Distinguishing features of CCD astrometry of faint GEO objects

The problem of initial reduction of CCD observations of faint GEO objects is studied. Several difficulties and questions arising in connection with image processing for this kind of observations are mentioned. A natural way to apply the PSF fitting technique to line-shaped trails of stars or GEO objects is described and illustrated by its implementation in the Apex II astronomical image processing package. Logical filtering technique to improve the automatic object detection is proposed. These rather convenient and versatile methods can increase astrometric and, to a lesser degree, photometric accuracy of faint GEO object observations.     

Debris swarms seen by SMEI

The large 3° × 60° fields-of-view of the Solar Mass Ejection Imager (SMEI) instruments are oriented on the stabilized Coriolis satellite to image most of the sky each Sun-synchronous orbit. Besides observing coronal mass ejections, the SMEI mission objective, SMEI also has detected a plethora of Earth-orbiting satellites (resident space objects or RSOs) brighter than ∼8th magnitude at a rate of about 1 per minute. Occasionally, SMEI sees an RSO swarm: a sudden onset of a large number of RSOs, many more than the nominal rate, upto dozens detected in a 4-s frame. These swarms usually last for a few minutes. A sample of six such RSO ensembles is analyzed in this paper in which the distance and the direction of the velocity vector for individual objects are estimated. We present the observational evidence indicating that the swarms must be near-field objects traveling in orbits near that of Coriolis, and that the relatively speeds between the objects and Coriolis are low. Further, analyses indicate that the RSOs are quite close (<20 m) and are generally moving radially away from the satellite. The predicted encounter geometries for Coriolis passing through or near a small debris cloud is, generally, quite inconsistent with the observations. The most likely explanation consistent with the observations is that SMEI is seeing debris being ejected from the Coriolis spacecraft itself. An analysis of distance and brightness for a subset of the RSOs indicates that the median diameter of the debris particles is ∼80 μm.     

Improving orbit prediction accuracy through supervised machine learning

Due to the lack of information such as the space environment condition and resident space objects’ (RSOs’) body characteristics, current orbit predictions that are solely grounded on physics-based models may fail to achieve required accuracy for collision avoidance and have led to satellite collisions already. This paper presents a methodology to predict RSOs’ trajectories with higher accuracy than that of the current methods. Inspired by the machine learning (ML) theory through which the models are learned based on large amounts of observed data and the prediction is conducted without explicitly modeling space objects and space environment, the proposed ML approach integrates physics-based orbit prediction algorithms with a learning-based process that focuses on reducing the prediction errors. Using a simulation-based space catalog environment as the test bed, the paper demonstrates three types of generalization capability for the proposed ML approach: (1) the ML model can be used to improve the same RSO’s orbit information that is not available during the learning process but shares the same time interval as the training data; (2) the ML model can be used to improve predictions of the same RSO at future epochs; and (3) the ML model based on a RSO can be applied to other RSOs that share some common features.     

Local orbital debris flux study in the geostationary ring

A local orbital debris flux analysis is performed in the geostationary (GEO) ring to investigate how frequently near-miss events occur for each longitude slot in the GEO ring. The current resident space object (RSO) environment at GEO is evaluated, and publicly-available two-line element (TLE) data are utilized in tandem with a geostationary torus configuration to simulate near-miss events incurred by the trackable RSO population at GEO. Methodology for determining near-miss events with this formulation is introduced, and the results of the analysis for a one-year time frame are provided to illustrate the need for active GEO remediation.     

The adjusted optical properties for Galileo/BeiDou-2/QZS-1 satellites and initial results on BeiDou-3e and QZS-2 satellites

