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.     

INTERBALL-1 Observations of the Kilometric “Continuum” of the Earth's Magnetosphere

The electromagnetic radio-frequency emission of the inner region of the Earth's plasmasphere discovered recently by the GEOTAIL satellite [4] and referred to as the kilometric continuum was observed by the INTERBALL-1 satellite (1995–2000) in the 100–500 kHz band in the AKR-X experiment. During a period of low solar activity (1995–1997), this continuum was found leaving the inner plasmasphere at geocentric distances of 2–4R _E as isolated pencil-like (1°–6°) beams located in the magnetic equator plane. During a time of high solar activity (1999–2000), the occurrence of the emission was extremely rare (it was observed only at a considerable fall of this activity). If detected, at the same geocentric distances (2–4R _E) the continuum demonstrated a strongly variable and perturbed character, as well as a considerably larger extension of the beam over the geomagnetic latitude (10°–20° and more). In addition, quasi-periodic (QP) signals, similar to the observed QP emissions of Jupiter, were sometimes detected in this period. The probable nature of the observed features of the kilometric continuum is briefly discussed.     

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.     

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.     

Manifestations of sudden commencement of a severe magnetic storm of November 20, 2003, in generation of an SC pulse, <Emphasis Type="Italic">P</Emphasis><Subscript>SC</Subscript> pulsations,and spatial modulation of the auroral brightness

The results of investigation of the geomagnetic and auroral response to the commencement of a severe magnetic storm of November 20, 2003, are presented. It is established that the onset of SC led to the brightening of the auroral arc in the dusk sector for 2–3 min with its extent to the east with a velocity of 10–20 km/s and to displacement poleward with a velocity of 1.0 km/s. Furtheron, the fast auroral expansions of short duration (5 min) to the pole up to 2–4°were observed, repeating every 5–10 min during 40 min, which led to the spatial modulation of the brightness of the glow and to generation of P_SC pulsations with similar periods of oscillations. The broadening of aurora poleward had a steplike character, with generation of new arcs poleward of previous ones 5 arcs per 1.5 min. The modulation of brightness of the glow and P_SC were observed against the background of intensification of a two-cell DP2 type current system and were accompanied by multiple turnings of the IMF B_z from south to north and back. It is assumed that the source of P_SC pulsations was a modulation of the intensity of the DP2 ionosphere currents as a result of variations of the magnetosphere convection level.Translated from Kosmicheskie Issledovaniya, Vol. 42, No. 6, 2004, pp. 608–615.Original Russian Text Copyright © 2004 by Baishev, Borisov, Velichko, Solovyev, Yumoto.     

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.     

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.     

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.     

Radial gradient of low-energy (∼0.5–2 MeV) protons at 20–80 AU in the solar activity minima of the 22nd and 23rd cycles

The value of the radial gradient of low-energy (0.5–2 MeV) protons in the heliosphere at distances of 20–80 AU in the periods of solar activity minima in 1985–1987 and 1994–1997 was estimated using the data of the Voyager-1 and Voyager-2 spacecraft (s/c). Preliminary results on the dependence of the radial gradient on the distance were obtained for protons of these energies. The value of the radial gradient varies from –3% (AU)^–1 to –1% (AU)^–1 at distances from the Sun of 20–60 AU, reaching +0.7% (AU)^–1 at maximum considered distances (80 AU). The sign reversal of the proton radial gradient at a distance of 60–70 AU is interpreted as the appearance of a new component: up to the point of inversion there are mainly particles of the solar origin and/or accelerated in the inner heliosphere, while after the reversal of the gradients sign the fluxes of particles prevail whose source is located far from the Sun (maybe in the vicinity of the heliosphere boundary in the region of existence of the termination shock).Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 1, 2005, pp. 3–8.Original Russian Text Copyright © 2005 by Logachev, Zeldovich, Surova.     

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.     

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).     

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.     

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.     

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.     

Results of Space-Flight Tests of the Vibration-Protective Platform VZP-1K

The data of microacceleration measurements performed onboard the Mirstation are analyzed. The data were taken while testing the passive vibration-protective platform VZP-1K developed by the NPO Kompozit. We have processed the results of simultaneous microacceleration measurements on the vibration-protective platform and on the station body close to the platform. Two sets of the French equipment Microaccelerometer were used for these measurements. It was found that the platform reduces the vibrational component of microaccelerations in the band of frequencies above 3 Hz by more than a factor of 10. In this case, all harmonics with large amplitudes are damped by a factor of 50 and more, and some harmonics with small amplitude are damped only by a factor of 10. In the band 0.3–0.6 Hz (close to natural frequencies of the platform), the several-fold increase in amplitude of the vibrational component of microaccelerations is observed, but since the initial values of this amplitude in all performed experiments were small, the above indicated increase practically has not decreased the vibration-protective properties of the platform. The estimations of natural frequencies and damping coefficients of the platform found as a result of data processing of microacceleration measurements made during its free oscillations are obtained. The dependence of frequencies on the amplitude of oscillations is revealed for one mode, which testifies to appreciable nonlinear effects.     

Sources and Losses of Energetic Electrons at Low Altitudes from Satellite Data

Fluxes and differential spectra of 0.04–2.0 MeV electrons at low altitudes in the Earth's magnetosphere are considered in comparison with the model spectra AE-8 MAX and AE-8 MIN. Possible causes of the discrepancy between the observational and model spectra are discussed. The coefficients of radial diffusion at various L-shells are estimated for the maximum of solar activity (using the Interkosmos-19 data) and for the minimum of solar activity (using the Kosmos-1686 data) and are derived from the model AE-8. A quantitative evaluation of the electron yield from radial diffusion at low L shells is derived. Ionization losses, Coulomb angle scattering, and resonant wave–particle interaction are considered as the loss mechanisms. A calculation of these losses at the low L-shells is given. The electron distribution at low L-shells is best fitted by a combination of dissipative terms from different models: Coulomb scattering dominates at the lower L-shells (L = 1.2–1.4) and the resonant wave–particle interaction controls the radiation belt maximum and the gap (L = 1.4–2.0).     

Observation of the Near Plasma Sheet,Ring Current,and Energetic Electrons from Radiation Belts at a Geosynchronous Orbit,March 11–25, 1992

The dynamics of near plasma sheet electrons and ions (E 0.1–12.4 keV), ring current protons (E _i 41–133 keV), and energetic electrons from the Earth's radiation belts (E _e 97–1010 keV) is considered using the data from the Gorizont-34and Gorizont-35geosynchronous satellites from March 11–25, 1992. Peculiarities of this period are a long (more than 4 days) interval of the northward interplanetary magnetic field (B _z> 0) and a high-speed stream of the solar wind with an enhanced particle density. The SC and compression of the magnetosphere to the geosynchronous orbit (GMC) preceded this interval. Under quiet and moderately disturbed geomagnetic conditions and under a prolonged northward interplanetary magnetic field, we observed a significant decrease of fluxes and softening of spectra of the electron component of plasma in the energy ranges of 0.1–12.4 keV and 97–1010 keV, and of the ion component of plasma at energies of 0.1–4 keV, while the intensity of 5–12.4 keV ion fluxes increases by about one order of magnitude. The peculiarities of distributions of energetic particle fluxes observed in the period under consideration can be associated with significant variations of the convection conditions and a decreased or fully suppressed injection of energetic electrons into the geosynchronous orbit region.     

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%.     

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.     

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.