Modeling of LEO orbital debris populations for ORDEM2008

The NASA Orbital Debris Engineering Model, ORDEM2000, is in the process of being updated to a new version: ORDEM2008. The data-driven ORDEM covers a spectrum of object size from 10 μm to greater than 1 m, and ranging from LEO (low Earth orbit) to GEO (geosynchronous orbit) altitude regimes. ORDEM2008 centimeter-sized populations are statistically derived from Haystack and HAX (the Haystack Auxiliary) radar data, while micron-sized populations are estimated from shuttle impact records. Each of the model populations consists of a large number of orbits with specified orbital elements, the number of objects on each orbit (with corresponding uncertainty), and the size, type, and material assignment for each object. This paper describes the general methodology and procedure commonly used in the statistical inference of the ORDEM2008 LEO debris populations. Major steps in the population derivations include data analysis, reference-population construction, definition of model parameters in terms of reference populations, linking model parameters with data, seeking best estimates for the model parameters, uncertainty analysis, and assessment of the outcomes. To demonstrate the population-derivation process and to validate the Bayesian statistical model applied in the population derivations throughout, this paper uses illustrative examples for the special cases of large-size (>1 m, >32 cm, and >10 cm) populations that are tracked by SSN (the Space Surveillance Network) and also monitored by Haystack and HAX radars operating in a staring mode.     

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.     

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.     

A modelling of the interaction between electromagnetic radiation and West Ford needles clusters: a preliminary study

Radar observations of small space debris made with the Goldstone radar facility have shown that a population of small particles do exist at an altitude larger than 2000 km. This population has been identified with clusters of copper needles created upon the deployment of the West Ford needles project, by MIDAS satellites in 1961 and 1963. This set of particles is either not taken into account in the debris models or only added to other populations. But owing to their specific physical and geometrical properties, the sunlight they scatter could affect, for instance, the spaceborne astronomical experiments. In order to assess this threat it is necessary to model their physical and geometric characteristics. A preliminary modelling using spheres suggests that some improvement is needed. We propose a better approach with long conductive cylinders as a model for the clusters. The interaction of solar light with these particles allows us to estimate the spurious flux scattered inside spaceborne instruments. We conclude that for a given spatial configuration light flashes can affect seriously the operating mode of high sensitivity instruments.     

雷达波束驻留模式下空间碎片数量的置信区间估计

碎片数量估计是空间碎片环境统计特征描述的重要内容之一,对于空间碎片环境模型验证、航天器碰撞风险分析以及碎片数量增长趋势预测有重要意义.针对波束指向正东、正南任意仰角的雷达波束驻留(Beam-park)模式(天顶指向是波束指向仰角为90°时的特例),给出了一种估计碎片数量置信区间的方法.对于给定轨道高度范围内一个具有穿越雷达波束可能性(即雷达散射截面足够大,且轨道倾角相对测站纬度足够大)的碎片,将其是否真正穿越波束这一随机事件用(0-1)分布来建模,根据所采集的轨道高度和倾角数据,计算出该轨道高度范围内碎片穿越波束的平均概率,进而采用中心极限定理来估计碎片数量的置信区间.仿真结果表明了方法的有效性.      

基于相控阵雷达波束篱笆的空间碎片数量与分布估计方法

随着载人航天与空间站等航天活动的增多,不能有效防护、也无法定期跟踪和编目的小尺寸(尤其是1～10 cm)碎片的危害越来越受到关注,这些碎片信息的获取依赖于统计采样技术.针对简化的相控阵雷达波束篱笆空间碎片探测模式,提出了一种采用统计技术估计空间碎片总数量以及高度和倾角分布的方法.将碎片穿越波束篱笆的过程用Poisson分布来建模,根据观测时段内穿越波束篱笆目标的平均到达率及测量的轨道高度和倾角数据来估计给定轨道高度范围或倾角范围内碎片的数量,进而得到碎片的总数量以及碎片数量随轨道高度或倾角的分布.在获取雷达散射截面信息时,该方法还可用于估计碎片数量随尺寸的分布.通过仿真实验验证了该方法的有效性.      

