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.     

Assessing the Impact Risk of Orbital Debris on Space Tethers

Tethers are being proposed for a growing number of space applications. However, they may be particularly vulnerable to orbital debris and meteoroid impacts. In order to provide useful reference data for tether systems design, detailed analytical and numerical computations were carried out to assess the average impact rate of artificial debris and meteoroids. The specific geometric properties of tethers as debris targets, when compared to typical satellites, are discussed, and the results obtained are presented in tabular form, as a function of debris size and tether diameter.The computations were carried out for six circular orbits, spanning three altitudes (600, 800 and 1000km) and two inclinations (30° and 50°). Tether diameters in between 1mm and 2cm and debris larger than 0.1mm were considered in the analysis. The collision risk of tethers with spacecraft and upper stages in orbit was estimated as well.In the debris interval and orbital regimes considered, artificial debris represent the dominant contributor to the impact rate. At 600km and in the 0.1–10mm size range, the meteoroid and orbital debris impact rates are still comparable; however, at higher altitudes and in the 1–10cm size range, meteoroids contribute 20–30 times less to the collision probability.The results obtained confirm that for single-strand tethers in low Earth orbit the probability to be severed by orbital debris and meteoroid impacts is quite significant, making necessary the adoption of innovative designs for long duration missions.     

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.     

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.     

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%.     

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.     

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.     

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).     

Empirical Modeling of the Statistical Structure of Radio Signals from Satellites Moving over Mid- and High-Latitude Trajectories in the Southern Hemisphere

The results of developing the empirical model of parameters of radio signals propagating in the inhomogeneous ionosphere at middle and high latitudes are presented. As the initial data we took the homogeneous data obtained as a result of observations carried out at the Antarctic Molodezhnaya station by the method of continuous transmission probing of the ionosphere by signals of the satellite radionavigation Transit system at coherent frequencies of 150 and 400 MHz. The data relate to the summer season period in the Southern hemisphere of the Earth in 1988–1989 during high (F > 160) activity of the Sun. The behavior of the following statistical characteristics of radio signal parameters was analyzed: (a) the interval of correlation of fluctuations of amplitudes at a frequency of 150 MHz ( _kA ); (b) the interval of correlation of fluctuations of the difference phase ( _k); and (c) the parameter characterizing frequency spectra of amplitude (P _A) and phase (P ) fluctuations. A third-degree polynomial was used for modeling of propagation parameters. For all above indicated propagation parameters, the coefficients of the third-degree polynomial were calculated as a function of local time and magnetic activity. The results of calculations are tabulated.     

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.     

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.     

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.     

Radio Wave Fluctuations and Layered Structure of the Upper Region of Venusian Clouds from Radio Occultation Data

The results of the cross-correlation analysis of the amplitude fluctuations of radio waves of the = 32 cm band in seven sessions of radio occultation measurements of the northern polar atmosphere of the planet are presented. The existence of the cross-correlation of fluctuations (b 0.6) is established in the altitude realizations in the interval 61.5–65.0 km for two different sessions of radio occultation. Inner layering is revealed in the upper layer of the clouds of the planet at altitudes of 61.5–65.0 km, which is specified by an enhanced turbulence of the atmosphere. It is found that the lifetime of the small-scale layered irregularities is no less than 2 days and that their horizontal extension in the meridional direction can exceed 130 km. A possible cause of the emergence of the layered structures inside the upper layer of the polar clouds of Venus is discussed.     

Gravitation Maneuver Using the Families of Super-Unstable Orbits around the Libration Points

The families of periodic solutions to an autonomous Hamiltonian system in that part where the solutions are unstable have their specific field of influence. Under strong instability, the orbits that have fallen in such a field of influence are drawn into the family as in a whirlpool and then are thrown away from it. In the particular case of the restricted three-body problem, the orbits around the libration points L ₁ and L ₂ are super-unstable and the Keplerian elements in motion over these orbits change drastically. When the orbits fall into such a domain, for some time the motion is close to the motion around the libration point, and after being thrown out of this domain, the Keplerian orbital elements also change essentially.     

The Potential and Equipotentiality of Spacecraft

The problem of maintenance of the equipotentiality of spacecraft surfaces is considered. The method under examination is the use of the conductive thermal-vacuum multilayer blanket (CMLB), whose outer surface represents a fabric woven of threads of glass fiber type with interwoven metal threads. The process of spacecraft potential formation and methods of the potential calculation are described, and the results of such a calculation for the illuminated and shadowed parts of spacecraft surfaces in some characteristic near-Earth plasma environments are presented. The CMLB model is described, and the potential distribution near the CMLB surface is calculated. The conclusion was drawn that the conductive thermal-vacuum multilayer blanket used in some cases on Russian spacecraft does not ensure the equipotentiality of spacecraft surfaces, and in the case of using CMLB, the differential spacecraft charging in outer regions of the Earth's magnetosphere may reach a dangerous level for onboard electronic systems. In spite of the fact that CMLB guards against large-scale powerful discharges, one cannot exclude discharges completely, what may result in broadband noise enhancement and cause onboard systems failures.     

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.     

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.     

Quasistatic Microaccelerations onboard the Foton Satellite during Its Flight at High-Altitude Orbits

The level of quasistatic microaccelerations onboard the Foton-M satellite is predicted for its flights in two orbits: the planned orbit with the altitudes in perigee h = 262 km and in apogee h = 304 km and the orbit with h = 262 km and h = 350 km. The prediction is based on mathematical simulation of the satellite motion with respect to its center of mass under the action of gravitational and aerodynamic moments. The model is represented by the system of equations of the satellite rotational motion. Parameters of this system are chosen from the condition of coincidence of the motion of preceding Foton satellites (h 220 km and h 400 km) calculated using this model with the results of determination of actual rotational motion of the Foton-11 and Foton-12 satellites. With the help of the model thus calibrated, a calculation is made of the rotational motion of the Foton-M satellite and of the quasistatic microaccelerations onboard it. As is shown by the results of simulation, the use of the first and the second orbits will result in reductions of microaccelerations by 30% and 60%, respectively.     

The Influence of Arrangement of Growth Setups onboard a Spacecraft on Microgravity Conditions of Experiments: An Example of Floating Zone Melting of InSb:Te onboard the Foton-3 Satellite

The results of experiments on the growth of InSb:Te by the floating zone melting in the Zona-4 setup during a flight of the Foton-3 satellite are discussed in comparison with the data on the microgravity situation typical for satellites of this type. When analyzing inhomogeneities in the crystals obtained, we reveal the frequencies corresponding to periodical variations of the impurity channel position (the facet effect), to interleaving of packs in which the growth layers are grouped, and to location of subgroups of the growth layers inside the packs. These frequencies are close to those discovered during measurements of low-frequency (quasistationary) microaccelerations (g) onboard the spacecraft Foton-8, Foton-10, Foton-11, and Foton-12. Calculated values of g at the place where the Zona-4 setup is installed confirm the possibility of impact of such g on the heat and mass transfer in the melt.