First laser measurements to space debris in Poland

The Borowiec Satellite Laser Ranging station (BORL 7811, Borowiec) being a part of the Space Research Centre of the Polish Academy of Sciences (SRC PAS) went through modernization in 2014–2015. One of the main tasks of the modernization was the installation of a high-energy laser module dedicated to space debris tracking. Surelite III by Continuum is a Nd:YAG pulse laser with 10?Hz repetition rate, a pulse width of 3–5?ns and a pulse energy of 450?mJ for green (532?nm). This new laser unit was integrated with the SLR system at Borowiec performing standard satellite tracking. In 2016 BORL 7811 participated actively to the observational campaigns related to the space debris targets from LEO region managed by the Space Debris Study Group (SDSG) of the International Laser Ranging Service (ILRS).Currently, Borowiec station regularly tracks 36 space debris from the LEO regime, including typical rocket bodies (Russian/Chinese) and cooperative targets like the inactive TOPEX/Poseidon, ENVISAT, OICETS and others. In this paper the first results of space debris laser measurements obtained by the Borowiec station in period August 2016 – January 2017 are presented. The results gained by the SRC PAS Borowiec station confirm the rotation of the defunct TOPEX/Poseidon satellite which spins with a period of approximately 10?s. The novelty of this work is the presentation of the sample results of the Chinese CZ-2C R/B target (NORAD catalogue number 31114) which is equipped (probably) with retroreflectors. Laser measurements to space debris is a very desirable topic for the next years, especially in the context of the Space Surveillance and Tracking (SST) activity. Some targets are very easy to track like defunct ENVISAT or TOPEX/Poseidon. On the other hand, there is a big population of different LEO targets with different orbital and physical parameters, which are challenging for laser ranging like small irregular debris and rocket boosters.     

Photon counting detector for space debris laser tracking and lunar laser ranging

We are reporting on a design, construction and performance of solid state photon counting detector package which has been designed for laser tracking of space debris. The detector has been optimized for top photon detection efficiency and detection delay stability. The active area of the commercially available avalanche photodiode manufactured on Si (SAP500 supplied by Laser Components, Inc.) is circular with a diameter of 500 μm. The newly designed control circuit enables to operate the detection sensor at a broad range of biases 5–50 V above its breakdown voltage of 125 V. This permits to select a right trade-off between photon detection efficiency, timing resolution and dark count rate. The photon detection efficiency exceeds 70% at the wavelength of 532 nm. This is the highest photon detection efficiency ever reported for such a device. The timing properties of the detector have been investigated in detail. The timing resolution is better than 80 ps r.m.s, the detection delay is stable within units of picoseconds over several hours of operation. The detection delay stability in a sense of time deviation of 800 fs has been achieved. The temperature change of the detection delay is 0.5 ps/K. The detector has been tested as an echo signal detector in laser tracking of space debris at the satellite laser station in Graz, Austria. Its application in lunar laser ranging is under consideration by several laser stations.     

LISA: Heliocentric formation design for the laser interferometer space antenna mission

The LISA (Laser Interferometer Space Antenna) mission has been selected by the European Space Agency’s Science Programme Committee as the third large-class mission of the Cosmic Vision Programme, addressing the science theme of the Gravitational Universe. With a planned launch date in 2034, LISA will be the first ever space-borne Gravitational Wave observatory, relying on laser interferometry between three spacecraft orbiting the Sun in a triangular formation. Airbus is currently leading an industrial Phase A system study on behalf of the European Space Agency. The paper will address the astrodynamics challenges associated with the LISA constellation design, driven by tight requirements on the geometric quality metrics of the near equilateral formation.     

