Faster algorithm of debris cloud orbital character from spacecraft collision breakup

Space debris is polluting the space environment. Collision fragment is its important source. NASA standard breakup model, including size distributions, area-to-mass distributions, and delta velocity distributions, is a statistic experimental model used widely. The general algorithm based on the model is introduced. But this algorithm is difficult when debris quantity is more than hundreds or thousands. So a new faster algorithm for calculating debris cloud orbital lifetime and character from spacecraft collision breakup is presented first. For validating the faster algorithm, USA 193 satellite breakup event is simulated and compared with general algorithm. Contrast result indicates that calculation speed and efficiency of faster algorithm is very good. When debris size is in 0.01–0.05 m, the faster algorithm is almost a hundred times faster than general algorithm. And at the same time, its calculation precision is held well. The difference between corresponding orbital debris ratios from two algorithms is less than 1% generally.     

Properties of the high area-to-mass ratio space debris population at high altitudes

In the framework of its space debris research activities ESA established an optical survey program to study the space debris environment at high altitudes, in particular in the geostationary ring and in the geostationary transfer orbit region. The Astronomical Institute of the University of Bern (AIUB) performs these surveys on behalf of ESA using ESA’s 1-m telescope in Tenerife. Regular observations were started in 1999 and are continued during about 120–140 nights per year. Results from these surveys revealed a substantial amount of space debris at high altitudes in the size range from 0.1 to 1 m. Several space debris populations with different dynamical properties were identified in the geostationary ring. During the searches for debris in the geostationary transfer orbit region a new population of objects in unexpected orbits, where no potential progenitors exist, was found. The orbital periods of these objects are clustered around one revolution per day; the eccentricities, however, are scattered between 0 and 0.6. By following-up some of these objects using the ESA telescope and AIUB’s 1-m telescope in Zimmerwald, Switzerland, it was possible to study the properties of this new population. One spectacular finding from monitoring the orbits over time spans of days to months is the fact that these objects must have extreme area-to-mass ratios, which are by several orders of magnitudes higher than for ‘normal-type’ debris. This in turn supports the hypothesis that the new population actually is debris generated in or near the geostationary ring and which is in orbits with periodically varying eccentricity and inclination due to perturbations by solar radiation pressure. In order to further study the nature of these debris, multi-color and temporal photometry (light curves) were acquired with the Zimmerwald telescope. The light curves show strong variations over short time intervals, including signals typical for specular reflections. Some objects exhibit distinct periodic variations with periods ranging from 10 to several 100 s. All this is indicative for objects with complicated shapes and some highly reflective surfaces.     

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.     

On the effect of considering more realistic particle shape and mass parameters in MMOD risk assessments

One of the primary mission risks tracked in the development of all spacecraft is that due to micro-meteoroids and orbital debris (MMOD). Both types of particles, especially those larger than 0.1 mm in diameter, contain sufficient kinetic energy due to their combined mass and velocities to cause serious damage to crew members and spacecraft. The process used to assess MMOD risk consists of three elements: environment, damage prediction, and damage tolerance. Orbital debris risk assessments for the Orion vehicle, as well as the Shuttle, Space Station and other satellites use ballistic limit equations (BLEs) that have been developed using high speed impact test data and results from numerical simulations that have used spherical projectiles. However, spheres are not expected to be a common shape for orbital debris; rather, orbital debris fragments might be better represented by other regular or irregular solids. In this paper we examine the general construction of NASA’s current orbital debris (OD) model, explore the potential variations in orbital debris mass and shape that are possible when using particle characteristic length to define particle size (instead of assuming spherical particles), and, considering specifically the Orion vehicle, perform an orbital debris risk sensitivity study taking into account variations in particle mass and shape as noted above. While the results of the work performed for this study are preliminary, they do show that continuing to use aluminum spheres in spacecraft risk assessments could result in an over-design of its MMOD protection systems. In such a case, the spacecraft could be heavier than needed, could cost more than needed, and could cost more to put into orbit than needed. The results obtained in this study also show the need to incorporate effects of mass and shape in mission risk assessment prior to first flight of any spacecraft as well as the need to continue to develop/refine BLEs so that they more accurately reflect the shape and material density variations inherent to the actual debris environment.     

