A Population Dynamics Approach to the Distribution of Space Debris in Low Earth Orbit

The presence of the debris in the Earth’s orbit poses a significant risk to human activity in outer space.This debris population continues to grow due to ground launches,the loss of external parts from space ships,and uncontrollable collisions between objects.A computationally feasible continuum model for the growth of the debris population and its spatial distribution is therefore critical.Here we propose a diffusion-collision model for the evolution of the debris density in the low-Earth orbit and its dependence on the ground-launch policy.We parametrize this model and test it against data from publicly available object catalogs to examine timescales for the uncontrolled growth.Finally,we consider sensible launch policies and cleanup strategies and how they reduce the future risk of collisions with active satellites or space ships.

Meteoroid and Space Debris Risk Assessment for Satellites Orbiting the Earth/Moon

Interplanetary meteoroids and space debris can impact satellites orbiting the Earth or spacecraft traveling to the Moon.Targeting China Space Station(CSS),7 satellites selected from the constellation of Beidou Navigation Satellite System Phase III(BDS-3),and 3 spacecraft orbiting the Moon,we have adopted in the paper the Meteoroid Engineering Model 3,Divine-Staubach meteoroid environment model,and Jenniskens-McBride meteoroid steam model to analyze the meteoroid environment with the mass range of 10–6~10 g.Orbital Debris Engineering Model 3.1 space debris model is used to analyze the orbital debris environment faced by these satellites.The flux of space debris with a size larger than 100μm is compared with that of the meteoroids.The results show that the space debris flux encountered by China Space Station is much higher than that of the meteoroids with sizes in the above range.And quite the opposite,the meteoroids flux impacting the 7 satellites from the BDS-3 is higher.Upon adopting the double-layer Whipple protection measure,the catastrophic collision flux of these satellites encountering meteoroids is about 10–6 times of that without protection,or even less,implying that the Whipple protection effectively guarantees the safety of the satellites in orbit.Besides,it is also found that the flux of the high-density meteoroid population encountered by each satellite is greater than that of the low-density population,whereas the impact velocity is lower for each satellite.These results can aid the orbit selection and the protection design for satellites and spacecraft.

The use of laser ranging to measure space debris

Space debris is a major problem for all the nations that are currently active in space. Adopting high-precision measuring techniques will help produce a reliable and accurate catalog for space debris and collision avoidance. Laser ranging is a kind of real-time measuring technology with high precision for space debris observation. The first space-debris laser-ranging experiment in China was performed at the Shanghai Observatory in July 2008 with a ranging precision of about 60-80 cm. The experi- mental results showed that the return signals from the targets with a range of 900 km were quite strong, with a power of 40W （2J at 20 Hz） using a 10ns pulse width laser at 532 nm wavelength. The performance of the preliminary laser ranging system and the observed results in 2008 and 2010 are also introduced.

Space Debris Research Progress of China

The rapid increase of space debris population has posed serious threaten to the safety of human space activities and became a global issue.How to enhance the technical capabilities of space debris threat coping ability is of great significance to the sustainable development of space activities,the further development,and utilization of outer space.In this paper,we describe space debris research progress of China on observation,collision avoidance,protection,mitigation,regulation,and standard during the last twenty years,and look forward to the future development direction of space debris.

Cutting-Edge Space Exploration Technology Maturity Level Facilitation with Support of Space Debris Removal Missions

Considering current space debris situation in outer space environment,different methods for debris removal missions are proposed.In addition,advanced technologies are needed to be demonstrated for future human space exploration programs.The main issue regarding to these missions is high mission cost for both debris removal missions and space environmental tests to achieve high maturity level for new space-usable technologies.Since,these missions are unavoidable for future of human space activities,a solution which can tackle these challenges is necessary.This paper will address to an idea which has the possibility to give a solution for facilitating technology readiness level(TRL)maturity tests by debris removal mission platform consideration.

