Estimation of ballistic coefficients of low altitude debris objects from historical two line elements

This paper presents a new method for estimating ballistic coefficients (BCs) of low perigee debris objects from their historical two line elements (TLEs). The method uses the drag perturbation equation of the semi-major axis of the orbit. For an object with perigee altitude below 700 km, the variation in the mean semi-major axis derived from the TLE is mainly caused by the atmospheric drag effect, and therefore is used as the source in the estimation of the ballistic coefficient. The method is tested using the GRACE satellites, and a number of debris objects with external ballistic coefficient values, and agreements of about 10% are achieved.     

Use of two-line element data for thermosphere neutral density model calibration

Traditional empirical thermospheric density models are widely used in orbit determination and prediction of low-Earth satellites. Unfortunately, these models often exhibit large density errors of up to around 30% RMS. Density errors translate into orbit errors, adversely affecting applications such as re-entry operations, manoeuvre planning, collision avoidance and precise orbit determination for geodetic missions. The extensive database of two-line element (TLE) orbit data contains a wealth of information on satellite drag, at a sufficiently high spatial and temporal resolution to allow a calibration of existing neutral density models with a latency of one to two days. In our calibration software, new TLE data for selected objects is converted to satellite drag data on a daily basis. The resulting drag data is then used in a daily adjustment of density model calibration parameters, which modify the output of an existing empirical density model with the aim of increasing its accuracy. Two different calibration schemes have been tested using TLE data for about 50 objects during the year 2000. The schemes involve either height-dependent scale factors to the density or corrections to CIRA-72 model temperatures, which affect the density output based on a physical model. Both schemes have been applied with different spherical harmonic expansions of the parameters in latitude and local solar time. Five TLE objects, varying in perigee altitude between 280 and 530 km, were deliberately not used during calibration, in order to provide independent validation. Even with a single daily parameter, the RMS density model error along their tracks can already be reduced from the 30% to the 15% level. Adding additional parameters results in RMS errors lower than 12%.     

Measuring atmospheric density using GPS–LEO tracking data

We present a method to estimate the total neutral atmospheric density from precise orbit determination of Low Earth Orbit (LEO) satellites. We derive the total atmospheric density by determining the drag force acting on the LEOs through centimeter-level reduced-dynamic precise orbit determination (POD) using onboard Global Positioning System (GPS) tracking data. The precision of the estimated drag accelerations is assessed using various metrics, including differences between estimated along-track accelerations from consecutive 30-h POD solutions which overlap by 6 h, comparison of the resulting accelerations with accelerometer measurements, and comparison against an existing atmospheric density model, DTM-2000. We apply the method to GPS tracking data from CHAMP, GRACE, SAC-C, Jason-2, TerraSAR-X and COSMIC satellites, spanning 12 years (2001–2012) and covering orbital heights from 400 km to 1300 km. Errors in the estimates, including those introduced by deficiencies in other modeled forces (such as solar radiation pressure and Earth radiation pressure), are evaluated and the signal and noise levels for each satellite are analyzed. The estimated density data from CHAMP, GRACE, SAC-C and TerraSAR-X are identified as having high signal and low noise levels. These data all have high correlations with anominal atmospheric density model and show common features in relative residuals with respect to the nominal model in related parameter space. On the contrary, the estimated density data from COSMIC and Jason-2 show errors larger than the actual signal at corresponding altitudes thus having little practical value for this study. The results demonstrate that this method is applicable to data from a variety of missions and can provide useful total neutral density measurements for atmospheric study up to altitude as high as 715 km, with precision and resolution between those derived from traditional special orbital perturbation analysis and those obtained from onboard accelerometers.     

Rarefied gas effects on the aerodynamics of high area-to-mass ratio spacecraft in orbit

The aerodynamic situation of a satellite-on-a-chip operating in low Earth orbit bears some resemblance to a classical Crookes radiometer. The large area-to-mass ratio characteristic of a SpaceChip means that very small surface-dependent forces produce non-negligible accelerations that can significantly alter its orbit. When the temperature of a SpaceChip changes, the drag force can be changed: if the temperature increases, the drag increases (and vice versa). Analytical expressions available in the literature that describe the change in drag coefficient with orbit altitude and SpaceChip temperature compare well with our direct simulation Monte Carlo results presented here. It is demonstrated that modifying the temperature of a SpaceChip could be used for relative orbit control of individual SpaceChips in a swarm, with a maximum change in position per orbit of 50 m being achievable at 600 km altitude.     

