Spectral response of Experimental Geodetic Satellite determined from high repetition rate SLR data

The design of the retroreflector array (RRA) of the fast spinning Experimental Geodetic Satellite (Ajisai) allows to determine orientation of its spin axis by means of frequency analysis. Moving spectral analysis (MSA) of the simulated Satellite Laser Ranging (SLR) data gives information about frequencies which can be obtained for the whole range of the incident angle between the laser beam vector and the spin axis of the spacecraft. This frequency signal changes as the incident laser beam crosses consecutive rings of the RRA.     

Spectral filter for signal identification in the kHz SLR measurements of the fast spinning satellite Ajisai

The high repetition rate satellite laser ranging (SLR) measurements to the fast spinning satellites contain a frequency signal caused by the rotational motion of the corner cube reflector (CCR) array. The spectral filter, developed here, is based on the Lomb algorithm, and is tested with the simulated and the observed high repetition rate SLR data of the geodetic satellite Ajisai (spin period ∼2 s). The filter allows for the noise elimination from the SLR data, and for identification of the returns from the single CCRs of the array – even for the low return rates. Applying the spectral filter to the simulated SLR data increases the S/N ratio by a factor 40–45% for all return rates. Filtering out the noise from the observed data strengthens the frequency signal by factor of ∼25 for the low return rates, which significantly helps to determine the spin phase of the satellite. The spectral filter is applied to the Graz SLR data and the spin rates of Ajisai are determined by two different methods: the frequency analysis and the phase determination of the spinning retroreflector array.The analysis of more than 8 years of the Graz SLR measurements indicates an exponential spin rate trend: f = 0.67034 exp(−0.0148542 Y) [Hz], RMS = 0.085 mHz, where Y is the year since launch. The highly accurate spin rate information demonstrates periodic changes related to the precession of the orbital plane of Ajisai, as it determines the amount of energy received by the satellite from the Sun. The rate of deceleration of Ajisai is not constant: the half life period of the satellite’s spin oscillates around 46.7 years with an amplitude of about 5 years.     

22 Years of AJISAI spin period determination from standard SLR and kHz SLR data

Satellite Laser Ranging (SLR) is a powerful and efficient technique to measure spin parameters of satellites equipped with corner cube reflectors. We obtained spin period determination of the satellite AJISAI from SLR data only: 17246 pass-by-pass estimates from standard 1–15 Hz SLR data (14/Aug/1986–30/Dec/2008) and 1444 pass-by-pass estimates (9/Oct/2003–30/Dec/2008) from data of the first 2 kHz SLR system from Graz, Austria. A continuous history of the slowing down of AJISAI spin is derived from frequency analysis, and corrected for the apparent effects. The apparent corrections, elaborated here, allowed very accurate determination of AJISAI initial spin period: 1.4855 ± 0.0007 [s]. The paper identifies also non-gravitational effects as a source of the periodical changes in the rate of slowing down of the satellite.     

10 Years of LAGEOS-1 and 15 years of LAGEOS-2 spin period determination from SLR data

Satellite Laser Ranging (SLR) stations measure distance to the satellites equipped with Corner Cube Reflectors (CCRs). These range measurements contain information about spin parameters of the spacecraft. In this paper we present results of spin period determination of two passive satellites from SLR data only: 10 years of LAGEOS-1 (10426 values), and 15 years of LAGEOS-2 (15580 values). The measurements have been made by standard 10 Hz SLR systems and the first 2 kHz SLR system from Graz (Austria). The obtained data allowed calculation of the initial spin period of the satellites: 0.61 s for LAGEOS-1 and 0.906 s for LAGEOS-2. Long time series of the spin period values show that the satellite’s slowing down rate is not constant but is oscillating with a period of 846 days for LAGEOS-1 and 578 days for LAGEOS-2. The results presented here definitely prove that the SLR is a very efficient technique able to measure spin period of the geodetic satellites.     