Solar Radiation Pressure (SRP) is the dominant non-gravitational perturbation for GNSS (Global Navigation Satellite System) satellites. In the absence of precise surface models, the Empirical CODE Orbit Models (ECOM, ECOM2) are widely used in GNSS satellite orbit determination. Based on previous studies, the use of an a priori box-wing model enhances the ECOM model, especially if the spacecraft is a stretched body satellite. However, so far not all the GNSS system providers have published their metadata. To ensure a precise use of the a priori box-wing model, we estimate the optical parameters of all the Galileo, BeiDou-2, and QZS-1 (Quasi Zenith Satellite System) satellites based on the physical processes from SRP to acceleration. Validation using orbit prediction proves that the adjusted parameters of Galileo and QZS-1 satellites exhibit almost the same performance as the corresponding published and “best guess” values. Whereas, the estimated parameters of BeiDou-2 satellites demonstrate an improvement of more than 60% over the initial “guess” values. The resulting optical parameters of all the satellites are introduced into an a priori box-wing model, which is jointly used with ECOM and ECOM2 model in the orbit determination. Results show that the pure ECOM2 model exhibits better performance than the pure ECOM model for Galileo, BeiDou-2 GEO and QZS-1 orbits. Combined with the a priori box-wing model the ECOM model (ECOM+BW) results in the best Galileo, BeiDou-2 GEO and QZS-1 orbits. The standard deviation (STD) of satellite laser ranging residuals reduce by about 20% and 5% with respect to the pure ECOM2 model for Galileo and BeiDou-2 GEO orbits, while the reductions are about 40% and 60% for QZS-1 orbits in yaw-steering and orbit-normal mode respectively. BeiDou-2 IGSO and MEO satellite orbits do not benefit much from the a priori box-wing model. In summary, we suggest setting up a unified SRP model of ECOM+BW for Galileo, QZS-1, and BeiDou-2 orbits based on the adjusted metadata. In addition, we estimate the optical parameters of BeiDou-3e and QZS-2 satellites using a limited number of tracking stations. Results regarding the unified SRP model indicate the same advantages, the STD of satellite laser ranging residuals reduces by about 30% and 20% for QZS-2 and BeiDou-3e orbits respectively over orbit products without a priori model. The estimation procedure is effective and easy to apply to the new emerging satellites in the future.     

Feasibility of performing space surveillance tasks with a proposed space-based optical architecture

Under ESA contract an industrial consortium including Aboa Space Research Oy (ASRO), the Astronomical Institute of the University of Bern (AIUB), and the Dutch National Aerospace Laboratory (NLR), proposed the observation concept, developed a suitable sensor architecture, and assessed the performance of a space-based optical (SBO) telescope in 2005. The goal of the SBO study was to analyse how the existing knowledge gap in the space debris population in the millimetre and centimetre regime may be closed by means of a passive optical instrument. The SBO instrument was requested to provide statistical information on the space debris population in terms of number of objects and size distribution. The SBO instrument was considered to be a cost-efficient with 20 cm aperture and 6° field-of-view and having flexible integration requirements. It should be possible to integrate the SBO instrument easily as a secondary payload on satellites launched into low-Earth orbits (LEO), or into geostationary orbit (GEO). Thus the selected mission concept only allowed for fix-mounted telescopes, and the pointing direction could be requested freely. Since 2007 ESA focuses space surveillance and tracking activities in the Space Situational Awareness (SSA) preparatory program. Ground-based radars and optical telescopes are studied for the build-up and maintenance of a catalogue of objects. In this paper we analyse how the proposed SBO architecture could contribute to the space surveillance tasks survey and tracking. We assume that the SBO instrumentation is placed into a circular sun-synchronous orbit at 800 km altitude. We discuss the observation conditions of objects at higher altitude, and select an orbit close to the terminator plane. A pointing of the sensor orthogonal to the orbital plane with optimal elevation slightly in positive direction (0° and +5°) is found optimal for accessing the entire GEO regime within one day, implying a very good coverage of controlled objects in GEO, too. Simulations using ESA’s Program for Radar and Optical Observation Forecasting (PROOF) in the version 2005 and a GEO reference population extracted from DISCOS revealed that the proposed pointing scenario provides low phase angles together with low angular velocities of the objects crossing the field-of-view. Radiometric simulations show that the optimal exposure time is 1–2 s, and that spherical objects in GEO with a diameter of below 1 m can be detected. The GEO population can be covered under proper illumination nearly completely, but seasonal drops of the coverage are possible. Subsequent observations of objects are on average at least every 1.5 days, not exceeding 3 days at maximum. A single observation arc spans 3° to 5° on average. Using a simulation environment that connects PROOF to AIUB’s program system CelMech we verify the consistency of the initial orbit determination for five selected test objects on subsequent days as a function of realistic astrometric noise levels. The initial orbit determination is possible. We define requirements for a correlator process essential for catalogue build-up and maintenance. Each single observation should provide an astrometric accuracy of at least 1”–1.5” so that the initially determined orbits are consistent within a few hundred kilometres for the semi-major axis, 0.01 for the eccentricity, and 0.1° for the inclination.     

