due to the noticeable differences in values of semi-major axes and orbital inclinations. The intersections’ existence makes it possible to create such a flyby sequence for LSSD group when the orbit of one LSSD object simultaneously serves as the drift orbit to attain another LSSD object. This flyby scheme requiring less ΔV was called “diagonal.” The RAANs deviations’ evolution portrait built for the fourth group (to be studied in the paper) contains both types of lines, so the simultaneous combination of diagonal and successive flyby schemes is possible. The value of total ΔV and temporal costs were calculated to cover all the elements of the 4th group. The article is also enriched by the results obtained for the flyby problem solution in case of all the five mentioned LSSD groups. The general recommendations are given concerned with the required reserve of total ΔV and with amount of detachable de-orbiting units onboard the maneuvering platform and onboard the refueling vehicle.     

Controlling the motion of a spacecraft when approaching a large object of space debris

The problem of calculating the parameters of maneuvering a spacecraft as it approaches a large object of space debris (LOSD) in close near-circular noncoplanar orbits has been considered. In [1–4], the results of analyzing the problem of the flyby of the separated LOSD groups have been presented. It has been assumed that a collector spacecraft approaches the LOSD and captures it or it is inserted into the nozzle of a small spacecraft that has a proper propulsion system (PS). However, in these papers, the flight from one object to another was only analyzed and the problem of approaching to LOSD with a given accuracy was not considered. This paper is a supplement to the cycle of papers [1–4]. It is assumed that, the final stage of approaching the LOSD is implemented by maneuvering in many orbits (up to several dozens) with low-thrust engines, but the PS operating time is fairly small compared with the orbit period in order to make it possible to use impulse approximation in the calculations.     

Exploring the Kuiper Belt: An extended Pluto mission

A robotic flyby mission to the planet Pluto is being planned for launch early in the next decade. The spacecraft will continue on out of the solar system in an almost radial direction traveling at about four AU per year and begin transiting the Kuiper Belt shortly after Pluto encounter. Recent discoveries and observations of Kuiper Belt objects have generated increased interest in the characteristics of these bodies. This paper examines the opportunities and requirements for extending the Pluto mission to include the search for, and encounters with, objects in the Kuiper Disk at 40+ AU. The trajectory and ΔV requirements will be presented. An automated, on-board sky survey will be proposed to inventory the Kuiper objects in the vicinity of the flight path and to identify which objects are candidates for altering the trajectory for a close flyby. A possible Kuiper object encounter science scenario will be described.     

Further analysis of infrared spectrophotometric observations of high area to mass ratio (HAMR) objects in GEO

Optical surveys have identified a class of high area-to-mass ratio (HAMR) objects in the vicinity of the Geostationary Earth Orbit (GEO) ring^. The exact origin and nature of these objects are not well known, although their proximity to the GEO belt poses a hazard to active GEO satellites. The prevalent conjecture is that many of these objects may be thermal materials shed from derelict spacecraft in ‘graveyard’ orbits above the GEO ring. Due to their high area-to-mass ratios and unknown attitude dynamics and material characteristics, solar radiation pressure (SRP) perturbs their orbits in ways that makes it difficult to predict their orbital trajectories over periods of time exceeding a week or less. To better understand and track these objects and infer their origins, we have made observations that allow us to determine physical characteristics that will improve the non-conservative force modeling used for orbit determination (OD) and prediction. Information on their temperatures, areas, emissivities, and albedos may be obtained from thermal infrared and visible measurements. Simultaneous observations in the thermal infrared and visible wavelengths may allow disentangling of projected area, albedo, and object emissivity.Further analysis and modeling of observational data on certain of the HAMR objects collected at the AMOS observatory 3.6 m AEOS telescope are presented. The thermal-IR spectra of these geosynchronous orbit objects acquired by the Broadband Array Spectrograph System (BASS) span wavelengths 3 to 13 μm and constitute a unique data set, providing a means of measuring object fluxes in the infrared and visible wavelengths. These, in turn, allow temperatures and emissivity-area products to be calculated, and in some cases provide information on rotation rates. We compare our observational results with the outputs of simple models, in terms of visible and infrared flux and orbital characteristics. The resulting temperatures and rotation rates are used in SRP acceleration models to demonstrate improvements in OD and prediction performance relative to models which assume default ambient temperature and static attitude dynamics. Additionally, we have the capability and plans to measure material properties with the same instrument in the lab as used at the telescope to facilitate direct comparisons.     