R3D-B2 – Measurement of ionizing and solar radiation in open space in the BIOPAN 5 facility outside the FOTON M2 satellite

Solar and space radiation have been monitored using the R3D-B2 radiation risks radiometer-dosimeter on board a recent space flight on the Russian satellite Foton M2 within the ESA Biopan 5 facility mounted on the outside of the satellite exposed to space conditions. The solar radiation has been assayed in four wavelength bands (UV-C, 170–280 nm, UV-B, 280–315 nm), UV-A (315–400 nm) and PAR (photosynthetic active radiation, 400–700 nm). The data show an increasing tumbling rotation of the satellite during the mission. The photodiodes do not show a cosine response to the incident light which has been corrected. After calibration of the signals using the extraterrestrial spectrum, doses have been calculated for each orbit, for each day and for the total mission as basic data for the biological material which has been exposed in parallel in the Biopan facility. Cosmic ionizing radiation has been monitored and separated in 256 deposited energy spectra, which were further used for determination of the absorbed dose rate and flux. Basic data tables were prepared to be used by other Biopan 5 experiments. The paper summarizes the results for the Earth radiation environment at the altitude (262–304 km) of the Foton M2 spacecraft. Comparisons with the predictions of NASA Earth radiation environment experimental models AE-8 and AP-8, and the PSB97 model are also presented, which calculate the fluxes of ionizing radiation from a simulation. AP-8 is a model for trapped radiation.     

Antarctic meteor observations using the Davis MST and meteor radars

This paper presents the meteor observations obtained using two radars installed at Davis (68.6°S, 78.0°E), Antarctica. The Davis MST radar was installed primarily for observation of polar mesosphere summer echoes, with additional transmit and receive antennas installed to allow all-sky interferometric meteor radar observations. The Davis meteor radar performs dedicated all-sky interferometric meteor radar observations. The annual count rate variation for both radars peaks in mid-summer and minimizes in early Spring. The height distribution shows significant annual variation, with minimum (maximum) peak heights and maximum (minimum) height widths in early Spring (mid-summer). Although the meteor radar count rate and height distribution variations are consistent with a similar frequency meteor radar operating at Andenes (69.3°N), the peak heights show a much larger variation than at Andenes, while the count rate maximum-to-minimum ratios show a much smaller variation. Investigation of the effects of the temporal sampling parameters suggests that these differences are consistent with the different temporal sampling strategies used by the Davis and Andenes meteor radars. The new radiant mapping procedure of [Jones, J., Jones, W., Meteor radiant activity mapping using single-station radar observations, Mon. Not. R. Astron. Soc., 367(3), 1050–1056, doi: 10.1111/j.1365-2966.2006.10025.x, 2006] is investigated. The technique is used to detect the Southern delta-Aquarid meteor shower, and a previously unknown weak shower. Meteoroid speeds obtained using the Fresnel transform are presented. The diurnal, annual, and height variation of meteoroid speeds are presented, with the results found to be consistent with those obtained using specular meteor radars. Meteoroid speed estimates for echoes identified as Southern delta-Aquarid and Sextantid meteor candidates show good agreement with the theoretical pre-atmospheric speeds of these showers (41 km s⁻¹ and 32 km s⁻¹, respectively). The meteoroid speeds estimated for these showers show decreasing speed with decreasing height, consistent with the effects of meteoroid deceleration. Finally, we illustrate how the new radiant mapping and meteoroid speed techniques can be combined for unambiguous meteor shower detection, and use these techniques to detect a previously unknown weak shower.     

