Debris Environment Research Articles

Modified Cour-Palais/Christiansen damage equations for double-wall structures

Ballistic limit equations (BLEs) are used for the damage prediction of spacecraft in a meteoroid and space debris environment. For double-wall configurations, the Cour-Palais/Christiansen equations have been modified to yield a general approach including the influence of the shield thickness. The ratio of shield thickness to particle diameter is considered as additional parameter in the equations. These equations result in the single-wall equation when the shield thickness approaches zero. The modifications can also be applied to other BLEs. Impact tests have been performed in order to validate the modified equations. In this paper, the test results are compared to the modified BLEs. Especially in the hypervelocity region, the new equations are more suitable for configurations with very thin shields than the original ones.

RCS-based ballistic limit curves for non-spherical projectiles impacting dual-wall spacecraft systems

Ballistic limit curves (BLCs) for dual- or multi-wall spacecraft wall systems impacted by spherical projectiles exist for a variety of impact conditions. However, meteoroids and orbital debris particles can take any shape, and non-spherical projectiles can be more damaging than equal mass spherical projectiles under the same impact conditions. In a recent study, a series of BLCs for a typical dual-wall configuration impacted by a variety of non-spherical projectiles were developed and presented in terms of equivalent spherical projectile diameter as a function of impact velocity. In order to be more consistent with debris environment predictions and to be useful for spacecraft design, such BLCs need to be drawn in units that are consistent with environment flux models used in that design process. In this paper, we have recast the equivalent spherical projectile diameter BLCs and now present them using radar cross-section (RCS) diameter as the characteristic length parameter. The recast BLCs are seen to be more tightly grouped and are not as spread out as they were when plotted using equivalent spherical projectile diameter. Thus, the effect of projectile shape on penetrating ability is shown to be somewhat reduced when considering characteristic length as the size parameter as opposed to an equivalent mass diameter.

Hypervelocity impacts on thin brittle targets: Experimental data and SPH simulations

The meteoroids and debris environment play an important role in the reduction of spacecraft lifetime. Ejecta or secondary debris, are produced when a debris or a meteoroid impact a spacecraft surface. Brittle materials are particularly sensitive to HVI in term of damages and amount of ejected matter: the ejected fragments total mass is in the order of 100 times bigger than the impacting mass. The French atomic energy commission (CEA) faces the same problem in the Laser MégaJoule project. The lasers optics will be bombarded by hypervelocity debris and shrapnel resulting from target disassembly. Two millimeter thick fused silica disposable debris shields (DDS) located in front of the main debris shields might be used to reduce very small shrapnel cratering on the main debris shields. The aim of this paper is to study the damaging and ejection processes that occur during HVI on thin brittle targets. A two-stage light-gas gun has been used to impact 2 mm DDS with 500 μm steel projectiles. Experimental characterization of ejected matter has also been performed: lightweight paperboards coated with adhesive have been used to collect ejected fragments including spalls. Numerical simulation using the smooth particle hydrodynamics (SPH) method of LS-DYNA and the Johnson Holmquist material model were performed. The results of these calculations are compared to experimental data which include the damage features in the targets (spalled zones and perforation hole) and the ejection clouds. Satisfying agreement between numerical and experimental simulations was obtained for damage characteristics and ejection phenomena.

A new stochastic impressionistic low Earth model of the space debris scenario

A new Stochastic IMPressionistic Low Earth (SIMPLE) model of the space debris environment using a stochastic approach is presented in this paper. The present approach and philosophy are similar to that utilized for evolving the international standard or other reference atmospheres. Presently, this model describes the debris scenario up to an altitude of 2000 km and with eccentricity less than 0.2 thus covering about 75% of the large space debris objects catalogued in USSPACECOM two line element (TLE) sets. Two types of models one called ‘gross’ provides insight into the physical process by characterizing the distribution of the number density ‘ n ’, eccentricity ‘ e ’, and the ballistic coefficient ‘ B ’ of objects over the whole of the LEO region for all inclinations put together as also separately. The other called ‘local’ model characterizes the distribution of ‘ e ’ and ‘ B ’ of the debris across suitable local altitude and perigee bins useful for mission analysis and risk assessment for spacecraft designers interested in specific altitude or perigee height bins and inclination bands. The number density ‘ n ’ in all the gross models can be represented in terms of a mixture of Laplace distributions. The SIMPLE model with much less parameters than in ORDEM96 captures closely all the peak fragment densities without loss of accuracy at other altitudes. The distribution of ‘ e ’ and the ‘ B ’ in each and every gross and local model can be represented by suitable lognormal distributions. Qualitatively the parameters of the ‘ n ’ and ‘ e ’ distributions in the gross and the local models exhibit statistically quasi-equilibrium state (though quantitatively the fragment density is varying all over) across the time period from 1999 to 2002 and hence an average is recommended as the model value. Since, the parameters of ‘ B ’ show large variations or trend in their values derived from the TLE data sets, the latest year 2002 value is suggested as a reference in the model. Lastly some application areas of the SIMPLE model are provided along with possible approaches to estimate the spatial density of debris objects and their flux in each altitude bin of interest.