平面度测量中的选线原则

在平板的平面度测量中,最常用的、精度最高的方法,是利用光电准直光管或激光干涉仪测量一族直线在与平板垂直方向的直线度,然后根据直线度数据来确定平板的平面度。如何选择这一族直线是平面度测量中的一个重要问题。本文提出了绝对基准与浮动基准的概念。对于采用浮动基准的方法,例如准直光管法和激光干涉仪法,从理论上阐明了选线原则为:(1)线族的总自由度必须小于或等于三;(2)至少必须测量三种不同方向的线;(3)二条对角线是确定平面轮廓的最佳线;(4)平板平面度测量中应取四条周线与二条对角线为基本测量线。     

Collisions of stars by oscillating orbits of the second kind

Ordinary estimations of the number of star collisions in our galaxy—by simple kinematic considerations—lead to a very small number of such collisions: about one or even less every millions of years. However star collisions can occur through the following indirect way which has a much higher probability. (a) Binary stars are very common in our galaxy, about 30–50% of the stars. (b) If two binary stars meet a triple system can be formed by an ordinary exchange type motion. (c) A triple system is generally decomposed into the “inner orbit” (i.e. the relative orbit of the two nearest stars) and the “outer orbit” (i.e. the relative orbit of the third star with respect to the center of mass of the two nearest stars). The major axes of these two orbits have generally small perturbations and it is the same for the eccentricity of the outer orbit. On the contrary, if the relative inclination of the two orbits is large, the perturbations of the eccentricity of the inner orbit are important and can even in some cases lead to an eccentricity equal to one, that is to a collision of the two stars of the inner orbit.Such orbits can be called “oscillating orbits of the second kind”, indeed the first oscillating orbits—conceived by Khilmi and described for the first time in an example by Sitnikov—have unbounded mutual distances r_ij, but the system always come back to small sizes, it has an infinite number of very large expansions followed by strong contractions and, in the three-body case, an upper bound of lim inf (r_1.2 + r_1.3 + r_2.3) can be given in terms of the three masses and the integrals of motion. For the oscillating orbits of the second kind the mutual distances r_ij are bounded, but the velocities are unbounded (i.e. lim inf r_ij = 0 for at least one r_ij) and the system goes to a collision if the bodies have non-zero radius even small. The analytical study of the oscillating orbits of the second kind is a part of the general analytical study of the three-body problem, a part which must be valid for large eccentricities and large inclinations. The use of Delaunay's variables and of a Von Zeipel transformation lead to a first order integrable approximation, valid for any eccentricities and any inclinations, and giving the following results: (a) The oscillating orbits of the second kind occur when the angular momentum of the outer orbit has a modulus sufficiently close to the modulus of the total angular momentum of the three-body system. Hence these orbits occur for inclinations in the vicinity of 90°. (b) The oscillating orbits represent a set of positive measure of phase space and the first order study allows to give a rough estimation of the probability of collisions—even for stars of infinitely small radius. This probability, for given initial major axes and eccentricities and for isotropic arbitrary initial orientations, is generally of the order of m₃$\text{R}\text{M}$ (m₃ being the mass of the outer star, M the total mass and R the ratio of the period of the inner orbit to that of outer orbit).One question remains to be solved: how many collisions of stars are due to that phenomenon? That question is difficult because the probability of formation of a triple system by a random meeting of two binaries is very uneasy to estimate. However it seems that, compared to the usual evaluations based on pure kinematic considerations without gravitational effects, the number of collisions must be multiplied by a factor between one thousand and one million.     