Determination of station positions and velocities from laser ranging observations to Ajisai,Starlette and Stella satellites

The positions and velocities of the four Satellite Laser Ranging (SLR) stations: Yarragadee (7090), Greenbelt (7105), Graz (7839) and Herstmonceux (7840) from 5-year (2001–2005) SLR data of low orbiting satellites (LEO): Ajisai, Starlette and Stella were determined. The orbits of these satellites were computed from the data provided by 20 SLR stations. All orbital computations were performed by means of NASA Goddard’s GEODYN-II program. The geocentric coordinates were transformed to the topocentric North–South, East–West and Vertical components in reference to ITRF2005. The influence of the number of normal points per orbital arc and the empirical acceleration coefficients on the quality of station coordinates was studied. To get standard deviation of the coordinates determination lower than 1 cm, the number of the normal points per site had to be greater than 50. The computed positions and velocities were compared to those derived from LAGEOS-1/LAGEOS-2 data. Three parameters were used for this comparison: station coordinates stability, differences from ITRF2005 positions and velocities. The stability of coordinates of LEO satellites is significantly worse (17.8 mm) than those of LAGEOS (7.6 mm), the better results are for Ajisai (15.4 mm) than for Starlette/Stella (20.4 mm). The difference in positions between the computed values and ITRF2005 were little bit worse for Starlette/Stella (6.6 mm) than for LAGEOS (4.6 mm), the results for Ajisai were five times worse (29.7 mm) probably due to center of mass correction of this satellite. The station velocities with some exceptions were on the same level (≈1 mm/year) for all satellites. The results presented in this work show that results from Starlette/Stella are better than those from Ajisai for station coordinates determination. We can applied the data from LEO satellites, especially Starlette and Stella for determination of the SLR station coordinates but with two times lower accuracy than when using LAGEOS data.     

Gravity waves and wind-shear in the MLT at 23°S

We have used the technique suggested by Hocking [Hocking, W. A new approach to momentum flux determinations using SKiYMET meteor radars. Ann. Geophys. 23, 2005.] to derive short period wind variances in the 80–100 km region from meteor radar data. We find that these fluctuating winds, assumed to correspond to gravity waves and turbulence, are closely correlated with the vertical shear of the horizontal tidal winds. This close correlation suggests that in situ wind shear may be a major source of gravity waves and turbulence in the MLT. If this is the case, gravity waves generated in the troposphere and propagating up to the MLT region, generally assumed to constitute an important influence on the climatology of the region, may be a less important source of energy and momentum in the 80–100 km region than has been hitherto believed.     

Ozone destruction by solar electrons in relation to solar variability and the terrestrial latitude

Precipitating electrons from the radiation belts with energies greater than from 150 keV to 5 MeV have been correlated with ozone data of a large number of stations located within 40–70° N. Energetic electrons have been collected by the low altitude polar Russian satellite METEOR while ozone data have been compiled from almost ninety (90) stations located all over the world within the latitude zone 40–70° N.     

Identification of a debris cloud from the nuclear powered SNAPSHOT satellite with haystack radar measurements

Data from the Massachusetts Institute of Technology Lincoln Laboratory Long Range Imaging Radar (known as the Haystack radar) have been used in the past to examine families of objects from individual satellite breakups or families of orbiting objects that can be isolated in altitude and inclination. This is possible because, for some time after a breakup, the debris cloud of particles can remain grouped together in similar orbit planes. This cloud will be visible to the radar, in fixed staring mode, for a short time twice each day, as the orbit plane moves through the field of view. There should be a unique three-dimensional pattern in observation time, range, and range rate which can identify the cloud. Eventually, through slightly differing precession rates of the right ascension of ascending node of the debris cloud, the observation time becomes distributed so that event identification becomes much more difficult.     

The ratio of hazardous meteoroids to orbital debris in near-Earth space

Orbital debris is known to pose a substantial threat to Earth-orbiting spacecraft at certain altitudes. For instance, the orbital debris flux near Sun-synchronous altitudes of 600–800 km is particularly high due in part to the 2007 Fengyun-1C anti-satellite test and the 2009 Iridium-Kosmos collision. At other altitudes, however, the orbital debris population is minimal and the primary impactor population is not man-made debris particles but naturally occurring meteoroids. While the spacecraft community has some awareness of the risk posed by debris, there is a common misconception that orbital debris impacts dominate the risk at all locations. In this paper, we present a damage-limited comparison between meteoroids and orbital debris near the Earth for a range of orbital altitude and inclination, using NASA’s latest models for each environment. Overall, orbital debris dominates the impact risk between altitudes of 600 and 1300 km, while meteoroids dominate below 270 km and above 4800 km.     