Design and analysis of an extended mission of CE-2: From lunar orbit to Sun–Earth L2 region

Chang’E-2 (CE-2) has firstly successfully achieved the exploring mission from lunar orbit to Sun–Earth L2 region. In this paper, we discuss the design problem of transfer trajectory and at the same time analyze the visible segment of Tracking, Telemetry & Control (TT&C) system for this mission. Firstly, the four-body problem of Sun–Earth–Moon and Spacecraft can be decoupled in two different three-body problems (Sun–Earth + Moon Restricted Three-Body Problems (RTBPs) and Earth–Moon ephemeris model). Then, the transfer trajectory segments in different model are computed, respectively, and patched by Poincaré sections. The full-flight trajectory including transfer trajectory from lunar orbit to Sun–Earth L2 region and target Lissajous orbit is obtained by the differential correction method. Finally, the visibility of TT&C system at the key time is analyzed. Actual execution of CE-2 extended mission shows that the trajectory design of CE-2 mission is feasible.     

Active debris removal of multiple priority targets

Today’s space debris environment shows major concentrations of objects within distinct orbital regions for nearly all size regimes. The most critical region is found at orbital altitudes near 800 km with high declinations. Within this region many satellites are operated in so called sun-synchronous orbits (SSO). Among those, there are Earth observation, communication and weather satellites. Due to the orbital geometry in SSO, head-on encounters with relative velocities of about 15 km/s are most probable and would thus result in highly energetic collisions, which are often referred to as catastrophic collisions, leading to the complete fragmentation of the participating objects. So called feedback collisions can then be triggered by the newly generated fragments, thus leading to a further population increase in the affected orbital region. This effect is known as the Kessler syndrome.     

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.     

Debris flux comparisons from the Goldstone Radar,Haystack Radar,and Hax Radar prior,during, and after the last solar maximum

The continual monitoring of the low Earth orbit (LEO) debris environment using highly sensitive radars is essential for an accurate characterization of these dynamic populations. Debris populations are continually evolving since there are new debris sources, previously unrecognized debris sources, and debris loss mechanisms that are dependent on the dynamic space environment. Such radar data are used to supplement, update, and validate existing orbital debris models. NASA has been utilizing radar observations of the debris environment for over a decade from three complementary radars: the NASA JPL Goldstone radar, the MIT Lincoln Laboratory (MIT/LL) Long Range Imaging Radar (known as the Haystack radar), and the MIT/LL Haystack Auxiliary radar (HAX). All of these systems are highly sensitive radars that operate in a fixed staring mode to statistically sample orbital debris in the LEO environment. Each of these radars is ideally suited to measure debris within a specific size region. The Goldstone radar generally observes objects with sizes from 2 mm to 1 cm. The Haystack radar generally measures from 5 mm to several meters. The HAX radar generally measures from 2 cm to several meters. These overlapping size regions allow a continuous measurement of cumulative debris flux versus diameter from 2 mm to several meters for a given altitude window. This is demonstrated for all three radars by comparing the debris flux versus diameter over 200 km altitude windows for 3 nonconsecutive years from 1998 to 2003. These years correspond to periods before, during, and after the peak of the last solar cycle. Comparing the year to year flux from Haystack for each of these altitude regions indicate statistically significant changes in subsets of the debris populations. Potential causes of these changes are discussed. These analysis results include error bars that represent statistical sampling errors.     

Two-spacecraft observations of reconnection at the magnetopause: Model results and data comparison

We revisit an example of “quasi-steady” magnetic reconnection at the dayside magnetopause on February 11, 1998, observed by Equator-S and Geotail at the dawnside magnetopause. Phan et al. [Phan, T.D. et al., 2000. Extended magnetic reconnection at the Earth’s magnetopause from detection of bi-directional jets. Nature 404, 848–850.] reported oppositely directed jets at these spacecrafts and inferred a length of the reconnection line of about 38R_E. Pinnock et al. [Pinnock, M., Chisham, G., Coleman, I.J., Freeman, M.P., Hairston, M., Villain, J.-P., 2003. The location and rate of dayside reconnection during an interval of southward interplanetary magnetic field. Ann. Geophys. 21, 1467–1482.] used measurements from SuperDARN radars to show that the reconnection electric field was variable. Here we complement this work by obtaining snapshots of the reconnection electric field from the in situ observations. To do this, we apply a reconstruction method based on a model of compressible Petschek-type magnetic reconnection. This independent method uses magnetic field observations as input data to calculate the reconnection electric field. We obtain average values of E_rec in the range of 0.4–2.4 mV/m. Further we infer a distance perpendicular to the reconnection line of 0.4–0.6R_E. The model results are compared with the two studies mentioned above. It thus appears that while the transfer of momentum for this event is indeed large-scale, the actual rate depends on the time it is measured.     

