Collision Risk Mitigation in Geostationary Orbit

The short- and long-term effects of spacecraft explosions, as a function of the end-of-life re-orbit altitude above the geostationary orbit (GEO), were analyzed in terms of their additional contribution to the debris flux in the GEO ring. The simulated debris clouds were propagated for 72yrs, taking into account all the relevant orbital perturbations.The results obtained show that 6–7 additional explosions in GEO would be sufficient, in the long term, to double the current collision risk with sizable objects in GEO. Unfortunately, even if spacecraft were to re-orbit between 300 and 500km above GEO, this would not significantly improve the situation. In fact, an altitude increase of at least 2000km would have to be adopted to reduce by one order of magnitude the long-term risk of collision among geostationary satellites and explosion fragments. The optimal debris mitigation strategy should be a compromise between the reliability and effectiveness of spacecraft end-of-life passivation, the re-orbit altitude and the acceptable debris background in the GEO ring. However, for as long as the re-orbit altitudes currently used are less than 500km above GEO, new spacecraft explosions must be avoided in order to preserve the geostationary environment over the long term.     

Study of Micrometeoroid and Orbital Debris Effects on the Solar Panels Retrieved from the Space Station “MIR”

A study of micrometeoroid and orbital debris (MMOD) long-term effects on solar cell samples of solar panels returned from the space station MIR has been carried out. Five samples from the solar array, which spent over 10 years in space, have been studied with the help of optical microscopes with magnification up to 1000. Craters with dimensions as small as 1m were registered. Additional large impact features were investigated by observing a large number of cells (150) with an optical microscope of small magnification. The aim of the study was to define morphological and statistical characteristics of samples surface damages as well as the extent of surface erosion caused by MMOD impacts. The results of statistical analysis of the data obtained in this study are shown to correlate with the experimental data obtained in the Hubble Telescope solar panel return experiment, and MMOD flux estimations are in good agreement with modern MMOD models. The relative surface area damaged by impacts of small size (1–100m) MMOD particles is estimated to be 0.01%, while the relative surface area of large impact features (greater than 0.1mm) is estimated to be 0.045%.     

A New Population of the Cusp Suprathermal Protons Formed at Mid-Altitudes: INTERBALL-2 Measurements

A new population of dispersed suprathermal ions descending into the ionosphere is discovered in the cusp region from theINTERBALL-2 measurements at altitudes of 2–3R _E. The proton energies of the population are below the low energy cut-off of the main dispersed proton population of the magnetosheath origin, and its intensity and density are also much lower. For IMF B _z 2 nT the region of the population observations is located partly coincident with (or sometimes poleward from) the main proton population of the cusp proper. The pitch-angle velocity dispersion in the population during a 2-min satellite rotation manifests itself as a typical pitch-angle V together with a velocity dispersion due to poleward convection. The satellite passes chosen for the detailed analysis and modeling lay approximately along the cusp/cleft band from afternoon till prenoon MLT sectors, thus emphasizing the pitch-angle dispersion role with respect to the dispersion due to convection. This allows one to observe the suprathermal proton population during several tens of minutes over the MLT range of 3 h around noon, i.e., similarly to the MLT extension of the cusp proper. A remarkable space/time stability of this new population is due to its low velocity (tens of km/s) and/or velocity diffusion in the flux tubes of the cusp proper. We have performed both backward tracing of proton trajectories in the Tsyganenko-96 model, and kinetic modeling of the kinematic variations of the distribution function for protons along their way from the bi-Maxwellian source in the form of a heating wall till the satellite. The parameters of the model were adjusted to the observed energy–time spectrograms. They consistently indicate the origin of the descending suprathermal proton population at intermediate altitudes of 5R _E, i.e., within cusp flux tubes but well below the magnetopause. Some published measurements from the POLAR satellite in the cusp region at altitudes of 4–5R _E seem to be consistent with the supposition of crossing the source region of this population, variable in space and time (though these measurements were interpreted in a different manner).     