Statistical Distribution of Keplerian Velocities

Introduction T HE use of generalized functions, in particular of Dirac’s delta functions, has already been proposed1−5 as a useful tool in simplifying the derivations of probability distribution functions related to the statistical description of Keplerian orbits. The formalism that derives from an extensive use of these functions permits an easy conversion from classical astrodynamic formulas to probability distributions. The methodology was independently discovered in different forms by Au and Tam,6 Meshcheryakov,4 and Izzo,1 and it has been used in various applications1−3,5 mainly related to the description of collision probabilities and to the modeling of the space debris environment. The limitations in the description of the Molnyia and geostationary orbits of the orbital debris environment model proposed by Kessler et al.7 were alleviated by using results derived with this methodology.3 These results also generalized previous expressions8−10 commonly used in space flight mechanics problems dealing with the statistics of a large number of orbits and objects. In the evaluation of collision risks as well as in the problem of inferring the orbital motion of space debris from a measurement campaign such as the one carried by the Long Duration Exposure Facility or by the more recent Space Dust11 instrument, it is often necessary to have statistical models also on the velocities of orbiting objects. In this Note Dirac’s delta formalism is applied to derive the absolute velocity distribution of an orbiting object having uncertain orbital parameters.

Introduction of a nozzle throat diameter dependency into the SRM dust size distribution

The ESA space debris population model MASTER (Meteoroid and Space Debris Terrestrial Environment Reference) considers 1032 firings of solid rocket motors (SRM) with the associated generation of SRM slag and dust particles in its current version. The resulting dust population is a major contribution to the sub-millimetre size space debris environment in Earth orbit. For the modelling of each SRM dust release event a detailed knowledge of the particle size distribution is essential. However, the knowledge of the particle sizes after passing the nozzle throat is poor. The current dust implementation in the MASTER model assumes a fixed size distribution which is identically used for both large upper stages and small apogee motors. This assumption can lead to an over-representation of large dust particles in regions, where mainly apogee motors are used (i.e., Geostationary Earth Orbit) and an under-representation in lower altitudes, where large stages predominate. In this paper, a concept for the improvement of SRM dust size modelling is discussed. It will be shown that an introduction of a nozzle throat diameter dependency into the dust size distribution enables a more precise modelling of SRM dust release events. The improved SRM dust size distribution is going to be used by the MASTER-2005 space debris model which is currently under development by the Institute of Aerospace Systems and QinetiQ (UK) under ESA contract.

DUNE-eXpress – Dust astronomy with ConeXpress

DUNE-eXpress (DUst measurement near Earth) is a scientific application of the ConeXpress platform developed by Dutch Space [ Scholten, H., Nugteren, P.R., de Kam, J., Cruijssen, H. ConeXpress – low cost access to space, white paper Dutch Space, Leiden, The Netherlands, 2003; Kassebom, M., Mahal, S., Scholten, H., et al. ConeXpress – a low cost satellite solution for GEO applications, DGLR-2003-115, in: Olbert, F. (Ed.), German Aerospace Congress, Munich, Germany, 2003] The goal of this mission is to investigate in situ the physical and dynamical properties of interstellar and interplanetary dust. The Dust Telescope on-board DUNE-eXpress consists of two large area mass analyzer ( LAMA) instrument modules and four dust Trajectory Sensors with a total weight of 60 kg. LAMA measures the chemical composition of individual dust grains whereas the Trajectory Sensor determines their orbital parameters. DUNE-eXpress reaches an orbit outside the geostationary distance in order to avoid interferences with the Earth debris and magnetosphere environment. A position at the Sun–Earth Lagrange points L1 and L2 is well suited and reachable with DUNE-eXpress. A mission scenario based on the SMART 1 mission is presented.