Removing orbital debris with lasers

Orbital debris in low Earth orbit (LEO) are now sufficiently dense that the use of LEO space is threatened by runaway collision cascading. A problem predicted more than thirty years ago, the threat from debris larger than about 1 cm demands serious attention. A promising proposed solution uses a high power pulsed laser system on the Earth to make plasma jets on the objects, slowing them slightly, and causing them to re-enter and burn up in the atmosphere. In this paper, we reassess this approach in light of recent advances in low-cost, light-weight modular design for large mirrors, calculations of laser-induced orbit changes and in design of repetitive, multi-kilojoules lasers, that build on inertial fusion research. These advances now suggest that laser orbital debris removal (LODR) is the most cost-effective way to mitigate the debris problem. No other solutions have been proposed that address the whole problem of large and small debris. A LODR system will have multiple uses beyond debris removal. International cooperation will be essential for building and operating such a system.     

Laser measurements to space debris from Graz SLR station

In order to test laser ranging possibilities to space debris objects, the Satellite Laser Ranging (SLR) Station Graz installed a frequency doubled Nd:YAG pulse laser with a 1 kHz repetition rate, a pulse width of 10 ns, and a pulse energy of 25 mJ at 532 nm (on loan from German Aerospace Center Stuttgart – DLR). We developed and built low-noise single-photon detection units to enable laser ranging to targets with inaccurate orbit predictions, and adapted our standard SLR software to include a few hundred space debris targets. With this configuration, we successfully tracked – within 13 early-evening sessions of each about 1.5 h – 85 passes of 43 different space debris targets, in distances between 600 km and up to more than 2500 km, with radar cross sections from >15 m² down to <0.3 m², and measured their distances with an average precision of about 0.7 m RMS.     

On the practical exploitation of perturbative effects in low Earth orbit for space debris mitigation

This paper presents the results of a numerical evaluation of the natural lifetime reduction in low Earth orbit, due to dynamical perturbations. The study considers two values for the area-to-mass ratio, a nominal ratio which resembles a typical value of spacecraft in orbit today, and an enhanced ratio which covers the surface augmentation. The results were obtained with two orbit propagators, one of a semi-analytical nature and the second one using non-averaged equations of motion. The simulations for both propagators were set up similarly to allow comparison. They both use the solar radiation pressure and the secular terms of the geopotential ($J_2,J_4$ and $J_6$). The atmospheric drag was turned on and off in both propagators to alternatively study the eccentricity build up and the residual lifetime. The non-averaging case also covers a validation with the full 6?×?6 geopotential. The results confirm the findings in previous publications, that is, the possibility for de-orbiting from altitudes above the residual atmosphere if a solar sail is deployed at the end-of-life, due to the combined effect of solar radiation pressure and the oblateness of the Earth. At near polar inclinations, shadowing effects can be exploited to the same end. The results obtained with the full, non-averaging propagator revealed additional de-orbiting corridors associated with solar radiation pressure which were not found by previous work on space debris mitigation. The results of both tools are compared for specific initial conditions. For nominal values of area-to-mass ratio, instead, it is confirmed that this resonance effect is negligible.The paper then puts the findings in the perspective of the current satellite catalogue. It identifies space missions which are currently close to a resonance corridor and shows the orbit evolution within the resonances with a significantly shorter residual orbital lifetime. The paper finishes with a discussion on the exploitation of these effects with regards to the long-term simulation of the space debris environment and a flux and collision probability comparison.     

International scientific optical network for space debris research

A joint team of researchers under the auspices of the Center for Space Debris Information Collection, Processing and Analysis of the Russian Academy of Sciences collaborates with 15 observatories around the world to perform observations of space debris. For this purpose, 14 telescopes were equipped with charge-coupled device (CCD) cameras, Global Positioning System (GPS) receivers, CCD frame processing and ephemeris computation software, with the support of the European and Russian grants. Many of the observation campaigns were carried out in collaboration with the Astronomical Institute of the University of Bern (AIUB) team operating at the Zimmerwald observatory and conducting research for the European Space Agency (ESA), using the Tenerife/Teide telescope for searching and tracking of unknown objects in the geostationary region (GEO). More than 130,000 measurements of space objects along a GEO arc of 340.9°, collected and processed at Space Debris Data Base in the Ballistic Center of the Keldysh Institute of Applied Mathematics (KIAM) in 2005–2006, allowed us to find 288 GEO objects that are absent in the public orbital databases and to determine their orbital elements. Methods of discovering and tracking small space debris fragments at high orbits were developed and tested. About 40 of 150 detected unknown objects of magnitudes 15–20.5 were tracked during many months. A series of dedicated 22-cm telescopes with large field of view for GEO survey tasks is in process of construction. 7 60-cm telescopes will be modernized in 2007.     