Energy Spectrum of Galactic 10–100 MeV Protons in Quiet Sun Periods

The dynamics of the proton energy spectrum during the solar cycle is studied. The spectra were determined by 1–100 MeV particle fluxes measured by different instruments mounted aboard the Earth's IMP-8 satellite for more than one hundred quiet-time intervals in the period between 1974 and 1991. The galactic branch of the spectra (E _p > 10 MeV) constructed for every quiet interval was fitted by a power law function, J =CE . The theory predicts that in the 1–100 MeV energy range, where the adiabatic cooling of particles is dominant, = 1, while we have derived a double-peak distribution. The main maximum has the mean value = 1.35. The mean value of the second, much weaker maximum, is = 0.95. Within the main maximum, values are distributed in accordance with the Gaussian law with a standard deviation D/ = 0.12. The substantial difference of from unity requires the elaboration of a new model of modulation processes in the inner heliosphere. The values corresponding to the second maximum show that modulation processes correspond sometimes to theoretical conceptions. It is shown that correlates weakly with parameters A and describing the solar branch of the spectrum (J(E) = AE ^–). At the same time, a more significant correlation is observed between and the solar activity index, R _z, the counting rate of the Deep River neutron monitor, and the energy value in the minimum of the energy spectrum flux, E _min.     

Some Technical Issues of an Optically Focused Small Space Debris Tracking and Cataloging System

Congressional language in the 1998 US Senate Armed Services Committee authorization bill directed ... the Secretary of the (United States) Air Force to undertake a design study of a system that could catalog and track debris down to one centimeter in size out to 1000kilometer in altitude. The US Air Force Research Laboratory, in conjunction with other US National Laboratories and the National Aeronautics and Space Administration (NASA) conducted a study that examined what technical systems and operations would be required to perform such a mission. This paper outlines the study process, details the findings, draws conclusions, and makes recommendations as to what would be needed to develop an optically based system capable of cataloging and tracking small debris in low Earth orbit.     

Tether Satellite System Collision Study

A study was performed to determine the probability of collision with resident space objects and untrackable debris for the tether component of the Tethered Satellite System (TSS) after it broke away from the Space Shuttle orbiter (mission STS-75) in February 1996. Both an analytical and a numerical approach were used in this study, and the results obtained with these two methods were found to be in good agreement. These results show that the deployed tether is expected to have been impacted by several particles 0.1mm or larger in size. The probability of collision with objects 10cm in size or larger was on the order of 10^–3 per month. Since the severed tether reentered within one month after deployment, the collision hazard to other objects while in orbit was small. The analytical methods used in this study are useful for tether collision evaluations in general.     

The effectiveness of end-of-life re-orbiting for debris mitigation in geostationary orbit

The effect of satellite breakups over 72 years, as a function of the end-of-life re-orbiting altitude (0–2000km), was analyzed in terms of fragment contribution to the object density in the geostationary orbit (GEO) ring, both in the short- and long-term. In the short-term, the explosions in GEO are the most detrimental for the GEO ring environment, though the average fragment density in the ring is never higher than 1/5 of the background, decreasing to less than 1/100 of the existing environment after 4 years (apart from a density rebound 5 decades later, due to luni-solar perturbations). Spacecraft end-of-life re-orbiting is a possible mitigation solution. But the re-orbiting altitude is critical if explosions continue to occur. In order to reduce the post-event average density by 1 order of magnitude with respect to an explosion occurring in GEO, more than 500km of re-orbiting is needed. Concerning the long-term environmental impact, the re-orbiting strategy supported by Inter-Agency Space Debris Coordination Committee (IADC) seems adequate to guarantee, after 2–3 years, a long-term average density of fragments in the GEO ring of at least 2 orders of magnitude below the existing background. But at least 1000km of re-orbiting are needed to stay below that threshold in the short-term too. In conclusion, the re-orbiting strategy recommended by IADC is totally adequate in the long-term, but only if satellite passivation is extensively carried out.     

Global geomagnetic response to a sharp compression of the magnetosphere and IMF variations on October 29, 2003

We study the response of the ionosphere and magnetosphere to a sudden commencement (SC) on October 29, 2003, at 06:11 UT. It is shown that the geomagnetic response had the form of two successive stages. In the first 5 min after the SC, a strong intensification of a two-vortex current system of the DP2 type was observed in latitudes 67°-65°, with variations of H -4000 nT (+700 nT). At the same time, energetic electrons were injected without dispersion to geosynchronous orbits simultaneously in the sectors 16, 04, and 07 MLT. In the subsequent 5–15 min, a new intensification of the western electrojet took place in all time sectors at latitudes 70°. Around midnight, this electrojet was extended in the poleward direction up to the polar cap latitudes ( 75°-83°). It had an unusually high velocity of extension (up to 5.0 km/s) and was accompanied by typical dispersionless substorm injections, but only at meridians 04 and 07 MLT. From comparing the development of electrojets with the data of satellite observations in the solar wind and magnetosphere, we suggest that 3–5 min after the SC onset a dipolization of the magnetic field at the geosynchronous orbit occurred. It was connected with the decay of the current flowing across the magnetotail. The subsequent extension of the region of current decay into the tail up to 150 R_E proceeded with a velocity of 1000 km/s, which exceeds the known velocities of such an extension by a factor of 5.Translated from Kosmicheskie Issledovaniya, Vol. 42, No. 6, 2004, pp. 622–631.Original Russian Text Copyright © 2004 by Solovyev, Moiseyev, Mullayarov, Du, Engebretson, Newitt.     