Collision activities in the future orbital debris environment

We have analyzed potential collision activities among orbiting objects for the next 100 years from the low Earth orbit (LEO), medium Earth orbit (MEO), to geosynchronous orbit (GEO) regions. The analysis was based on results from the NASA orbital debris evolutionary model, LEGEND. A total of 30 Monte-Carlo simulations were performed. The 1996-to-2003 launch cycle was repeated in the future projection. No postmission disposal options were applied to satellites and rocket bodies. All collisions among objects 10 cm and larger were identified for the analysis. One of the new features of LEGEND is its ability to identify objects involved in collisions individually. This allows the user to better quantify the characteristics of future collision events, for example, by orbit type (e.g., LEO/GTO/GEO, inclination, right ascension of the ascending node), by object type (satellite, rocket body, breakup fragment), by breakup time, by location, and by mass. Our analysis shows that almost all future collisions occur in LEO. Intact–intact catastrophic collisions contribute the most to the generation of future debris populations. The majority of intacts involved in collisions come from future launches. This underlines the importance of postmission disposal of satellites and rocket bodies to reduce future collision activities. More than half of the “projectile fragments” involved in intact–fragment collisions originated from future collisions, indicating the nature of the feedback process in future collisions. Most LEO collisions occur in regions of high spatial density, around 800 and 1000 km altitudes. Although there is a wide spread in impact speed, about half of the collisions occur with impact speeds greater than 14 km/s. Since collisions are likely to produce more fragments than explosions in the future, it is critical to have a high fidelity model to analyze future collision activities to ensure reliable environment predictions. With the new capabilities of LEGEND we are able to examine the process in great detail and have a better understanding of the nature of collisions.

Modeling of RORSAT NaK droplets for the MASTER 2005 upgrade

Sixteen nuclear powered RORSATs launched between 1980 and 1988 activated a reactor core ejection system in sufficiently high orbits, mostly between 900 and 950 km altitude. The core ejection causes an opening of the primary coolant circuit. The liquid coolant consists of eutectic sodium–potassium alloy (NaK) and has been released into space during these core ejections. The NaK coolant has been forming droplets up to a diameter of 5.67 cm. The primary coolant circuit of the reactor contains 13 kg NaK-78. NaK releases are restricted to a very narrow region near 65 ∘ inclination. They contributed to the space debris environment in the centimeter and millimeter size regime. NaK droplets have been modeled before in ESA's MASTER Debris and meteoroid environment model. The approach is currently revised for the MASTER 2005 upgrade. The new NaK modeling approach considers a directional release of the droplets. The release is modeled with low additional velocities of about 15 m/s. The additional velocities are mainly a function of the pressure difference over the orifice. The outflow is considered as a discrete event for each of the 16 core ejections in total. Results of orbit propagation simulation runs are presented in terms of spatial density.

Dust detection in the ISS environment using filmed microchannel plates

Microchannel plates bearing a 60 nm thick aluminum film have been exposed to the external International Space Station (ISS) environment for 756 days. Postretrieval analysis has revealed holes in the aluminum film, which may have resulted from impacts by dust particles as small as a few tens of nanometers in diameter. Such particles have been undetectable by previously flown, much thicker foils. The flux of such particles appears to be consistent with the extrapolation, to this particle size regime, of current models for the near‐Earth dust and debris environment and data from previously flown foils.

A LEO satellite postmission disposal study using legend

This paper summarizes results from two postmission disposal (PMD) parametric analyses based on the high fidelity NASA orbital debris evolutionary model LEGEND. The first analysis includes a non-mitigation reference scenario and four test scenarios, where the mission lifetimes of spacecraft are set to 5, 10, 20, and 30 years, respectively, before they are moved to the 25-year decay orbits. The comparison among the five scenarios quantifies how a prolonged spacecraft mission lifetime decreases the effectiveness of the 25-year decay rule in the low Earth orbit region (LEO). The second analysis includes three 25-year decay PMD scenarios where the mission lifetimes of spacecraft are set to 5 years but with disposal success rates set to 50%, 70%, and 90%, respectively. It illustrates how the PMD success rate impacts the long-term debris environment. The conclusion of this paper is that a prolonged spacecraft mission lifetime and a lower PMD success rate can have noticeable negative impact on the debris environment in the long run.

The long-term interaction of the Italian satellites abandoned in GEO with the orbital debris environment

Four Italian satellites have been launched, so far, in geostationary orbit: SIRIO, Italsat 1, Italsat 2, and SICRAL. The latter is the only one still operational: in fact, Sirio was abandoned close to the geopotential equilibrium point at 75 ∘ E in 1985, Italsat 1 was re-orbited above the geosynchronous altitude at the beginning of 2001 and Italsat 2 was moved, in July 2002, below the synchronous height, due to an unexpected malfunction. A study was carried out in order to investigate and quantify the long-term environmental impact of the abandoned satellites on the geosynchronous region. As they were all successfully passivated, eliminating the possibility of future explosions, the only significant detrimental effect on the environment might derive from catastrophic collisions with other sizable space objects. However, the probability of such events was calculated to be extremely low, of the order of 10 - 7 in one century.