Influence of Solid Rocket Motor Slag on the Space Debris Environment

The resulting slag particles from solid rocket motor( SRM) firings are an important component of space debris environment. Slag sizes as large as 1 cm have been witnessed in ground tests,and comparable sizes have been also estimated via observations of sub-orbital tail-off events. We achieve slag initial data based on MASTER slag model and SRM historical launch data,and propagate slag long-term orbital evolution taking into account the zonal harmonics J2,atmospheric drag,solar radiation pressure and luni-solar attraction to discuss the slag size distribution and orbital characteristics. Finally,future slag debris environment is evaluated based on two different launch rate assumptions. The result shows that current launch frequency will make the slag population sustain growth and the population will not decrease at once even if there are no more launches in the future.

Space debris tracking based on fuzzy running Gaussian average adaptive particle filter track-before-detect algorithm

Although tracking with a passive optical telescope is a powerful technique for space debris observation, it is limited by its sensitivity to dynamic background noise. Traditionally, in the field of astronomy, static background subtraction based on a median image technique has been used to extract moving space objects prior to the tracking operation, as this is computationally efficient. The main disadvantage of this technique is that it is not robust to variable illumination conditions. In this article, we propose an approach for tracking small and dim space debris in the context of a dynamic background via one of the optical telescopes that is part of the space surveillance network project, named the Asia- Pacific ground-based Optical Space Observation System or APOSOS. The approach combines a fuzzy running Gaussian average for robust moving-object extraction with dim-target tracking using a particle- filter-based track-before-detect method. The performance of the proposed algorithm is experimentally evaluated, and the results show that the scheme achieves a satisfactory level of accuracy for space debris tracking.

Analysis of the Impact of Large Constellations on the Space Debris Environment and Countermeasures

Large constellations have developed rapidly in recent years because of their unique advantages, but they will inevitably have a major negative impact on the space debris environment, leading to its deterioration. The key to mitigate the impact is the success rate and duration of the post-mission disposal(PMD) process. Aiming at solving this problem, this paper further studies the impact of large constellations on other space assets under different PMD strategies through simulation, and proposes corresponding strategies and suggestions for mitigation.According to One Web’s large constellation launch plan, the dangerous intersection of the large constellation with existing space assets at different stages of the constellations life cycle is calculated by simulation. Based on this, the influence of the large constellation operation on existing space assets at different times and strategies of PMD is analyzed. The conclusion shows that in the PMD stage, large constellations have the greatest impact on existing space assets;the PMD duration and number of satellites performing PMD at the same time are key factors to the degree of negative impact. The faster the PMD is, the less threat it poses to other spacecraft. More results and conclusions are still being analyzed.

Simple Method for Tethered Space Debris Retrieval

Space debris retrieval problem utilizing a tethered system in an elliptical orbit is studied in this paper.An analytical control law specified by a tether length rate for retrieval is derived from a dumbbell model of the system.The proposed control method can suppress large swings around the local vertical position of the tethered system.Under such a control strategy,the debris retrieval behaves in asymptotic stable motion towards the expected angle.The stability of the non-autonomous system during the retrieval control is analyzed using the Floquet theory.The result demonstrates that an orbital region exists,on which the retrieval process maintains asymptotically stable.The proposed analytical control law is validated via numerical simulations.

Progress of China's Space Debris Research

China has continually worked on space debris research,complying with the White Paper“China’s Space Program:A 2021 Perspective”.This paper aims to clarify China’s research and application progress from 2020 to 2021 in space debris observation,prediction,protection,and mitigation.In this context,it also summarizes the space debris mitigation efforts made by the Chinese government and provides the expectation of future direction for the work.

Chemical Classification of Space Debris

Space debris, here referring to all non-operating orbital objects, has steadily increased in number so that it has become a potential barrier to the exploration of space. The ever-increasing number of space debris pieces in space has created an increasingly threatening hazard to all on-the-orbit spacecraft, and all future space exploration activities have to be designed and operated with respect to the increasing threat posed by space debris. Generally, space debris is classified as large, medium and small debris pieces based on their sizes. The large debris piece is easily catalogued, but medium to small debris pieces are very difficult to track and also quite different in damage mechanisms from the large ones. In this paper, a scheme of chemical classification of space debris is developed. In our scheme, the first-order classification is employed to divide space debris into two groups: natural micrometeoroids and artificial space debris. The second-order classification is based on their chemical patterns and compositions. The natural micrometeoroids are further divided into three types, namely mafic, metal and phyllosilicate micrometeorites, while the artificial space debris is divided into seven types, which are polymers, non-metal debris, metals and their alloys, oxides, sulphides and their analogs, halides and carbides. Of the latter seven types, some can also be further divided into several sub-types. Chemical classification of space debris is very useful for the study of the chemical damage mechanism of small debris pieces, and also is of great significance in constraining the origin and source of space debris and assessing their impact on spacecraft and human space activities.