Apparent rotation properties of space debris extracted from photometric measurements

Knowledge about the rotation properties of space debris objects is essential for the active debris removal missions, accurate re-entry predictions and to investigate the long-term effects of the space environment on the attitude motion change. Different orbital regions and object’s physical properties lead to different attitude states and their change over time.Since 2007 the Astronomical Institute of the University of Bern (AIUB) performs photometric measurements of space debris objects. To June 2016 almost 2000 light curves of more than 400 individual objects have been acquired and processed. These objects are situated in all orbital regions, from low Earth orbit (LEO), via global navigation systems orbits and high eccentricity orbit (HEO), to geosynchronous Earth orbit (GEO). All types of objects were observed including the non-functional spacecraft, rocket bodies, fragmentation debris and uncorrelated objects discovered during dedicated surveys. For data acquisition, we used the 1-meter Zimmerwald Laser and Astrometry Telescope (ZIMLAT) at the Swiss Optical Ground Station and Geodynamics Observatory Zimmerwald, Switzerland. We applied our own method of phase-diagram reconstruction to extract the apparent rotation period from the light curve. Presented is the AIUB’s light curve database and the obtained rotation properties of space debris as a function of object type and orbit.     

FocusGEO望远镜观测地球同步轨道目标的光度特性分类

基于FocusGEO望远镜2017年12月至2019年6月的测光观测数据,开展台站上空地球同步轨道(GEO)目标光度曲线的分类研究.通过对GEO卫星光度曲线特征的统计分析,建立了一种全新的GEO卫星分类系统,确定了各类GEO卫星光度曲线的占比,分析了光度特征类别与卫星平台的相关性.本研究将197颗GEO卫星的光度曲线分...     

Ariane 5 GTO debris mitigation using natural perturbations

GTO objects can potentially collide with operative satellites in LEO and GEO protected regions. Internationally accepted debris mitigation guidelines require that these objects exit these protected regions within 25?years, e.g. by re-entering and burning up in Earth’s atmosphere. In this paper, an inventory of the GTO debris generated from Ariane 5 launches in the period 2012–2017 is provided, and it is expected that none of these objects will re-enter within 25?years. For future launches, natural perturbations can be exploited to increase compliance with mitigation guidelines without the use of extra propellant or complex de-orbiting systems, which is attractive from an economic point of view. The lifetime of GTO objects is very sensitive to initial conditions and some environmental and body-related parameters, mainly due to the effect of solar gravity on the perigee altitude. As a consequence, the lifetime of a specific GTO object cannot be predicted accurately, but its probability of re-entering in less than 25?years can be estimated with proper accuracy by following a statistical approach. By propagating the orbits of over 800,000 simulated Ariane 5 GTO objects, it was found that the launch time leading to the highest probability of compliance with debris mitigation guidelines for GEO launches from Kourou corresponds to about 2 PM local time, regardless of the date of launch, which leads to compliance rates ranging from 60 to 100%. Current practice is to launch at around 5–9?PM, so a change in procedures would be required in order to reach a higher degree of compliance with debris mitigation guidelines, which was predicted to be on average below 20% for the objects generated in the period 2012–2017.     

Space debris observations with the Slovak AGO70 telescope: Astrometry and light curves

The Faculty of Mathematics, Physics and Informatics of Comenius University in Bratislava, Slovakia (FMPI) operates its own 0.7-m Newtonian telescope (AGO70) dedicated to the space surveillance tracking and research, with an emphasis on space debris. The observation planning focuses on objects on geosynchronous (GEO), eccentric (GTO and Molniya) and global navigation satellite system (GNSS) orbits. To verify the system’s capabilities, we conducted an observation campaign in 2017, 2018 and 2019 focused on astrometric and photometric measurements. In last two years we have built up a light curve catalogue of space debris which is now freely available for the scientific community. We report periodic signals extracted from more than 285 light curves of 226 individual objects. We constructed phase diagrams for 153 light curves for which we obtained apparent amplitudes.     

Performance of GPS-based accelerometry: A simulation experiment

Recent studies have shown that with the availability of high-quality CHAMP and GRACE gravity field models, it is feasible to determine accurate non-gravitational accelerations for low Earth orbiting satellites indirectly from precise GPS satellite-to-satellite observations. Possible applications of this so-called GPS-based accelerometry approach consist of accelerometer calibration and atmospheric density and wind computations. With the growing number of high-quality space-borne GPS receivers, this method could be applied to a large range of satellites. In this paper an extensive simulation study has been carried out, based on real accelerometer data from the GRACE mission, in order to determine the optimal processing strategy and the resulting accuracy of the estimated non-gravitational accelerations. It is shown that the optimal processing strategy consists of a piecewise linear parameterization of the estimated empirical accelerations, together with short 6-h orbit arcs. The GPS-based accelerometry approach makes use of triple-differenced GPS observations and the impact of considering the correlated observation noise was found to be marginal in the presence of other error sources such as GPS ephemeris errors. Using a priori non-gravitational force models improves the recovery of low temporal resolution accelerations, except during huge geomagnetic storms. With this strategy, non-gravitational accelerations can be recovered during high solar activity with an accuracy of better than 10% of the total signal in along-track direction and around 25–40% in cross-track direction, at time resolutions of around 8–20 min. During solar minimum conditions, the relative recovery error will increase to approximately 50% in along-track direction and around 60–70% in cross-track direction, due to the reduced atmospheric drag signal. Unfortunately, GPS-based accelerometry is hardly sensitive in the radial direction.     