Size distribution of NaK droplets released during RORSAT reactor core ejection

NaK droplets consist of eutectic sodium–potassium alloy and have been released during RORSAT reactor core ejections mostly on orbits close to 950 km altitude. They contributed to the space debris environment in the centimeter and millimeter regime. NaK droplets have been modeled before in ESAs MASTER Debris and Meteoroid Environment Model. The approach is currently revised for the MASTER 2005 upgrade. The new NaK model gives estimations of the parameters of the size distribution function, which are based on physical relations only. NASA radar observations confirm this physical approach. A bimodal size distribution is derived, which is based on the Rosin–Rammler equation. The Rosin–Rammler equation is an empirical volume distribution function. The number of parameters is limited to two. It is likely that the coolant system contains two types of orifice diameters. This makes it necessary to apply the Rosin–Rammler distribution twice, resulting in a bimodal size distribution with altogether four parameters. The comparison shows that the new NaK model is in good agreement with the NASA model, which is based on radar observations. Results of orbit propagation simulation runs are presented.

Hypervelocity impacts on HST solar arrays and the debris and meteoroids population

Accurate debris and meteoroid flux models are crucial for the design of manned and unmanned space missions. For the most abundant particle sizes smaller than a few millimetres, knowledge of the populations can only be gained from in situ detectors or the analysis of retrieved space hardware. The measurement of impact flux from exposed surfaces improves with increased surface area and exposure time. A post-flight impact investigation was initiated by the European Space Agency to record and analyse the impact fluxes and any potential resulting damage on the two flexible solar arrays of the Hubble Space Telescope. The arrays were deployed during the first Hubble Space Telescope servicing mission in December 1993 and retrieved in March 2002. They have a total exposed surface area of roughly 120 m 2, including 42 m 2 covered with solar cells. This new Hubble post-flight impact study follows a similar activity undertaken after the retrieval of one of the first solar arrays, in 1993. The earlier study provided the first opportunity for a numerical survey of damage to exposed surfaces from more than 600 km altitude, and of impacts from particles larger than 1 mm. The results have proven very valuable in validation of important flux model regimes. The second set of Hubble solar arrays has again provided an unrivalled opportunity to measure the meteoroid and debris environment, now sampled during a long interval in low Earth orbit, and to identify changes in the space debris environment since the previous survey. The retrieved solar array wings exhibit thousands of craters, many of which are visible to the naked eye. A few hundred impacts have completely penetrated the 0.7 mm thick array. The largest impact features are about 7–8 mm in diameter. The cover glass of the solar cells is particularly well suited to the recognition of small impact features by optical and electron microscopy. In this paper, we present the first results of the impact survey. Data upon the abundance of craters of specific measured size ranges are plotted as cumulative flux curves, and compared to the results of model predictions. The most significant change to the particle flux since 1993 is a decrease in the small debris population.

Detection of small radar cross-section orbital debris with the Haystack radar

NASA has been making statistical measurements of the orbital debris environment for more than a decade using the MIT Lincoln Laboratory Haystack radar. The goal has been to characterize the environment for debris sizes as small as possible. Like all sensors which operate in the presence of noise, the Haystack radar has limited sensitivity. As the returned energy from small targets begins to approach the sensitivity limit of the radar, the probability-of-detection decreases, eventually approaching zero. The slope of the cumulative size distribution of debris begins to flatten out. This paper explores the possibility of extending the cumulative size distribution to smaller sizes by adjusting the distribution for probability-of-detection.

The earth orbiting space debris

The space debris population is similar to the asteroid belt, since it is subject to a process of high-velocity mutual collisions that affects the long-term evolution of its size distribution. Presently, more than 10 000 artificial debris particles with diameters larger than 10 cm (and more than 300 000 with diameters larger than 1 cm) are orbiting the Earth, and are monitored and studied by a large network of sensors around the Earth. Many objects of different kind compose the space debris population, produced by different source mechanisms ranging from high energy fragmentation of large spacecraft to slow diffusion of liquid metal. The impact against a space debris is a serious risk that every spacecraft must face now and it can be evaluated with ad-hoc algorithms. The long term evolution of the whole debris population is studied with computer models allowing the simulation of all the known source and sink mechanisms. One of these codes is described in this paper and the evolution of the debris environment over the next 100 years, under different traffic scenarios, is shown, pointing out the possible measures to mitigate the growth of the orbital debris population. .