Lunar apex–antapex cratering asymmetry as an impactor recorder in the Earth–Moon system

The degree of apex–antapex cratering asymmetry of a synchronously rotating satellite primarily depends on the mean encounter velocity of impactors with respect to the planetary system and the orbital velocity of the satellite. This means that we can estimate the mean encounter velocity of impactors by observing the apex–antapex cratering asymmetry, if the relationship between these is known. To apply this technique to the Moon, we attempt to derive the relationship between the mean encounter velocity of impactors and the degree of the lunar cratering asymmetry as a function of time, considering the temporal variation in the lunar orbital velocity during the last 4.0 Gyr. We used the cratering asymmetry of Zahnle et al. [Zahnle, K., Schenk, P., Sobieszczyk, S. et al. Differential cratering of synchronously rotating satellites by ecliptic comets. Icarus 153, 111–129, 2001] to obtain the relationship. Applying this relationship enables us to estimate the impactor’s velocity of the Earth–Moon system from an investigation of the spatial distribution of lunar craters. Furthermore, we re-evaluate the cratering asymmetry’s influence on lunar cratering chronology.     

Use of coated silicon field emitters as neutralisers for fundamental physics space missions

Spacecraft neutralisers are required as part of the ion propulsion system for accurate station keeping in fundamental physics missions. This paper describes the use of thin layers of insulating materials as coatings for the gated silicon field emitter array structure used in a spacecraft neutraliser. These thin coatings are postulated to reduce power consumption and reduce overheating. The power consumption and lifetime of aluminium nitride and amorphous hydrogenated diamond-like carbon coatings have been tested by current–voltage and endurance tests. Diamond-like carbon coatings were promising, performing better in endurance tests than uncoated samples, but further work is required to characterise the coating’s physical properties and its effects on field emission. The thermal conductivity of the coating material had little effect on measured sample lifetimes. Aluminium nitride had reduced power consumption compared to diamond-like carbon coated and uncoated samples. A thin (∼5 nm) layer of aluminium nitride was found to be optimal, meeting European Space Agency specifications for the neutraliser engineering model.     

Improved orbit predictions using two-line elements

The density of orbital space debris constitutes an increasing environmental challenge. There are two ways to alleviate the problem: debris mitigation and debris removal. This paper addresses collision avoidance, a key aspect of debris mitigation. We describe a method that contributes to achieving a requisite increase in orbit prediction accuracy for objects in the publicly available two-line element (TLE) catalog. Batch least-squares differential correction is applied to the TLEs. Using a high-precision numerical propagator, we fit an orbit to state vectors derived from successive TLEs. We then propagate the fitted orbit further forward in time. These predictions are validated against precision ephemeris data derived from the international laser ranging service (ILRS) for several satellites, including objects in the congested sun-synchronous orbital region. The method leads to a predicted range error that increases at a typical rate of 100 m per day, approximately a 10-fold improvement over individual TLE’s propagated with their associated analytic propagator (SGP4). Corresponding improvements for debris trajectories could potentially provide conjunction analysis sufficiently accurate for an operationally viable collision avoidance system based on TLEs only.     

基于解体事件的空间碎片轨道演化算法研究

针对航天器解体事件所生成的空间碎片的演化过程,进行了数学分析,确定了新生成的空间碎片的速度增量,在该增量作用下碎片轨道会发生变更,本文根据该增量得出了空间碎片在轨道变更后的轨道根数,分析了在大气阻力摄动作用下,空间碎片的数目和轨道分布的演化情况,给出了相关结果,结果表明此算法可行。     

The impact of alternative mission models on the future orbital debris environment

In reviewing discussions of future directions for space activity, it becomes obvious that there are a large number of groups formulating a wide diversity of plans for the future use of space. These plan alternatives are being made to account for user needs, technology development constraints, economic constraints, and launch support, and each of the plans will have direct or indirect effects on the orbital debris environment in terms of mass to orbit, deposition of operational debris, and control of accidental breakups. Thus it is important to develop the ability to project future debris states for a range of possible space traffic scenarios. The impact that these possible traffic environments would have on space operations forms the basis for studies of alternative options for the usage of space. In this paper, the effects on the orbital debris environment of a base-line mission model and two alternatives are investigated, using a numerical debris environment simulation code under development at JSC.     