Dynamical cartography of Earth satellite orbits

We have carried out a numerical investigation of the coupled gravitational and non-gravitational perturbations acting on Earth satellite orbits in an extensive grid, covering the whole circumterrestrial space, using an appropriately modified version of the SWIFT symplectic integrator, which is suitable for long-term ($～$120?years) integrations of the non-averaged equations of motion. Hence, we characterize the long-term dynamics and the phase-space structure of the Earth-orbiter environment, starting from low altitudes ($～$400?km) and going up to the GEO region and beyond. This investigation was done in the framework of the EC-funded “ReDSHIFT” project, with the purpose of enabling the definition of passive debris removal strategies, based on the use of physical mechanisms inherent in the complex dynamics of the problem (i.e., resonances). Accordingly, the complicated interactions among resonances, generated by different perturbing forces (i.e., lunisolar gravity, solar radiation pressure, tesseral harmonics in the geopotential) are accurately depicted in our results, where we can identify the regions of phase space where the motion is regular and long-term stable and regions for which eccentricity growth and even instability due to chaotic behavior can emerge. The results are presented in an “atlas” of dynamical stability maps for different orbital zones, with a particular focus on the (drag-free) range of semimajor axes, where the perturbing effects of the Earth’s oblateness and lunisolar gravity are of comparable order. In some regions, the overlapping of the predominant lunisolar secular and semi-secular resonances furnish a number of interesting disposal hatches at moderate to low eccentricity orbits. All computations were repeated for an increased area-to-mass ratio, simulating the case of a satellite equipped with an on-board, area-augmenting device. We find that this would generally promote the deorbiting process, particularly at the transition region between LEO and MEO. Although direct reentry from very low eccentricities is very unlikely in most cases of interest, we find that a modest “delta-v” ($\mathrm{\Delta }V$) budget would be enough for satellites to be steered into a relatively short-lived resonance and achieve reentry into the Earth’s atmosphere within reasonable timescales ($～$50?years).     

Spacecraft formation and orbit control using differential attitude-dependent solar radiation pressure

This paper introduces a linear model for spacecraft formation dynamics subject to attitude-dependent solar radiation pressure (SRP) disturbance, with the SRP model accounting for both absorption and specular/diffuse reflection. Spacecraft attitude is represented in modified Rodriguez parameters (MRPs), which also parameterize the orientation of individual facets for a spacecraft with fixed geometry. Compared to earlier work, this model incorporates analytic approximation of the SRP-perturbed chief orbit behavior in a manner enabling its use in applications with infrequent guidance updates. Control examples are shown for single-plate representations of hypothetical spacecraft with generally realistic optical parameters. The results demonstrate the validity of the model and the feasibility of SRP-based formation and rendezvous control in orbits around small bodies and in high orbits around the Earth such as the GEO belt.     

DebrisWatch I: A survey of faint geosynchronous debris

Recent anomalies exhibited by satellites and rocket bodies have highlighted that a population of faint debris exists at geosynchronous (GEO) altitudes, where there are no natural removal mechanisms. Despite previous optical surveys probing to around 10–20 cm in size, regular monitoring of faint sources at GEO is challenging, thus our knowledge remains sparse. It is essential that we continue to explore the faint debris population using large telescopes to better understand the risk posed to active GEO satellites. To this end, we present photometric results from a survey of the GEO region carried out with the 2.54 m Isaac Newton Telescope in La Palma, Canary Islands. We probe to 21st visual magnitude (around 10 cm, assuming Lambertian spheres with an albedo of 0.1), uncovering 129 orbital tracks with GEO-like motion across the eight nights of dark-grey time comprising the survey. The faint end of our brightness distribution continues to rise until the sensitivity limit of the sensor is reached, suggesting that the modal brightness could be even fainter. We uncover a number of faint, uncatalogued objects that show photometric signatures of rapid tumbling, many of which straddle the limiting magnitude of our survey over the course of a single exposure, posing a complex issue when estimating object size. This work presents the first instalment of DebrisWatch, an ongoing collaboration between the University of Warwick and the Defence Science and Technology Laboratory (UK) investigating the faint population of GEO debris.     