Semi-analytical investigations of high area-to-mass ratio geosynchronous space debris including Earth’s shadowing effects

This paper investigates the long-term perturbations of the orbits of geosynchronous space debris influenced by direct radiation pressure including the Earth’s shadowing effects. For this purpose, we propose an extension of our homemade semi-analytical theory [Valk, S., Lemaître, A., Deleflie, F. Semi-analytical theory of mean orbital motion for geosynchronous space debris under gravitational influence. Adv. Space Res., submitted for publication], based on the method developed by Aksnes [Aksnes, K. Short-period and long-period perturbations of a spherical satellite due to direct solar radiation. Celest. Mech. Dyn. Astron. 13, 89–104, 1976] and generalized into a more convenient non-singular formalism. The perturbations accounting for the direct radiation pressure with the Earth’s shadow are computed on a revolution-by-revolution basis, retaining the original osculating Hamiltonian disturbing function. In this framework, we compute the non-singular mean longitude at shadow entry and shadow exit at every orbital revolution in opposition to classical approaches where the singular eccentric anomalies at shadow entry and shadow exit are computed. This new algorithm is developed using non-singular variables. Consequently, it is particularly suitable for both near-circular and near-equatorial orbits as well as orbits which transit periodically around null eccentricities and null inclinations.The algorithm is tested by means of numerical integrations of the equations, averaged over the short periods, including radiation pressure, J₂, the combined Moon and Sun third body attraction as well as the long-term effects of the 1:1 resonance occurring for geosynchronous objects. As an extension of [Valk, S., Lemaître, A., Anselmo, L. Analytical and semi-analytical investigations of geosynchronous space debris with high area-to-mass ratios influenced by solar radiation pressure. Adv. Space Res., doi:10.1016/j.asr.2007.10.025, 2007b], we especially apply our analysis to space debris with area-to-mass as high as 20 m²/kg. This paper provides numerical and semi-analytical investigations leading to a deep understanding of the long-term evolution of the semi-major axis. Finally, these semi-analytical investigations are compared with accurate numerical integrations of the osculating equations of motion over time scales as high as 25 years.     

Accurate orbit predictions for debris orbit manoeuvre using ground-based lasers

Orbit manoeuvre of low Earth orbiting (LEO) debris using ground-based lasers has been proposed as a cost-effective means to avoid debris collisions. This requires the orbit of the debris object to be determined and predicted accurately so that the laser beam can be locked on the debris without the loss of valuable laser operation time. This paper presents the method and results of a short-term accurate LEO (<900 km in altitude) debris orbit prediction study using sparse laser ranging data collected by the EOS Space Debris Tracking System (SDTS). A main development is the estimation of the ballistic coefficients of the LEO objects from their archived long-term two line elements (TLE). When an object is laser tracked for two passes over about 24 h, orbit prediction (OP) accuracy of 10–20 arc seconds for the next 24–48 h can be achieved – the accuracy required for laser debris manoeuvre. The improvements in debris OP accuracy are significant in other applications such as debris conjunction analyses and the realisation of daytime debris laser tracking.     

Impact effects from small size meteoroids and space debris

When the impact risk from meteoroids and orbital debris is assessed the main concern is usually structural damage. With their high impact velocities of typically 10–20 km/s millimeter or centimeter sized objects can puncture pressure vessels and other walls or lead to destruction of complete subsystems or even whole spacecraft. Fortunately chances of collisions with such larger objects are small (at least at present). However, particles in the size range 1–100 μm are far more abundant than larger objects and every orbiting spacecraft will encounter them with certainty. Every solar cell (8 cm² area) of the Hubble Space Telescope encountered on average 12 impacts during its 8.25 years of space exposure. Most were from micron sized particles.     