Model of energetic populations at Ganymede,implications for an orbiter

A model is developed to study the energetic particle populations in Ganymede’s magnetosphere. The main objective is to estimate to what extent the moon could protect an orbiter from radiations. Using Liouville’s theorem, the phase space density of particles coming from Jupiter’s magnetosphere is calculated at any point of Ganymede’s environment. Up to energies of ∼50–100 keV for ions and ∼10–20 MeV for electrons, Ganymede’s magnetic field appears to be able to form distinctive populations as loss-cones over the polar caps and radiation belts. At larger energies, these features are blurred by Larmor radius effects; the moon absorption simply creates a quasi-isotropic layer of ∼500 km thickness where the flux is reduced by ∼40–50%. The predictions are compared to Galileo measurements. In particular, we demonstrate the importance of the moon sweeping in reducing the flux over the polar caps. Interestingly, this can be accounted for by assuming that the particles bouncing between Jupiter and Ganymede are ideally scattered in pitch angle and permanently re-fill the loss-cone, which increases the precipitation on Ganymede’s polar cap. In overall, it is estimated that the radiation dose received by an orbiter of Ganymede will be reduced by more than 50–60% compared to the expected dose at Jupiter/Ganymede distance. This should have a positive impact on the design of a future orbiter of Ganymede.     

Effective non-vertical and apparent cutoff rigidities for a cosmic ray latitude survey from Antarctica to Italy in minimum of solar activity

In this paper we will report the results of the computation of cutoff rigidities of vertical and non-vertical incident cosmic ray particles. Non-vertical effective cutoff rigidities have been computed by tracing particle trajectories through the “real” geomagnetic magnetic field comprising the International Geomagnetic Reference Field model (IGRF95, IAGA Division 5 Working Group 8, 1996: Sabaka, T.J., Langel, R.A., Baldwin, R.T., Conrad, J.A. The geomagnetic field, 1900–1995, including the large scale fields from magnetospheric sources and NASA candidate models for the 1995 IGRF revision. J. Geomag. Geoelect. 49, 157–206, 1997.) and the Tsyganenko [Tsyganenko, N.A. A magnetospheric magnetic field model with a warped tail current sheet. Planet. Space Sci. 37, 5–20, 1989.] magnetosphere model. The computation have been done for the backward route (from Antarctica to Italy) of the Italian Antarctic ship survey 1996–1997, for geographic points corresponding to the daily average coordinates of the ship; for zenith angles 15°, 30°, 45° and 60°, and azimuth angles from 0° to 360° in steps of 45°. By means of the obtained non-vertical cutoffs the apparent cutoff rigidities have been calculated. The information on integral multiplicities of secondary neutrons detected by the neutron monitor in dependence of the zenith angle of incoming primary cosmic ray particles have also been used. This information is based on the theoretical calculations of meson-nuclear cascades of primary protons with different rigidities arriving to the Earth’s atmosphere at the zenith angles of 0°, 15°, 30°, 45°, 60° and 75°. The difference between the computed apparent and vertical cutoff rigidities reaches ∼1 GV at rigidities >7–8 GV. At rigidities of 10–16 GV, the difference between the apparent and vertical cutoff rigidities is larger than that obtained earlier by Clem et al. [Clem, J.M., Bieber, J.W., Duldig, M., Evenson, P., Hall, D., Humble, J.E. Contribution of obliquely incident particles to neutron monitor counting rate. J. Geophys. Res. 102, 26919–26926, 1997.] and Dorman et al. [Dorman, L.I., Villoresi, G., Iucci, N., Parisi, M., Tyasto, M.I., Danilova, O.A., Ptitsyna, N.G. Cosmic ray survey to Antarctica and coupling functions for neutron component near solar minimum (1996–1997), 3. Geomagnetic effects and coupling functions. J. Geophys. Res. 105, 21047–21056, 2000.].     

Instability of the present LEO satellite populations

Several studies conducted during 1991–2001 demonstrated, with some assumed launch rates, the future unintended growth potential of the Earth satellite population, resulting from random, accidental collisions among resident space objects. In some low Earth orbit (LEO) altitude regimes where the number density of satellites is above a critical spatial density, the production rate of new breakup debris due to collisions would exceed the loss of objects due to orbital decay.     

Reentry survival analysis of tumbling metallic hollow cylinder

The survival of orbital debris reentering the Earth’s atmosphere is considered. The numerical approach of NASA’s Object Reentry Survival Analysis Tool (ORSAT) is reviewed, and a new equation accounting for reradiation heat loss of hollow cylindrical objects is presented. Based on these, a code called Survivability Analysis Program for Atmospheric Reentry (SAPAR) has been developed, and the new equation for reradiation heat loss is validated. Using this equation in conjunction with the formulation used in ORSAT, a comparative case study on the Delta-II second stage cylindrical tank is given, demonstrating that the analysis using the proposed equation is in good agreement with the actual recovered object when a practical value for thermal emissivity is used. A detailed explanation of the revised formulation is given, and additional simulation results are presented. Finally, discussions are made to address the applicability of the proposed equation to be incorporated in future survival analyses of orbital debris.