An Evolution Model of Space Debris Environment

Various types of models including engineering models and evolution models have been developed to understand space debris environment since 1960s. Evolution model, consisting of a set of supporting models such as Launch Model, Breakup Model and Atmosphere Model, can reliably predicts the evolution of space debris environment. Of these supporting models, Breakup Model is employed to describe the distribution of debris and debris cloud during a explosion or collision case which is one of the main factors affecting the amount of total space debris. An analytical orbit debris environment model referred to as the "Particles In Boxes" model has been introduced. By regarding the orbit debris as the freedom particles running in the huge volume, the sources and sinks mechanism is established. Then the PIB model is expanded to the case of multiple species in multiple tier system. Combined with breakup model, the evolution of orbit debris environment is predicted.

Enhancing Space Debris Studies

With the expansion of hu-man activities in space and thesteady increase in space debris re-sulting therefrom,the space envi-ronment is constantly deteriorat-ing.The space debris hazard hasalready introduced new safety is-sues for consideration by space a-gencies,spacecraft designers,manufacturers,scientists and in-surance underwriters. The problem of the pollutionof the space environment causedby space debris has become agrowing concern within interna-tional astronautical circles and theinternational community as awhole. And the management of thespace environment is a matter forinternational cooperation and

Mitigation and Avoidance of Space Debris

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Space debris environment engineering model 2019:Algorithms improvement and comparison with ORDEM 3.1 and MASTER-8

As an essential tool for realistic description of the current or future debris environment,the Space Debris Environment Engineering Model(SDEEM)has been developed to provide support for risk assessment of spacecraft.In contrast with SDEEM2015,SDEEM2019,the latest version,extends the orbital range from the Low Earth Orbit(LEO)to Geosynchronous Orbit(GEO)for the years 1958-2050.In this paper,improved modeling algorithms used by SDEEM2019 in propagating simulation,spatial density distribution,and spacecraft flux evaluation are presented.The debris fluxes of SDEEM2019 are compared with those of three typical models,i.e.,SDEEM2015,Orbital Debris Engineering Model 3.1(ORDEM 3.1),and Meteoroid and Space Debris Terrestrial Environment Reference(MASTER-8),in terms of two assessment modes.Three orbital cases,including the Geostationary Transfer Orbit(GTO),Sun-Synchronous Orbit(SSO)and International Space Station(ISS)orbit,are selected for the spacecraft assessment mode,and the LEO region is selected for the spatial density assessment mode.The analysis indicates that compared with previous algorithms,the variable step-size orbital propagating algorithm based on semi-major axis control is more precise,the spatial density algorithm based on the second zonal harmonic of the non-spherical Earth gravity(J_(2))is more applicable,and the result of the position-centered spacecraft flux algorithm is more convergent.The comparison shows that SDEEM2019 and MASTER-8 have consistent trends due to similar modeling processes,while the differences between SDEEM2019 and ORDEM 3.1 are mainly caused by different modeling approaches for uncatalogued debris.

Prediction and experimental verification of tether net entanglement for space debris capture

This study involved simulations and experiments aimed at assessing the efficacy of a tether net in encapsulating space debris.The tether net was modeled as a spring–mass–damper system considering the influence of aerodynamic and gravitational forces and the occurrence of debris collisions.To examine the influence of collision position and size disparity between the debris and the net on debris capture status,the entanglement nodes of the net were identified.Experiments were conducted to evaluate the wrapping capabilities of the tether net,focusing specifically on debris capture.Subsequently,the results were compared with those of the numerical simulation.In the experiments,radio frequency identification was used to identify the entanglement points of the tether net.Previous studies have indicated that the ideal collision point for capturing debris using a tether net with the debris intended to be captured is located at the center of the net.However,the experimental results of this study revealed that a collision position that is slightly shifted from the center of the tether net is more advantageous for capturing debris in terms of tether net entanglement.