Simulation of long-term rotational dynamics of large space debris: A TOPEX/Poseidon case study

Accurate knowledge of the rotational dynamics of a large space debris is crucial for space situational awareness (SSA), whether it be for accurate orbital predictions needed for satellite conjunction analyses or for the success of an eventual active debris removal mission charged with stabilization, capture and removal of debris from orbit. In this light, the attitude dynamics of an inoperative satellite of great interest to the space debris community, the joint French and American spacecraft TOPEX/Poseidon, is explored. A comparison of simulation results with observations obtained from high-frequency satellite range measurements is made, showing that the spacecraft is currently spinning about its minor principal axis in a stable manner. Predictions of the evolution of its attitude motion to 2030 are presented, emphasizing the uncertainty on those estimates due to internal energy dissipation, which could cause a change of its spin state in the future. The effect of solar radiation pressure and the eddy-current torque are investigated in detail, and insights into some of the satellite’s missing properties are provided. These results are obtained using a novel, open-source, coupled orbit-attitude propagation software, the Debris SPin/Orbit Simulation Environment (D-SPOSE), whose primary goal is the study of the long-term evolution of the attitude dynamics of large space debris.     

Spin parameters of nanosatellite BLITS determined from Graz 2 kHz SLR data

The nanosatellite BLITS (Ball Lens In The Space) is the first object designed as a passive, spherical retroreflector of the Luneburg type, dedicated for Satellite Laser Ranging (SLR). The 2 kHz SLR station Graz measures spin parameters of this satellite, providing information about the rotational dynamics of the body. The measurements obtained during the period from September 26, 2009 to November 24, 2010 show a significant change of the spin configuration. The spin axis was dynamically precessing since the launch and currently is sinus-like behaving between coordinates RA 120°…150°, Dec 30°…60° (J2000 inertial reference frame). The angle between the symmetry axis and the spin axis of BLITS is not constant, but is decreasing since the launch, while its spin period is rather stable with a mean value of 5.613 s (clockwise rotation). The satellite was dynamically changing its attitude during the first three months after deployment; after this time the spin parameters are relatively stable.     

重力梯度力矩作用下近地卫星自旋运动规律分析

为研究近地卫星自旋运动规律,建立了近地卫星在受摄动影响的轨道上运行并受重力梯度力矩作用下的姿态运动模型,推导了自旋角速率满足一定条件下自旋运动的进动角、章动角、自旋角的解析解,对重力梯度作用下的自旋姿态运动规律进行了仿真分析,并用仿真计算结果验证了解析解的正确性。在轨道面缓慢进动情况下,当卫星绕最大主惯量轴自旋时,给出了自旋角速率取值范围表达式,在该取值范围内卫星自旋运动能够跟随轨道面一起进动,自旋轴以恒定的平均角速率进动,章动角在小范围内波动。建立的自旋姿态运动模型和分析结论可用于近地卫星姿态失控后的姿态确定和预测、在轨姿态设计及在轨备份等。     

Optical response of nanosatellite BLITS measured by the Graz 2 kHz SLR system

The nanosatellite BLITS (Ball Lens In The Space) is the first object designed as a passive, spherical retroreflector of the Luneburg type, dedicated for Satellite Laser Ranging (SLR). The optical response of BLITS has been measured by the Graz 2 kHz SLR station and compared with the response of the classical retroreflector arrays (RRA) of the Low Earth Orbiting satellites such as ERS-2 and Stella. This work demonstrates that the optical response of BLITS is flat and featureless, comparable with the signature of a point-source or a flat target, and suggests that this innovative design will deliver a higher normal point (NP) accuracy (2.55 mm) than any other SLR target currently in orbit. The high reflectivity of the glassy BLITS (about 60% of the return rate from the multi-reflector Stella) is found to be decreasing by about 30% per year, probably due to the solar irradiation. Detailed analysis of the reflective half-shell demonstrates that a high return rate of SLR measurements can be achieved regardless of the incident angle of the laser beam, thus making the spherical lens a perfect successor of the classical RRA panels mounted on active satellites such as CHAMP, GOCE and GRACE.     

航天器应急姿态捕获中GPS信号的应用

星载全球定位系统（GPS）卫星接收机在测量接收各GPS卫星信号时,可同时得到接收信号的信号强度测量辅助数据E。理论分析表明,接收信号的强度E与信号入射天线的法向夹角α强相关。如建立E与α稳定的先验模型,E就可以作为测量值,计算入射天线的角度α。在同一时刻,通过三个以上GPS卫星信号入射天线的角度α,可计算星载GPS卫星接收机接收天线的空间姿态。确定姿态的精度取决于E与α相关先验模型的稳定性。利用CHAMP卫星星载接收机在轨实测数据检验,估算的初始姿态精度为2°~3°。该方法可作为航天器故障状态下应急姿态捕获的一种辅助手段,也可为携带星载GPS而无高精度定姿要求的简易航天器提供一种新的无附加成本的定姿途径。     

