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.     

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.     

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.     

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.     

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).     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

The Hidden Costs of Reliability and Failure in Launch Systems

In comparing the costs of different launch vehicles, the possibility of the risk of failure is assumed to be accounted for by the cost of insurance. The satellite may be insured against loss during launch, and the launch services provider may offer a free relaunch. However, actual costs of reliability and failure extend beyond this. Each failure necessitates an investigation and a get well programme by the operating agency, while putting the operations team on hold until services can resume. A commercial operator may also lose customer revenue and actual customers through loss of confidence or unavailability. Such costs tend to be hidden, and not evaluated in assessing the effectiveness of a system, but count towards total costs. Failure investigations help to improve system reliability, but this could equally have been achieved by expenditure in development and qualification. Reusable launch vehicles will have different costs associated with reliability and failure. The relationship between reliability and cost, properly assessed, ought to influence the design of both expendable and reusable launch systems.     

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.     

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.     

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.     

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.     

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.