A universal on-orbit servicing system used in the geostationary orbit

The geostationary orbit (GEO), a unique satellite orbit of the human beings, is a very precious orbit resource. However, the continuous increasing of GEO debris makes the GEO orbit more and more crowded. Moreover, the failures of GEO spacecrafts will result in large economic cost and other bad impacts. In this paper, we proposed a space robotic servicing system, and developed key pose (position and orientation) measurement and control algorithm. Firstly, the necessity of orbit service in GEO was analyzed. Then, a servicing concept for GEO non-cooperative targets was presented and a universal space robotic servicing system was designed. The system has a 2-DOF docking mechanism, a 7-DOF redundant manipulator and a set of stereo vision, in addition to the traditional subsystems of a spacecraft. This system can serve most existing satellites in GEO, not requiring specially designed objects for grappling and measuring on the target. The servicing contents include: (a) visual inspecting; (b) target tracking, approaching and docking; (c) ORUs (Orbital Replacement Units) replacement; (d) Malfunctioned mechanism deploying; (e) satellites life extension by taking over its control, or re-orbiting the abandoned satellites. As an example, the servicing mission of a malfunctioned GEO satellite with three severe mechanical failures was designed and simulated. The results showed the validity and flexibility of the proposed system.     

Bayesian linking of geosynchronous orbital debris tracks as seen by the Large Synoptic Survey Telescope

We describe a Bayesian sampling model for linking and constraining orbit models from angular observations of “streaks” in optical telescope images. Our algorithm is particularly suited to situations where the observation times are small fractions of the orbital periods of the observed objects or when there is significant confusion of objects in the observation field. We use Markov Chain Monte Carlo to sample from the joint posterior distribution of the parameters of multiple orbit models (up to the number of observed tracks) and parameters describing which tracks are linked with which orbit models. Using this algorithm, we forecast the constraints on geosynchronous (GEO) debris orbits achievable with the planned Large Synoptic Survey Telescope (LSST). Because of the short 15 s exposure times, preliminary orbit determinations of GEO objects from LSST will have large and degenerate errors on the orbital elements. Combined with the expected crowded fields of GEO debris it will be challenging to reliably link orbital tracks in LSST observations given the currently planned observing cadence.     

空间碎片环境近况

根据国际上近年来对空间碎片跟踪、观测、统计分析以及对从轨道上回收的试验装置和样品的分析研究,介绍了地球周围空间环境中存在的空间碎片的数量、质量及其分布的最新状况。     

Track detection of high-velocity resident space objects in Low Earth Orbit

The world’s economy has become heavily dependent on the services provided by satellites. With the exponential increase in satellite launches, the population of defunct or inactive hardware in space has grown substantially. This is especially true in sensitive orbits such as the Low Earth Orbit (LEO) and Geostationary Earth Orbit (GEO) regimes. These objects, collectively known as orbital debris, can reach speeds of up to 28 000km h^?1 in LEO. At these orbital speeds, even the smallest of objects can pose a considerable threat to operational satellites or astronauts. This makes the monitoring, and detection, of these objects of the utmost importance. This work describes the latest detection strategy used in one of Europe’s largest Space Situational Awareness (SSA) installation; the BIstatic RAdar for LEo Survey (BIRALES) space debris radar. We present a novel bottom-up approach that makes use of single-linkage clustering to identify faint radar streaks in spectrogram data. Tests on synthetic data have shown that the detection strategy presented in this study obtains a higher detection rate when it is compared against existing methods. Unlike other approaches, this detection strategy, using the Multi-beam streak detection strategy (MSDS) algorithm, was still able to recall 90% of the track information at an Signal-to-Noise Ratio (SNR) of 2dB.     

Horizontal and vertical thermospheric cross-wind from GOCE linear and angular accelerations

Thermospheric wind measurements obtained from linear non-gravitational accelerations of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite show discrepancies when compared to ground-based measurements. In this paper the cross-wind is derived from both the linear and the angular accelerations using a newly developed iterative algorithm. The two resulting data sets are compared to test the validity of wind derived from angular accelerations and quantify the uncertainty in accelerometer-derived wind data. In general the difference is found to be less than 50?m/s vertically after high-pass filtering, and 100?m/s horizontally. A sensitivity analysis reveals that continuous thrusting is a major source of uncertainty in the torque-derived wind, as are the magnetic properties of the satellite. The energy accommodation coefficient is identified as a particularly promising parameter for improving the consistency of thermospheric cross-wind data sets in the future. The algorithm may be applied to obtain density and cross-wind from other satellite missions that lack accelerometer data, provided the attitude and orbit are known with sufficient accuracy.