Accurate orbit predictions for debris orbit manoeuvre using ground-based lasers

Orbit manoeuvre of low Earth orbiting (LEO) debris using ground-based lasers has been proposed as a cost-effective means to avoid debris collisions. This requires the orbit of the debris object to be determined and predicted accurately so that the laser beam can be locked on the debris without the loss of valuable laser operation time. This paper presents the method and results of a short-term accurate LEO (<900 km in altitude) debris orbit prediction study using sparse laser ranging data collected by the EOS Space Debris Tracking System (SDTS). A main development is the estimation of the ballistic coefficients of the LEO objects from their archived long-term two line elements (TLE). When an object is laser tracked for two passes over about 24 h, orbit prediction (OP) accuracy of 10–20 arc seconds for the next 24–48 h can be achieved – the accuracy required for laser debris manoeuvre. The improvements in debris OP accuracy are significant in other applications such as debris conjunction analyses and the realisation of daytime debris laser tracking.     

Orbital debris–debris collision avoidance

We focus on preventing collisions between debris and debris, for which there is no current, effective mitigation strategy. We investigate the feasibility of using a medium-powered (5 kW) ground-based laser combined with a ground-based telescope to prevent collisions between debris objects in low-Earth orbit (LEO). The scheme utilizes photon pressure alone as a means to perturb the orbit of a debris object. Applied over multiple engagements, this alters the debris orbit sufficiently to reduce the risk of an upcoming conjunction. We employ standard assumptions for atmospheric conditions and the resulting beam propagation. Using case studies designed to represent the properties (e.g. area and mass) of the current debris population, we show that one could significantly reduce the risk of nearly half of all catastrophic collisions involving debris using only one such laser/telescope facility. We speculate on whether this could mitigate the debris fragmentation rate such that it falls below the natural debris re-entry rate due to atmospheric drag, and thus whether continuous long-term operation could entirely mitigate the Kessler syndrome in LEO, without need for relatively expensive active debris removal.     

Impact effects from small size meteoroids and space debris

When the impact risk from meteoroids and orbital debris is assessed the main concern is usually structural damage. With their high impact velocities of typically 10–20 km/s millimeter or centimeter sized objects can puncture pressure vessels and other walls or lead to destruction of complete subsystems or even whole spacecraft. Fortunately chances of collisions with such larger objects are small (at least at present). However, particles in the size range 1–100 μm are far more abundant than larger objects and every orbiting spacecraft will encounter them with certainty. Every solar cell (8 cm² area) of the Hubble Space Telescope encountered on average 12 impacts during its 8.25 years of space exposure. Most were from micron sized particles.     

Active debris removal of multiple priority targets

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

Analysis of the orbit lifetime of CubeSats in low Earth orbits including periodic variation in drag due to attitude motion

It is estimated that more than 22,300 human-made objects are in orbit around the Earth, with a total mass above 8,400,000 kg. Around 89% of these objects are non-operational and without control, which makes them to be considered orbital debris. These numbers consider only objects with dimensions larger than 10 cm. Besides those numbers, there are also about 2000 operational satellites in orbit nowadays. The space debris represents a hazard to operational satellites and to the space operations. A major concern is that this number is growing, due to new launches and particles generated by collisions. Another important point is that the development of CubeSats has increased exponentially in the last years, increasing the number of objects in space, mainly in the Low Earth Orbits (LEO). Due to the short operational time, CubeSats boost the debris population. One of the requirements for space debris mitigation in LEO is the limitation of the orbital lifetime of the satellites, which needs to be lower than 25 years. However, there are space debris with longer estimated decay time. In LEÓs, the influence of the atmospheric drag is the main orbital perturbation, and is used in maneuvers to increment the losses in the satellite orbital energy, to locate satellites in constellations and to accelerate the decay.The goal of the present research is to study the influence of aerodynamic rotational maneuver in the CubeSat?s orbital lifetime. The rotational axis is orthogonal to the orbital plane of the CubeSat, which generates variations in the ballistic coefficient along the trajectory. The maneuver is proposed to accelerate the decay and to mitigate orbital debris generated by non-operational CubeSats. The panel method is selected to determine the drag coefficient as a function of the flow incident angle and the spinning rate. The pressure distribution is integrated from the satellite faces at hypersonic rarefied flow to calculate the drag coefficient. The mathematical model considers the gravitational potential of the Earth and the deceleration due to drag. To analyze the effects of the rotation during the decay, multiple trajectories were propagated, comparing the results obtained assuming a constant drag coefficient with trajectories where the drag coefficient changes periodically. The initial perigees selected were lower than 400 km of altitude with eccentricities ranging from 0.00 to 0.02. Six values for the angular velocity were applied in the maneuver. The technique of rotating the spacecraft is an interesting solution to increase the orbit decay of a CubeSat without implementing additional de-orbit devices. Significant changes in the decay time are presented due to the increase of the mean drag coefficient calculated by the panel method, when the maneuver is applied, reducing the orbital lifetime, however the results are independent of the angular velocity of the satellite.     