Developing a Low-Velocity Collision Model Based on the Nasa Standard Breakup Model

We have conducted a series of low-velocity impact experiments to understand the dispersion properties of fragments newly created by low-velocity impacts possible in space, especially in geostationary Earth orbit. The test results are utilized to establish a mathematical prediction model to be used in debris generation and propagation codes. Since the expected collision velocity between catalogued objects in geostationary Earth orbit shows a peak at a few hundreds meters per second, these impact experiments were conducted at a velocity range lower than 300m/s. As a typical structure of satellites in geostationary Earth orbit, thin aluminum honeycomb sandwich panels with carbon fiber reinforced plastics face sheets were prepared, while the projectile was a stainless steel ball of 9mm diameter. The data collected through these impact experiments have been re-analyzed based on the method used in the National Aeronautics and Space Administration (NASA) standard breakup model 1998 revision. The results indicate that the NASA standard breakup model derived from hypervelocity impacts could be applied to low-velocity collision possible in geostationary Earth orbit with some modifications.     

Stationary Nose Structures of Protons in the Inner Magnetosphere: Observations by the ION Instrument onboard the Interball-2 Satellite and Modeling

Nose structures are objects formed by H⁺ particles penetrating into the inner magnetosphere [1, 2]. We present the results of experimental studies and numerical modeling of the nose structures. Statistical processing of the observations of nose structures in 1997 by the ION instrument onboard the Interball-2 satellite at heights of 10000–15000 km demonstrates that the probability of formation of the nose structures under quiet magnetic conditions (with current values K _p = 0–1) in the nighttime sector of the magnetosphere is 90%. The probability of observation of the nose structures in the daytime sector equals 50% at the current value K _p = 0–1, and the correlation between the observations of nose structures and K _p can be improved (up to 75%) if the K _p index is taken 6 h before the observed events. It is shown that nose structures are a characteristic feature not only of the substorm processes but also of quasi-stationary phenomena in the quiet magnetosphere. The nose structures observed in magnetically quiet periods are called stationary nose structures in this work. By modeling drift trajectories for protons, it is shown that the stationary nose structures are formed in all sectors of the MLT. The stationary nose structures observed by the ION instrument are modeled in the night, morning, and daytime sectors of the MLT. The relation between the stationary nose structures and ion spectral gaps is considered.     

Peculiarities of the Orbital Motion of Submicron Particles in the Earth's Plasmasphere

On the basis of numerical calculations of trajectories, the peculiarities of motion of submicron-sized particles in the Earth's plasmasphere are investigated. The most important result of these investigations is the found possibility of long-term residence of a microparticle in the Earth's vicinity. This effect is a result of the interaction of the electric charge, induced on a microparticle, with the magnetic field of the Earth. It is shown that the effect of microparticle capture by the Earth's magnetic field takes place in the case when the microparticles having a dimension of about 10^–2 m and made of a material having high yield of photoemission are injected into the plasmasphere at altitudes of about several thousand kilometers and also in the case when the microparticles with a dimension of about 10^–3 m and made of a material having low yield of photoemission are injected into the plasmasphere at altitudes of about 15000–20000 km and are moving close to the equatorial plane.     

A new method of determining the spectral index for protons in the energy range about 10<Superscript>13</Superscript> eV

We consider a relationship between the difference in spectral indices of the spectra of single hadrons and all hadrons (_sngl – _h) and the difference in the indices of the spectra of galactic cosmic ray (GCR) protons and nuclei. It is demonstrated that at the mountain level the ratio (_p – _Z)/(_sngl – _h) is always larger than unity, if (_sngl – _h) > 0.1. From the experimental value _sngl – _h = 0.4 ± 0.05 we derive that, in the vicinity of E = 10 TeV, _p – _Z 0.49 ± 0.06 , i.e., _p 3.09 ± 0.06.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 2, 2005, pp. 83–87.Original Russian Text Copyright © 2005 by Grigorov, Tolstaya.     