One optimization problem for trajectories of spacecraft rendezvous mission to a group of asteroids

The optimization problem is considered for the trajectory of a spacecraft mission to a group of asteroids. The ratio of the final spacecraft mass to the flight time is maximized. The spacecraft is controlled by changing the value and direction of the jet engine thrust (small thrust). The motion of the Earth, asteroids, and the spacecraft proceeds in the central Newtonian gravitational field of the Sun. The Earth and asteroids are considered as point objects moving in preset elliptical orbits. The spacecraft departure from the Earth is considered in the context of the method of a point-like sphere of action, and the excess of hyperbolic velocity is limited. It is required sequentially to have a rendezvous with asteroids from four various groups, one from each group; it is necessary to be on the first three asteroids for no less than 90 days. The trajectory is finished by arrival at the last asteroid. Constraints on the time of departure from the Earth, flight duration, and final mass are taken into account in this problem.     

在轨物体接近算法研究

根据NORAD公布的在轨物体(空间碎片或航天器) 的轨道数据,给出了计算在轨物体两两间发生接近事件的方法。该方法结合了计算在轨物体 接近的运动学筛选法和相对距离函数法,以提高计算效率。以该方法为基础,提出了特定航 天器与全体在轨物体间的接近事件算法。算法采用了改进后的几何筛选法。该方法并不求解 两轨道的最近点,而是求解包含最近点的时间窗口,从而解决了原方法漏报接近事件的问题 。该方法在理论上可以检测到所有的接近事件,数值仿真验证支持了该结论。在计算效率 上新方法相对于原算法也有约10倍的提高。     

Design and development of correlation techniques to maintain a space surveillance system catalogue

A growing interest exists in a future, autonomous European Space Surveillance System (ESSS). Currently, most of the knowledge about Earth-orbiting space objects is based on information provided by the USASPACECOM. This paper presents the required initial orbit determination (IOD) and correlation techniques to process optical measurements. Former studies were focused on the handling of radar measurements, which are summarised with the aim of describing a global procedure for processing hybrid measurement types (combination of radar and optic data for catalogue maintenance). The introduction of manoeuvres are presented due to their importance in the space object catalogue maintenance.The detection of uncatalogued objects and the successful correlation of already catalogued objects involve two different tasks for telescopes: survey and tasking. Assumptions for both strategies are developed on the basis of the previous work developed at the University of Berne (see [T. Flohrer, T. Schildknecht, R. Musci, E. Stöveken, Performance estimation for GEO space surveillance, Advances in Space Research 35 (2005). [1]; T. Flohrer, T. Schildknecht, R. Musci, Proposed strategies for optical observations in a future European Space Surveillance Network, presented in the 36th COSPAR Scientific Assembly (2006). [2]; R. Musci, T. Schildknecht, M. Ploner, Orbit improvement for GEO objects using follow-up observations, Advances in Space Research 34 (2004). [3]; R. Musci, T. Schildknecht, M. Ploner, G. Beutler, Orbit improvement for GTO objects using follow-up observations, Advances in Space Research 35 (2005). [4]; R. Musci, T. Schildknecht, T. Flohrer, G. Beutler, Concept for a catalogue of space debris in GEO, Proceedings of the Fourth European Conference on Space Debris, (ESA SP-587, 2005). [5]]). When a new object appears in the field of view, initial orbit determination must be performed. When only one telescope per site is available, the initial measurements are separated by only a few seconds. Therefore, the initial orbit determination is quite inaccurate due to bad mathematical conditioning of the problem. In order to improve the accuracy of the initial orbit determination, several follow-up observations of the object are required. This implies that the telescope needs to track the detected objects over a long period, and therefore the time available for surveying is reduced. By processing the additional follow-up measurements, separated now by a few hours, the initial orbit determination gives more accurate results and the object can be recovered after an orbital revolution. When several telescopes per site are available, the optical strategies may be modified. The survey tasks can be distributed between the available telescopes. In this way the number of images corresponding to each object increases and to track the detected object over long periods is not always needed. Numerical results will be shown in order to evaluate the accuracy and features of the different telescope strategies. A key point for performing efficiently the cataloguing process is the calculation of the estimated state vector covariance matrix. The covariance matrix analysis allows an adaptive tasking-survey telescope scheduling. Moreover, the implementation of a proper batch orbit determination process by means of a square root information filter (SRIF) requires a realistic initial covariance matrix.Hybrid measurements are available from objects that can be observed through both radar and optical sensors (e.g. GTO objects). The batch orbit determination and correlation process of hybrid measurements is also based on SRIF using an extended measurement model. Both the initial orbit determination methods using radar and optical measurements have to be sufficiently accurate to initialise SRIF correctly. In order to avoid filter divergence, the estimated covariance must be correctly updated after processing both kinds of measurements. The implemented algorithms are explained and their performance is shown through realistic simulations.Techniques to detect and characterise object manoeuvres during the cataloguing process have been developed and implemented. Four main groups of manoeuvre objects have been established by means of their observed permitted orbital ranges (GEO, LEO, MEO–GPS, Molniya). The study is based on the historical TLEs files. When an object with an uncatalogued orbit appears, a comparison between the new orbit and the orbits contained in the permitted ranges of one of the manoeuvre groups is performed. If the required Δa and/or Δi to convert the lost orbit into the detected orbit seems to be feasible, a manoeuvre will be identified and the orbit will be updated in the catalogue. Otherwise, it will be decided that a new object was found. For this purpose, a procedure to estimate the manoeuvres and reset orbits have been developed.     