Space Debris Reentry Analysis Methods and Tools

The reentry of uncontrolled spacecraft may be broken into many pieces of debris at an altitude in the range of 75-85 km. The surviving fragments could pose great hazard and risk to ground and people. In recent years, methods and tools for predicting and analyzing debris reentry and ground risk assessment have been studied and developed in National Aeronautics and Space Ad-ministration （NASA）, European Space Agency （ESA） and other organizations, including the group of the present authors. This paper reviews the current progress on this topic of debris reentry briefly. We outline the Monte Carlo method for uncertainty analysis, breakup prediction, and parameters affecting survivability of debris. The existing analysis tools can be classified into two categories, i.e. the object-oriented and the spacecraft-oriented methods, the latter being more accurate than the first one. The past object-oriented tools include objects of only simple shapes. For more realistic simulation, here we present an object-oriented tool debris reentry and ablation prediction system （DRAPS） developed by the present authors, which introduces new object shapes to 15 types, as well as 51 predefined motions and relevant aerodynamic and aerothermal models. The aerodynamic and aerothermal models in DRAPS are validated using direct simulation Monte Carlo （DSMC） method.

Cleaning space debris with a space-based laser system

High-energy pulsed laser radiation may be the most feasible means to mitigate the threat of collision of a space station or other valuable space assets with orbital debris in the size range of 1–10 cm. Under laser irradiation, part of the debris material is ablated and provides an impulse to the debris particle. Proper direction of the impulse vector either deflects the object trajectory or forces the debris on a trajectory through the upper atmosphere, where it burns up. Most research concentrates on ground-based laser systems but pays little attention to space-based laser systems.There are drawbacks of a ground-based laser system in cleaning space debris. Therefore the placement of a laser system in space is proposed and investigated. Under assumed conditions,the elimination process of space debris is analyzed. Several factors such as laser repetition frequency, relative movement between the laser and debris, and inclination of debris particles which may exercise influence to the elimination effects are discussed. A project of a space-based laser system is proposed according to the numerical results of a computer study. The proposed laser system can eliminate debris of 1–10 cm and succeed in protecting a space station.

Fuel-optimal deorbit scheme of space debris using tethered space-tug based on pseudospectral method

This paper proposes a fuel-optimal deorbit scheme for space debris deorbit using tethered space tug.The scheme contains three stages named respectively as dragging,maintenance and swinging.In the first stage,the tug,propelled by continuous thrust,tows deorbit to a transfer orbit with a tether.Then in the second stage,the combination of the tug and the debris flies unpowered and uncontrolled to a swing point on the transfer orbit.Finally,in the third stage,the tug is propelled at the swing point and the rotation speed of the tethered system increases such that the debris obtains enough velocity increment.The trajectory optimization of the first stage is established considering the total fuel consumption of the three stages,whereas the dynamic model is simplified for computation efficiency.The solution to the optimal problem is obtained using a direct method based on Gauss pesudospectral discretization.Then a model predictive controller is designed to track the open-loop optimal reference trajectories,reducing the states’deviations caused by model simplification and ignorance of perturbations.Furthermore,it is proved that the fuel-optimal swing point is the apogee of the transfer orbit.The paper analyzes the fuel consumption of a typical scenario and demonstrates effectiveness of the proposed deorbit scheme numerically.

A method of separating blended images in space debris observation

Due to the relative movement between space debris and background stars,the blending of objects and stars is ineluctable through observation.It brings down position accuracy of objects and even makes the tracking break down in worse conditions.In view of the difference of geometry between stars and objects in space debris observation,a technique for separating blended objects based on mathematical morphology is presented.It's sufficiently flexible to be applied in image processing,and the blending images can be separated effectively with a high degree of centroid precision.