基于多项式近似的空间碎片群体轨道预报算法

快速准确地分析空间碎片群轨道演化行为对于其他在轨航天器碰撞规避至关重要。在各摄动力的作用下,空间碎片群演化运动呈现出复杂的非线性特征。空间碎片群体个体数量巨大,如果通过对空间碎片群中每个空间碎片进行轨道积分来分析群体预报的方法会导致计算量过大。针对该问题,提出一种基于多项式近似的轨道快速预报分析方法。该方法将空间碎片群分为少量的标称碎片和其他大量关联碎片。针对标称碎片的轨道预报采用数值积分求解保证预报精度;而针对其他大量的关联碎片轨道预报问题,采用多项式泰勒展开半解析方法求解,从而在保证预报精度的前提下有效减少空间碎片群轨道预报的计算量。为了验证方法的有效性,对不同空间碎片群进行了轨道预报仿真。仿真结果表明,当轨道预报精度设定在1m范围内时,多项式近似算法的计算量较蒙特卡洛方法计算效率提高了2.2~17.2倍,验证了所提出方法的有效性。     

Semi-analytical theory of mean orbital motion for geosynchronous space debris under gravitational influence

This paper provides a hamiltonian formulation of the equations of motion of an artificial satellite or space debris orbiting the geostationary ring. This theory of order 1 has been formulated using canonical and non-singular elements for eccentricity and inclination. The analysis is based on an expansion in powers of the eccentricity and of the inclination. The theory accounts for the influence of the Earth gravity field expanded in spherical harmonics, paying a particular attention to the resonance occurring for geosynchronous objects. The luni-solar perturbations are also taken into account. We present the resonant motion and its main characteristics: equilibria, stability, fundamental frequencies and width of the resonant area by comparison with a basic analytical model. Finally, we show some results concerning the long term dynamics of a typical space debris under the influence of the gravitational field of the Earth and the luni-solar interactions.     

天基激光移除空间碎片仿真平台研究与开发

为了从空间碎片和天基移除系统两方面分析激光驱动碎片变轨过程,优化移除任务规划和策略,基于真实的可观测空间碎片数据,设计并开发了一套天基激光移除空间碎片三维数值仿真平台。首先从总体设计出发,对三维数值仿真平台的需求分析、总体框架、模块功能进行了明确的描述。其次通过对激光驱动空间碎片变轨过程数学模型的分析,确定了各模块的具体实现方法。最后采用C++/Qt开发了三维数值仿真平台,通过仿真验证了设计平台的有效性。该仿真平台可用于不同天基平台和目标碎片的任务规划、碎片分布热点区域和航天器防护区域的方案设计及空间环境治理体系的优化设计。     

Space debris: Assessing risk and responsibility

We model the orbital debris environment by a set of differential equations with parameter values that capture many of the complexities of existing three-dimensional simulation models. We compute the probability that a spacecraft gets destroyed in a collision during its operational lifetime, and then define the sustainable risk level as the maximum of this probability over all future time. Focusing on the 900- to 1000-km altitude region, which is the most congested portion of low Earth orbit, we find that – despite the initial rise in the level of fragments – the sustainable risk remains below 10^-3${10}^{-3}$ if there is high (>98%) compliance to the existing 25-year postmission deorbiting guideline. We quantify the damage (via the number of future destroyed operational spacecraft) generated by past and future space activities. We estimate that the 2007 FengYun 1C antisatellite weapon test represents ≈1%$\approx 1\%$ of the legacy damage due to space objects having a characteristic size of ?10$?10$ cm, and causes the same damage as failing to deorbit 2.6 spacecraft after their operational life. Although the political and economic issues are daunting, these damage estimates can be used to help determine one-time legacy fees and fees on future activities (including deorbit noncompliance), which can deter future debris generation, compensate operational spacecraft that are destroyed in future collisions, and partially fund research and development into space debris mitigation technologies. Our results need to be confirmed with a high-fidelity three-dimensional model before they can provide the basis for any major decisions made by the space community.     