论绳系卫星系统的运动中心

讨论了稳定状态下绳系系统运动中心及相关的力学与应用问题。绳系系统运动中心与系统质心不重合。确定了运动中心在系绳上的位置,并从运动中心概念出发,导出系绳拉力的表示式,阐述了系绳拉力偏差对摆动频率计算的影响。     

Attitude analysis of space debris using SLR and light curve data measured with single-photon detector

Attitude is the important parameter for active debris removal and collision avoidance. This paper deduced the spin axis orientation and spin period of the rocket body, CZ-3B R/B (NORAD ID 38253), using the satellite laser ranging and light curve data measured with single-photon detector at Graz station. The epoch method and LC & SLR residuals fitting were combined to determine these values. The derived right ascension angle was around 220°, the declination angle was near 64° and the sidereal period was calculated to be 117.724 s, for 2017-07-03. The results derived from the two distinct methods were mutually validated. Rocket bodies are a major contributor to space debris and this work provides a reference for attitude determination and attitude modelling.     

A deorbiter CubeSat for active orbital debris removal

This paper introduces a mission concept for active removal of orbital debris based on the utilization of the CubeSat form factor. The CubeSat is deployed from a carrier spacecraft, known as a mothership, and is equipped with orbital and attitude control actuators to attach to the target debris, stabilize its attitude, and subsequently move the debris to a lower orbit where atmospheric drag is high enough for the bodies to burn up. The mass and orbit altitude of debris objects that are within the realms of the CubeSat’s propulsion capabilities are identified. The attitude control schemes for the detumbling and deorbiting phases of the mission are specified. The objective of the deorbiting maneuver is to decrease the semi-major axis of the debris orbit, at the fastest rate, from its initial value to a final value of about 6471?km (i.e., 100?km above Earth considering a circular orbit) via a continuous low-thrust orbital transfer. Two case studies are investigated to verify the performance of the deorbiter CubeSat during the detumbling and deorbiting phases of the mission. The baseline target debris used in the study are the decommissioned KOMPSAT-1 satellite and the Pegasus rocket body. The results show that the deorbiting times for the target debris are reduced significantly, from several decades to one or two years.     

Spin rate and spin axis orientation of LARES spectrally determined from Satellite Laser Ranging data

Satellite Laser Ranging (SLR) is a powerful technique able to measure spin rate and spin axis orientation of the fully passive, geodetic satellites. This work presents results of the spin determination of LARES – a new satellite for testing General Relativity. 529 SLR passes measured between February 17 and June 9, 2012, were spectrally analyzed. Our results indicate that the initial spin frequency of LARES is f₀ = 86.906 mHz (RMS = 0.539 mHz). A new method for spin axis determination, developed for this analysis, gives orientation of the axis at RA = 12^h22^m48^s (RMS = 49^m), Dec = −70.4° (RMS = 5.2°) (J2000.0 celestial reference frame), and the clockwise (CW) spin direction. The half-life period of the satellite’s spin is 214.924 days and indicates fast slowing down of the spacecraft.     

Attitude stability and periodic attitudes of rigid spacecrafts on the stationary orbits around asteroid 216 Kleopatra

In this work, equilibrium attitude configurations, attitude stability and periodic attitude families are investigated for rigid spacecrafts moving on stationary orbits around asteroid 216 Kleopatra. The polyhedral approach is adopted to formulate the equations of rotational motion. In this dynamical model, six equilibrium attitude configurations with non-zero Euler angles are identified for a spacecraft moving on each stationary orbit. Then the linearized equations of attitude motion at equilibrium attitudes are derived. Based on the linear system, the necessary conditions of stability of equilibrium attitudes are provided, and stability domains on the spacecraft’s characteristic plane are obtained. It is found that the stability domains are distributed in the first and third quadrants of the characteristic plane and the stability domain in the third quadrant is separated into two regions by an unstable belt. Subsequently, we present the linear solution around a stable equilibrium attitude point, indicating that there are three types of elemental periodic attitudes. By means of numerical approaches, three fundamental families of periodic solutions are determined in the full attitude model.     