Theory of Singular Optimal Controls with Applications to Space Flight Mechanics

The problem of existence of solutions to the problems of optimum control with a singularity condition H(x, , u) const, u U is studied. The necessary conditions of appearance of the singular control, as well as time location and the numbers of singular sections of the trajectories of a controlled object under consideration, are obtained. The numerical algorithms of solving the problems with the condition of singularity of control are constructed. The widely known problem of optimum control of the motion of a high-altitude rocket probe is also considered, and it is proved that in this problem no intermediate section can exist in the law of variation of the thrust. The results of numerical experiments are presented together with their relative evaluation.     

Influence of Trapped Plasma on the Structure of Collisionless Thin Current Sheets

Using both analytical and numerical models of the collisionless anisotropic current sheet generated by the impinging flows of transient ions, we have studied the self-consistent solutions taking the plasma trapped in the sheet into account. It is demonstrated that there exists a limited window in the space of system parameters where self-consistent solutions can exist. When the density of the quasi-trapped plasma is sufficiently large, a redistribution of the total current can be a cause of the sheet decay, when the local current of the trapped particles compensate (totally or in part) the main current in the center and at the edges of the sheet, while the total current generated by ions on the trapped trajectories vanishes.     

Time Variations of Low-Energy Protons and Helium Nuclei (0.3–10 MeV/nucleon) during the Quiescent Time of Solar Activity in the Inner Heliosphere

Time variations with a duration of 0.6–1.5 years are studied in the interplanetary space for protons and helium nuclei with energies of 0.3–10 MeV per nucleon at a quiescent time of solar activity. It is shown that at 1 AU in the periods 1978–1981 and 1988–1990, at the phases of growth of the 21st and 22nd solar cycles, the background fluxes of these particles determined as minimum intensity levels in every month increased demonstrating steplike variations. At the same time, the intensity of galactic cosmic rays (GCRs) decreased also with the formation of modulation steps. Each step of low-energy particles was finished by a deep minimum of intensity (gap) in both protons and helium nuclei and with a simultaneous short-term increase of the GCR intensity. We present the results of studying five such steps in the intensity of low-energy particles that were observed simultaneously and were opposite in phase with modulation steps of galactic particles. The lowest values of the H/He ratio were recorded at the end of every step, at the lowest intensities of these particles, i.e., in the gap. The true background population at 1 AU was detected precisely at these time intervals, when the contributions of flare particles and those accelerated in the international space were minimum. Various possibilities of the origination of the steplike variations of the background fluxes of protons and helium nuclei with energies of 0.3–10 MeV per nucleon, correlated with similar GCR variations, are discussed.     

Ray Based Diffraction Tomography of the Ionosphere and Laboratory Inhomogeneous Plasma

A new procedure for restoration of the plasma inhomogeneities with improved resolution is suggested. The procedure deals with the double weighted Fourier transform (DWFT) of the observed wavefield in coordinates of both receivers = (x, y) and sources ₀ = (x ₀, y ₀) [1]. Phase increments between the sources and receivers, being found from DWFT representation, can be used for extracting information on small perturbations of the dielectric constant ~(, z) in a way similar to traditional radio tomography. The resulting resolution of the method is close to the diffraction limit = h/D in the horizontal direction and z = (h/D)² in the vertical direction, where h is the height of inhomogeneities and D is the length of the ground-based receiving system.     

Beam-Park-Experiment-1/2000 with TIRA

A monostatic 24-h debris observation campaign (BPE-1/2000) has been prepared and conducted using FGAN's TIRA L-Band system. Based on experiences from previous Beam-park experiments a similar largely automated data processing is applied on an extended range window of 300–2000km. More than 1500 detections are encountered, 471 of them are verified as being real objects in Low-Earth-Orbit (LEO). PROOF's observation forecasting of catalogued objects is evaluated against the observed objects, and the difficulties obtaining radar cross-sections (RCSs) and object sizes from Beam-park experiments are discussed. Sidelobe detections are identified by using background information like two-line element (TLE) sets and/or catalogued RCSs.In comparison with previous experiments, the statistics show similarities confirming the concept of Beam-park experiments for space debris observations, despite the snapshot character of 24-h experiments. The comparison with MASTER/PROOF'99 and ORDEM2000 leads to a reasonable agreement between models and observations.     