Comparison of mesopause region meteor radar winds,medium frequency radar winds and low frequency drifts over Germany

During 2004 and 2005 measurements of mesospheric/lower thermospheric (80–100 km) winds have been carried out in Germany using three different ground-based systems, namely a meteor radar (36.2 MHz) at the Collm Observatory (51.3°N, 13°E), a MF radar (3.18 MHz) at Juliusruh (54.6°N, 13.4°E) and the LF D1 measurements using a transmitter (177 kHz) at Zehlendorf near Berlin and receivers at Collm with the reflection point at 52.1°N, 13.2°E. This provides the possibility of comparing the results of different radar systems in nearly the same measuring volume. Meteor radar winds are generally stronger than the winds observed by MF and especially by LF radars. This difference is small near 80 km but increases with height. The difference between meteor radar and medium frequency radar winds is larger during winter than during summer, which might indicate an indirect influence of gravity waves on spaced antenna measurements.     

Titan’s new pole: Implications for the Huygens entry and descent trajectory and landing coordinates

The European Space Agency’s Huygens probe separated from the NASA Cassini spacecraft on 25 December 2004, after having been attached for a 7-year interplanetary journey and three orbits around Saturn. The probe reached the predefined NASA/ESA interface point on 14 January 2005 at 09:05:52.523 (UTC). It performed a successful entry and descent sequence and softly landed on Titan’s surface on the same day at 11:38:10.77 (UTC) with a speed of about 4.54 m/s. Since the publication of the official project entry and descent trajectory reconstruction effort by the Descent Trajectory Working Group in 2007 (referred to as DTWG#4) various other efforts have been performed and published. This paper presents an overview of the most relevant reconstructions and compares their methodologies and results. Furthermore, the results of a new reconstruction effort (DTWG#5) are presented, which is based on the same methodology as DTWG#4 but takes into account new estimates of Titan’s pole coordinates which were derived from radar images of different Cassini Titan flybys. It can be shown that the primary effect can be observed in the meridional direction which is represented by a stark southward shift of the trajectory by about 0.3 deg. A much smaller effect is seen in the zonal direction (i.e., less than 0.01 deg in the west to east direction). The revised probe landing coordinates are 192.335 deg W and 10.573 deg S. A comparison of these coordinates with results of recent landing site investigations using visual and radar images of the Cassini VIMS instrument shows excellent agreement of the two independently derived landing coordinates, i.e., longitude and latitude residuals of respectively 0.035 deg and 0.007 deg.     

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.     

An analytical model for the prediction of a micro-dosimeter response function

A rapid analytical procedure for the prediction of a micro-dosimeter response function in low Earth orbit (LEO), correlated with the Space Transportation System (STS, shuttle) Tissue Equivalent Proportional Counter (TEPC) measurements is presented. The analytical model takes into consideration the energy loss straggling and chord length distribution of the detector, and is capable of predicting energy deposition fluctuations in a cylindrical micro-volume of arbitrary aspect ratio (height/diameter) by incoming ions through both direct and indirect (δ ray) events. At any designated (ray traced) target point within the vehicle, the model accepts the differential flux spectrum of Galactic Cosmic Rays (GCRs) and/or trapped protons at LEO as input. On a desktop PC, the response function of TEPC for each ion in the GCR/trapped field is computed at the average rate of 30 s/ion. The ionizing radiation environment at LEO is represented by O’Neill’s GCR model (2004), covering charged particles in the 1 ? Z ? 28 range. O’Neill’s free space GCR model is coupled with the Langley Research Center (LaRC) angular dependent geomagnetic cutoff model to compute the transmission coefficient in LEO. The trapped proton environment is represented by a LaRC developed time dependent procedure which couples the AP8MIN/AP8MAX, Deep River Neutron Monitor (DRNM) and F10.7 solar radio frequency measurements. The albedo neutron environment is represented by the extrapolation of the Atmospheric Ionizing Radiation (AIR) measurements. The charged particle transport calculations correlated with STS 51 and 114 flights are accomplished by using the most recent version (2005) of the LaRC deterministic High charge (Z) and Energy TRaNsport (HZETRN) code. We present the correlations between the TEPC model predictions (response function) and TEPC measured differential/integral spectra in the lineal energy (y) domain for both GCR and trapped protons, with the conclusion that the model correctly accounts for the increase in flux at low y values where energetic ions are the primary contributor. We further discuss that, even with the incorporation of angular dependency in the cutoffs, comparison of the GCR differential/integral flux between STS 51 and 114 TEPC measured data and current calculations indicates that there still exists an underestimation by the simulations at low to mid range y values. This underestimation is partly related the exclusion of the secondary pion particle production from the current version of HZETRN.     