Detection of Small LEO Debris with Line Detection Method

This paper proposes a new method known as “the line detection method” to detect small pieces of low Earth orbit (LEO) debris. A direction is assumed for the line created by small LEO debris on a CCD image and the values of pixels along that direction are accumulated to improve the signal-to-noise ratio. This method can detect LEO debris that is 30 to 40 times darker than debris that can be detected by usual methods. We tested this method by using the 35-cm telescope and back-illuminated CCD camera at the Mt. Nyukasa Astronomical Observatory. One small piece of LEO debris with a radar cross section of 0.0047 m2 was detected. By using this method, the 1-m telescope and back-illuminated wide-field camera at the Bisei Spaceguard Center (BSGC) are expected to be able to detect LEO debris with a size of a few cm. The line detection method will be used to probe the LEO small debris environment and contribute to solving the space debris problem.

Design of Orbit Debris Environment and Collision Alert System

Since the number of targets near the earth orbit has already been beyond 9000, it is necessary and much important to analyze targets near the mission orbit to bring the mission to access both before the launch and during the orbital mission. NORAD maintains general element perturbation element sets (Two-Line Element Sets, TLEs) on all resident objects. In turn, these element sets are provided to users. These element sets are periodically refined so as to maintain a reasonable prediction capability on all objects. At the same time, NORAD developed a set of models named SGP/SDP series as models for propagation of NORAD element sets. Five mathematical models for prediction of satellite position and velocity are available. And the NORAD element sets are currently generated with either SGP4 or SDP4 depending on whether the satellite is near-Earth or deep-space. These two models, SGP4 for near-earth objects and SDP4 for deep space objects, are widely used in satellite tracking software and can produce very accurate results when used with current NORAD two-line element datum. A brief review is taken at these element sets and propagation models first. Then through the precision analysis, it is believed that using SGP4/SDP4 models for taking quick collision alert among targets is suitable. Based on this conclusion, an orbit debris environment and collision alert system was designed. In this system, targets and the corresponding TLEs are saved in a database based on MS SQL Server, and the data visual is realized by OpenGL. The orbit propagation models being used is SGP4/SDP4 since this model is the generator of current TLEs and will be supported in the future.

Population models of space debris

More than 300 000 artificial debris particles with diameter larger than 1 cm are orbiting the Earth. The space debris population is similar to the asteroid belt, since it is subject to a process of high-velocity mutual collisions that affects the long-term evolution of its size distribution. The near–Earth space can be divided in three major regions where orbital debris is of concern: Low Earth Orbits (LEOs), below about 2000 km, Geosynchronous Orbits (GEOs), at an altitude of about 36000 km and the Medium Earth Orbits (MEOs) in between. The issues are in principle the same in the three regions, nevertheless they require different approaches and solutions. The space debris are composed by several different populations according to their source and their orbital region. A description of the nature and dynamics of the different populations in the low, medium and high orbital regimes is given. The impact risk posed by these debris is then briefly outlined.The long term evolution of the whole debris population can be studied with computer models allowing the simulation of all the known source and sinks mechanisms. One of these codes is described and the evolution of the debris environment, over the next 100 years, under different traffic scenarios is shown, pointing out the possible measures to mitigate the growth of the orbital debris population.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Toward a comprehensive GEO debris measurement strategy

In recent years there has been increasing interest in the effects of orbital debris on the Geosynchronous Earth Orbit (GEO) environment. This region has great economic importance that is only expected to grow stronger in the foreseeable future. The lifetime of any debris created is very long, so that there is no effective sink to remove the debris in a timely manner. Considerable resources have been brought to bear to understand the current debris environment at GEO. A number of optical telescopes in different countries are now systematically making observations of this region specifically to understand the debris population. We are now at a stage where we can begin to answer specific questions about orbital debris in these orbits, but what are these questions? Are we asking the right questions? Are the observations we are pursuing answering the most important questions? Are there changes needed in the observation techniques to better address the most important issues? Are there changes needed in the types of instruments to answer the most important questions? This paper will outline the broad questions that GEO observations should be designed to answer. I will discuss how observations so far have begun to answer those questions and where they need to concentrate in the future. This will include discussions of the benefits and limitations of the statistical sampling methodology versus the cataloguing methodology. I hope to provide a framework for future observations that will be of benefit to all GEO users.