基于视觉技术的非合作航天器相对位姿测量方法

提出一种基于特征信息融合的非合作目标相对位姿测量方法,该方法以航天器自有的特征信息作为识别目标,采用椭圆轮廓和特征角点相结合的方法对非合作目标特征进行识别,解决了位姿测量中无合作标志器提供理想特征信息的问题。针对典型的卫星目标模型,进行了非合作目标相对位置姿态测量方法的验证试验,实验结果表明:该方法可以成功识别目标物体并对目标物体进行准确定位。     

In-orbit assessment of laser retro-reflector efficiency onboard high orbiting satellites

The navigation and geodetic satellites that orbit the Earth at altitudes of approximately 20,000 km are tracked routinely by many of the Satellite Laser Ranging (SLR) stations of the International Laser Ranging Service (ILRS). In order to meet increasing demands on SLR stations for daytime and nighttime observations, any new mission needs to ensure a strong return signal so that the target is easily acquirable. The ILRS has therefore set a minimum effective cross-section of 100 million square metres for the on-board laser retro-reflector arrays (LRAs) and further recommends the use of ‘uncoated’ cubes in the arrays. Given the large number of GNSS satellites that are currently supported by SLR, it is informative to make an assessment of the relative efficiencies of the various LRAs employed. This paper uses the laser ranging observations themselves to deduce and then compare the efficiencies of the LRAs on the COMPASS-M1 navigation satellite, two satellites from the GPS and three from the GLONASS constellations, the two GIOVE test satellites from the upcoming Galileo constellation, the two Etalon geodetic spheres and the geosynchronous communications test satellite, ETS-8. All the LRAs on this set of satellites employ back-coated retro-reflector cubes, except those on the COMPASS-M1 and ETS-8 vehicles which are uncoated. A measure of return signal strength, and thus of LRA-efficiency, is calculated using the laser-range full-rate data archive from 2007 to 2010, scaled to remove the effects of variations in satellite range, atmospheric attenuation and retro-reflector target total surface area. Observations from five SLR stations are used in this study; they are Herstmonceux (UK), Yarragadee (Australia), Monument Peak and McDonald (USA) and Wettzell (Germany). Careful consideration is given to the treatment of the observations from each station in order to take account of local working practices and system upgrades. The results show that the uncoated retro-reflector cubes offer significant improvements in efficiency.     

飞船舱段应急分离过程的动力学分析和计算

在上升段大气层外当出现紧急情况时航天飞船的逃逸及随后的舱段应急分离过程是复杂的多个舱段的相对运动过程。针对这个过程,建立了舱段的相对轨迹运动和相对姿态运动的数学模型,包括动力学方程、运动学方程和几何关系方程,定义了对象组合体,强调了主体和客体的关系;并且按工程实际情况划分了飞行阶段。在数学模型以及对象定义和阶段划分的基础上建立了一个大规模的软件来进行全面的分析和仿真,并给出了典型工况下的结果示例。     

Stability of relative equilibria of the full spacecraft dynamics around an asteroid with orbit–attitude coupling

The full dynamics of spacecraft around an asteroid, in which the spacecraft is considered as a rigid body and the gravitational orbit–attitude coupling is taken into account, is of great value and interest in the precise theories of the motion. The spectral stability of the classical relative equilibria of the full spacecraft dynamics around an asteroid is studied with the method of geometric mechanics. The stability conditions are given explicitly based on the characteristic equation of the linear system matrix. It is found that the linearized system decouples into two entirely independent subsystems, which correspond to the motions within and outside the equatorial plane of the asteroid respectively. The system parameters are divided into three groups that describe the traditional stationary orbit stability, the significance of the orbit–attitude coupling and the mass distribution of the spacecraft respectively. The spectral stability of the relative equilibria is investigated numerically with respect to the three groups of system parameters. The relations between the full spacecraft dynamics and the traditional spacecraft dynamics, as well as the effect of the orbit–attitude coupling, are assessed. We find that when the orbit–attitude coupling is strong, the mass distribution of the spacecraft dominates the stability of the relative equilibria; whereas when the orbit–attitude coupling is weak, both the mass distribution and the traditional stationary orbit stability have significant effects on the stability. We also give a criterion to determine whether the orbit–attitude coupling needs to be considered.     

近距离星间相对姿轨耦合动力学建模与控制

针对在轨服务过程中近距离星间相对位置以及相对姿态精确控制的问题,考虑相对姿态与相对轨道之间的耦合作用,建立星间相对姿轨耦合动力学模型.提出编队星相对基准星进行接近绕飞的任务需求,给出相对姿态以及相对轨道的期望状态.设计相对姿态轨道联合控制算法对相对姿态和轨道进行联合控制.仿真结果表明,所设计的控制算法能够很好地抑制相对姿态与相对轨道的相互影响作用,最终实现编队星对基准星的精确指向绕飞运动.