Solar EUV flux variation and flare brightenings

On 2010 February 8, the Extreme ultraviolet (EUV) flux variation in 195 Å and flare brightening has been examined in different sizes of active regions by using SOHO/EIT, MDI and Hα$\alpha$ observational data. These three active regions represent a large active region with a sunspot group, a moderate active region without a sunspot and a small region with weak plage in Hα$\alpha$ band respectively. Our study shows that the main full disk EUV flux comes from active regions, especially from large active regions. The sudden increases of EUV flux are corresponding to the EUV flare brightenings. For the large active region, the local EUV 195 Å flux peaks are well correlated to that of the GOES X-ray flux. The EUV 195 Å flux peaking time of M-class flares delay GOES X-ray flux a few minutes. For the moderate active region, the local EUV 195 Å flux is not well correlated to GOES X-ray flux. The EUV 195 Å flare brightenings in the moderate active region appeared in the duration of sudden increase of its own local EUV flux. For the small active region, the local EUV 195  Å flux varied almost independently of the GOES X-ray flux. Our study suggests that for an active region its local EUV 195 Å flux is more closely correlated to the EUV flare brightening than the full disk GOES X-ray flux.     

Photoelectron flux variations observed from the FAST satellite

This paper examines high resolution (ΔE/E = 0.15) photoelectron energy spectra from 10 eV to 1 keV, created by solar irradiances between 1.2 and 120 nm. The observations were made from the FAST satellite at ∼3000 km, equatorward of the auroral oval for the July–August, 2002 solar rotation. These data are compared with the solar irradiance observed by the Solar EUV Experiment (SEE) on the Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) satellite and fluxes calculated using the Field Line Interhemispheric Plasma (FLIP) code. The 41 eV photoelectron flux, which corresponds to solar EUV fluxes near 20 nm, shows a clear solar rotation variation in very good agreement with the EUV flux measurements. This offers the possibility that the 41 eV photoelectron flux could be used as a check on measured solar EUV fluxes near 20 nm. Because of unexpected noise, the solar rotation signal is not evident in the integral photoelectron flux between 156 and 1000 eV corresponding to EUV wavelengths between 0.1 and 7 nm measured by the SEE instrument. Examination of daily averaged photoelectron fluxes at energies between 25 and 500 eV show significant changes in the photoelectron spectra in response X and M class flares. The intensity of photoelectrons produced in this energy region is primarily due to two very narrow EUV wavelength regions at 2.3 and 3 nm driving Auger photoionization in O at 500 eV and N₂ at ∼360 eV. Comparison of calculated and daily averaged electron fluxes shows that the HEUVAC model solar spectrum used in the FLIP code does not reproduce the observed variations in photoelectron intensity. In principle, the 21 discrete photoelectron energy channels could be used to improve the reliability of the solar EUV fluxes at 2.3 and 3 nm inferred from broad band observations. In practice, orbital biases in the way the data were accumulated and/or noise signals arising from natural and anthropogenic longitudinally restricted sources of ionization complicate the application of this technique.     

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.