Influence of Earth’s shadowing effects on space debris stability

Solar radiation pressure affects the evolution of high area-to-mass geostationary space debris. In this work, we extend the stability study of Valk et al. (2009) by considering the influence of Earth’s shadows on the short- and long-term time evolutions of space debris. To assess the orbits stability, we use the Mean Exponential Growth factor of Nearby Orbits (MEGNO), which is an efficient numerical tool to distinguish between regular and chaotic behaviors. To reliably compute long-term space debris motion, we resort to the Global Symplectic Integrator (GSI) of Libert et al. (2011) which consists in the symplectic integration of both Hamiltonian equations of motion and variational equations. We show how to efficiently compute the MEGNO indicator in a complete symplectic framework, and we also discuss the choice of a symplectic integrator, since propagators adapted to the structure of the Hamiltonian equations of motion are not necessarily suited for the associated variational equations. The performances of our method are illustrated and validated through the study of the Arnold diffusion problem. We then analyze the effects of Earth’s shadows, using the adapted conical and cylindrical Earth’s shadowing models introduced by Hubaux et al. (2012) as the smooth shadow function deriving from these models can be easily included into the variational equations. Our stability study shows that Earth’s shadows greatly affect the global behaviour of space debris orbits by increasing the size of chaotic regions around the geostationary altitude. We also emphasize the differences in the results given by conical or cylindrical Earth’s shadowing models. Finally, such results are compared with a non-symplectic integration scheme.     

Analysis of laser ranges and angular measurements data fusion for space debris orbit determination

In the framework of space debris, the orbit determination process is a fundamental step, both, for researchers and for satellite operators. The accurate knowledge of the orbit of space debris objects is needed to allow space debris characterization studies and to avoid unnecessary collision avoidance maneuvers.The accuracy of the results of an orbit determination process depends on several factors as the number, the accuracy, the kind of processed measurements, their distribution along the orbit, and the object-observer relative geometry. When the observation coverage of the target orbit is not homogeneous, the accuracy of the orbit determination can be improved processing different kind of observables. Recent studies showed that the satellite laser ranging technique can be successfully applied to space debris.In this paper, we will investigate the benefits of using laser ranges and angular measurements for the orbit determination process. We will analyze the influence of the number of used observations, of the covered arc of orbit, of each observable, and of the observation geometry on the estimated parameters. Finally, using data acquired on short observation arcs, we analyze the achievable accuracies for the orbital regimes with the highest space debris density, and to the consequences of the data fusion on catalog maintenance operations. The results shown are obtained using only real data (both angular and laser measurements) provided by sensors of the Swiss Optical Ground Station and Geodynamics Observatory Zimmerwald owned by the Astronomical Institute of the University of Bern (AIUB) and for some studies also using ranges provided from other stations of the International Laser Ranging Service (ILRS).     

Spacecraft formation flying for Earth-crossing object deflections using a power limited laser ablating

A formation flying strategy with an Earth-crossing object (ECO) is proposed to avoid the Earth collision. Assuming that a future conceptual spacecraft equipped with a powerful laser ablation tool already rendezvoused with a fictitious Earth collision object, the optimal required laser operating duration and direction histories are accurately derived to miss the Earth. Based on these results, the concept of formation flying between the object and the spacecraft is applied and analyzed as to establish the spacecraft’s orbital motion design strategy. A fictitious “Apophis”-like object is established to impact with the Earth and two major deflection scenarios are designed and analyzed. These scenarios include the cases for the both short and long laser operating duration to avoid the Earth impact. Also, requirement of onboard laser tool’s for both cases are discussed. As a result, the optimal initial conditions for the spacecraft to maintain its relative trajectory to the object are discovered. Additionally, the discovered optimal initial conditions also satisfied the optimal required laser operating conditions with no additional spacecraft’s own fuel expenditure to achieve the spacecraft formation flying with the ECO. The initial conditions founded in the current research can be used as a spacecraft’s initial rendezvous points with the ECO when designing the future deflection missions with laser ablation tools. The results with proposed strategy are expected to make more advances in the fields of the conceptual studies, especially for the future deflection missions using powerful laser ablation tools.