Qualitative Properties of Orbits for Minimum-Fuel Impulsive Transfers between Circular Coplanar Orbits with a Given Launch Time

The coplanar problem of minimizing propellant consumption in impulsive transfer between circular boundary orbits is investigated. The launch time and the initial configuration of objects on the boundary orbits are specified arbitrarily. The qualitative properties of optimal two-impulse trajectories and their optimality in the class of multi-impulse transfers are studied.     

航天器再入制导方法综述

航天器再入制导方法国内外已有不少的学者进行了研究。本文对国内学者这方面的工作作一综述。目前国内研究的大多为有标准轨道的再入制导方法，且从最优原理出发对再入标准轨道进行了优化。对纵向再入制导规律也找出了最佳增益系数。侧向制导采用漏斗型开关曲线其效果良好。预测制导方法也开始了研究工作。     

Ground assisted rendezvous with geosynchronous satellites for the disposal of space debris by means of Earth-oriented tethers

Previous studies have shown that extended length Earth-oriented tethers in the geosynchronous (GEO) region can be used to re-orbit satellites to disposal orbits. One such approach involves the extension of a GEO based tether, collection of a debris object, and retraction of the tether, which transfers the retracted configuration to a higher energy orbit for debris disposal. The re-extension of the tether after debris disposal returns the configuration to the near-GEO altitude. The practical feasibility of such a system depends on the ability to collect GEO debris objects, attach them to a deployed tether system, and retract the tethers for transfer to the disposal orbits.This study addresses the collection and delivery of debris objects to the deployed tether system in GEO. The investigation considers the number, type and the characteristics of the debris objects as well as the collection tug that can be ground controlled to detect, rendezvous and dock with the debris objects for their delivery to the tethers system.A total of more than 400 objects are in drift orbits crossing all longitudes either below or above the geostationary radius. More than 130 objects are also known to librate around the stable points in GEO with periods of libration up to five or more years. A characterization of the position and velocity of the debris objects relative to the collection tug is investigated. Typical rendezvous performance requirements for uncooperative GEO satellites are examined, and the similarities with other approaches such as the ESA's CX-OLEV commercial mission proposal to extend the life of geostationary telecommunication satellites are noted.     

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.     