Plasma Jet Motion Across the Geomagnetic Field in the “North Star” Active Geophysical Experiment

The active geophysical rocket experiment North Star was carried out in the auroral ionosphere on January 22, 1999, at the Poker Flat Research Range (Alaska, USA) using the American research rocket Black Brant XII with explosive plasma generators on board. Separable modules with scientific equipment were located at distances of from 170 to 1595 m from the plasma source. The experiment continued the series of the Russian–American joint experiments started by the Fluxus experiment in 1997. Two injections of aluminum plasma across the magnetic field were conducted in the North Star experiment. They were different, since in the first injection a neutral gas cloud was formed in order to increase the plasma ionization due to the interaction of neutrals of the jet and cloud. The first and second injections were conducted at heights of 360 and 280 km, respectively. The measurements have shown that the charged particle density was two orders of magnitude higher in the experiment with the gas release. The magnetic field in the first injection was completely expelled by the dense plasma of the jet. The displacement of the magnetic field in the second injection was negligible. The plasma jet velocity in both injections decreased gradually due to its interaction with the geomagnetic field. One of the most interesting results of the experiment was the conservation of high plasma density during the propagation of the divergent jet to considerable distances. This fact can be explained by the action of the critical ionization velocity mechanism.     

Dynamics of the 0.3–100 MeV Proton Energy Spectra in the Inner Heliosphere in Quiet Periods of 1974–1991

Variations of the proton spectra in the 0.3–100 MeV energy range based on the data of various instruments installed onboard the IMP-8 satellite are studied for very quiet, quiet, and quasi-stable solar activity periods during the years 1974–1991. As many as 118 spectra were approximated by two power laws: the left-hand and galactic branches of the spectrum were fitted by the AE ^– function and a dependence of the CE type, respectively, the sum J(E) = AE ^– + CE providing the total spectrum. It is shown that the spectra vary within a solar cycle with a shift of the minimum energy (E _min) to higher energies with increasing solar activity. It follows from the relations between the spectrum parameters thus obtained that, in particular periods of time, an increase (decrease) of the particle flux in the low-energy branch of the spectrum and an intensification (depression) of the GCR particle flux modulation take place simultaneously. This is manifested in a shift of the spectrum parallel to the energy axis. The study of the spectra in the most quiet time during three successive solar minima have shown that low-energy (0.3–10 MeV) protons, as well as GCR, are subject to the 22-year variation in the solar magnetic cycle.     

Metallic and Oxidized Aluminum Debris Impacting the Trailing Edge of the Long Duration Exposure Facility (LDEF)

A total of 87 microcraters >30 m in diameter that were found in gold substrates exposed on the trailing edge of the non-spinning Long Duration Exposure Facility (LDEF) yielded analyzable projectile residues in their interiors. Using qualitative SEM-EDS analysis methods, some 60 of these craters were formed by natural cosmic-dust particles, while 27 residues (31%) were assigned to orbital debris (Hörz et al., 1993). The far majority of the orbital-debris impacts, 24 (89%) of the 27 events, contained only aluminum in their X-ray spectra. The present study evaluates these aluminum-rich residues in detail and employs a windowless X-ray detector, which permits for the analysis of low-Z elements and specifically of oxygen. This makes it possible to discriminate between oxidized (Al₂O₃) and metallic (Al) projectiles from dramatically different sources, the former produced during solid-fuel rocket firings, the latter resulting from explosively or collisionally disrupted spacecraft.Of the 24 craters analyzed with the windowless detector, 13 (54%) contained Al₂O₃ and 11 (46%) yielded structurally disintegrated Al metal. The oxidized residues preferentially occur in the smaller craters, all <60 m in diameter. Corresponding particles on LDEF's trailing edge are <35 m in diameter. Some 70% of this particle population is composed of Al₂O₃. Although solid-fuel rocket exhaust products are typically <5 m in size, they tend to coagulate into crusts at the rocket nozzle to be shed occasionally as relatively large, aggregate particles. Structurally disintegrated, metallic fragments compose one-third of all particles <35 m, but they dominate all particles >35 m, and thus all craters >60 m. These findings clearly establish that solid-rocket exhaust particles, as well as explosively or collisionally produced debris, exist in low-inclination, high-eccentricity orbits in sufficient quantities that they must be accounted for in models describing the present and future orbital-debris population at typical Shuttle and Space Station altitudes.