Calculation of quasisynchronous orbits of a spacecraft around Phobos for solving the problem of landing on its surface

The problem of selecting quasi-synchronous orbits of a spacecraft around Phobos is considered. These quasi-synchronous orbits are far (with respect to the Hill’s sphere) quasi-satellite orbits with retrograde rotation in the restricted three body problem. The orbit should pass through a given point at a specified time instant. It should also possess a property of minimum distance from the Phobos surface at every passage above the region of planned landing. The equations of dynamics are represented in the form describing the orbit as a combination of motions in two drifting ellipses, inner and outer ellipses. The center of the outer ellipse is located on the inner ellipse. A formula is derived that relates averaged values of half-axes of the inner and outer ellipses. It is used for construction of the first approximation of numerically designed orbit, which makes it possible to simplify and speed up the computing process. The tables of initial conditions obtained as a result of calculations are presented.     

Biobjective planning of an active debris removal mission

The growth of the orbital debris population has been a concern to the international space community for several years. Recent studies have shown that the debris environment in Low Earth Orbit (LEO, defined as the region up to 2000 km altitude) has reached a point where the debris population will continue to increase even if all future launches are suspended. As the orbits of these objects often overlap the trajectories of satellites, debris create a potential collision risk. However, several studies show that about 5 objects per year should be removed in order to keep the future LEO environment stable. In this article, we propose a biobjective time dependent traveling salesman problem (BiTDTSP) model for the problem of optimally removing debris and use a branch and bound approach to deal with it.     

Halo orbits in the vicinity of the L 2 libration point in the Sun-Earth system

Methods are proposed for constructing the orbits of spacecraft remaining for long periods of time in the vicinity of the L ₂ libration point in the Sun-Earth system (so-called halo orbits), and the trajectories of uncontrolled flights from low near-Earth orbits to halo orbits. Halo orbits and flight trajectories are constructed in two stages: A suitable solution to a circular restricted three-body problem is first constructed and then transformed into the solution for a restricted four-body problem in view of the real motions of the Sun, Earth, and Moon. For a halo orbit, its prototype in the first stage is a combination of a periodic Lyapunov solution in the vicinity of the L ₂ point and lying in the plane of large-body motion, with the solution for the linear second-order system describing small deviations of the spacecraft from this plane along the periodic solution. The desired orbit is found as the solution to the three-body problem best approximating the prototype in the mean square. The constructed orbit serves as a similar prototype in the second stage. In both stages, the approximating solution is constructed by continuation along a parameter that is the length of the approximation interval. Flight trajectories are constructed in a similar manner. The prototype orbit in the first stage is a combination of a solution lying in the plane of large-body motion and a solution for a linear second-order system describing small deviations of the spacecraft from this plane. The planar solution begins near the Earth and over time tends toward the Lyapunov solution existing in the vicinity of the L ₂ point. The initial conditions of both prototypes and the approximating solutions correspond to the spacecraft’s departure from a low near-Earth orbit at a given distance, perigee, and inclination.     

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.     

Space patrol: Variants of the optical barrier scheme

Different variants of the space patrol system to be designed for discovering and cataloging space objects hazardous for the Earth have been investigated. The basic idea of this system is to create an optical barrier using the telescopes deployed in a heliocentric orbit. Difficulties (as well as ways of overcoming them) of this program are analyzed, associated with form and position of the orbit of a space object relative to the patrol spacecraft, determination of orbit parameters, and mutual motion of space objects and the telescopes on spacecraft. The barrier’s schemes with scanning vertical or horizontal belts are considered. Some examples of observational conditions are presented for space objects crossing the barrier region: angular positions, velocities, distances, and numbers of days during which they are observed in the barrier region. The barrier’s characteristics are given for telescopes deployed in the orbits of the Earth and Venus.     

基于并行禁忌遗传算法(PTGA)的预警卫星传感器调度研究

对预警卫星的传感器调度进行了研究，提出了传感器管理调度的系统组成。通过对传感器调度的分析，建立起相应的数学模型，定义了评价指标。结合并行遗传算法和禁忌搜索的特点，提出了一种新的解决预警卫星传感器调度问题的并行禁忌遗传算法(PTGA)。该算法采用多种群和禁忌搜索思想改进遗传算法的性能，从而提高整个算法的收敛速度和精度。实验结果表明该算法有效地解决了多目标情况下的传感器实时调度问题，并优于一般启发式算法。