High energy charged particle experiment – A payload proposal to KuaFu-B mission

High Energy Charged Particle Experiment (HECPE) is to measure the fluxes of MeV electrons and tens of MeV protons. The two satellites of KuaFu-B are in the same polar orbit with apogee 7.0R_E, perigee 1.8R_E. They can sweep large L values and pass through the inner and outer radiation belts. The high energy electrons and protons in the radiation belts are principal sources for failures of satellites and spacecrafts in the Earth orbits. The enhancements of the high energy electrons and protons, so-called energetic particle events, are important phenomena of the Space Weather. The energy ranges monitored by HECPE are 0.3–0.5 MeV, 0.5–1.0 MeV, 1.0–2.0 MeV, and E > 2.0 MeV for electrons, 5–10 MeV, 10–20 MeV, 20–40 MeV, and 40–80 MeV for protons.     

Charging of dust grains by anisotropic solar wind multi-component plasma

In this paper we study the charging process of small grain particles by anisotropic multi-component solar wind plasmas (electrons, protons and heavy ions), versus two-component (electron/proton) plasmas. We are focusing attention on the important characteristics of the charging process, namely the charging time, floating potential and current content as functions of plasma parameters such as He⁺⁺/H⁺ (α/p) number density and T_α/T_p temperature ratios of alpha particles to protons, as well as plasma streaming velocity v₀. Measured statistical properties of solar wind plasma parameters at 1 AU show considerable variations in α/p-temperature ratios from 1 to 10, in α/p-number density ratio from 0.01 to 0.35, as well as in values of streaming velocity v₀ from 200 km/s to 1000 km/s and more. Periods of these variations could last for several days each, leading to significant variability in the charging process, according to newly derived general analytical expressions. Numerical calculations performed for protons/alphas plasmas showed large disparity in the charging characteristics. For example, in anisotropic plasma, grain charging time varies up to 90% depending on α/p-particles temperature and number density ratios, whereas changes in floating potential are up to 40%. In contrast, in isotropic plasma, charging characteristic for grains do not change very much for the same plasma parameters variations, with charging time varying about 12% and floating potential only varying about 4%. It is also shown that in highly anisotropic plasma, with all ballistic electrons and ions, dust grains could not hold their charges, and characteristic discharged time is calculated. We note that the analysis is equally applicable to any sized body immersed in solar wind plasma.     

Some peculiarities of longitudinal distribution of proton fluxes at high latitudes

Dynamical features of proton fluxes at high and middle latitudes were studied based on data measured by Sun-synchronous low-altitude (800 km height) polar-orbiting three NOAA series satellites: POES 15, 16, and 17 during the geomagnetic storm on January, 21–22, 2005. Data from three satellites that passed the Northern hemisphere along different MLTs allow reconstructing the longitudinal distribution of the proton fluxes. Measurements of protons with energies of 30–80 keV and 80–240 keV (the ring current energy range) by 0- and 90-detectors were used to evaluate and compare the longitudinal asymmetry of proton flux distribution measured in the regions equatorward and poleward of the isotropic boundary. It was found that during all the phases of the geomagnetic storm distribution of the maximum flux of precipitating protons (0-detector data) is sufficiently asymmetric. The maximal flux position along MLT is moving from pre-midnight sector in quiet time to post-midnight one before and during SSC and moving back during recovery phase. The longitudinal distribution of precipitation maxima demonstrates the local increase in afternoon sector (approximately at 13:30 MLT) and decrease in the dusk one during SSC. These features are evident consequence of the magnetosphere compression. To identify the origin of the particles, the locations of maximum fluxes have been projected to the magnetosphere. It was determined that during geomagnetic storm main and recovery phases maximum fluxes were measured at latitudes poleward of the isotropic boundary. To evaluate the trapped particle flux asymmetry, the particle fluences (90-detector data) were calculated along the satellite orbit from L = 2 to the isotropic boundary. The total fluences of trapped particles calculated along the satellite orbit show regular asymmetry between dusk and dawn during main and recovery phases. The maximal intensity of proton fluxes of both investigated populations located poleward and equatorward of the isotropic boundary is achieved during SSC. The total flux measured during crossing the anisotropic region can be considered as a proxy for ring current injection rate.     

Energy spectrum of proton flux near geomagnetic equator at low altitudes

The results of proton energy (tens keV – several MeV) spectrum measurements near geomagnetic equator (L < 1.15) at low altitudes (<1000 km) are presented. We used data of experiments onboard ACTIVE, SAMPEX, NOAA TIROS-N satellites and SPRUT-VI (MIR station) and cover a time range of about 30 years (including previous measurements). It was found that the kappa-distribution function fits the experimental spectrum with the best correlation coefficient. A comparison of energy spectra of near-equatorial protons and ring-current protons was made. Using the estimation of the life time of near-equatorial protons we explain the difference in spectral indices of radiation belt and near-equatorial proton formation. We conclude that the ring current is the main source of the near-equatorial protons.     

Creation of model of quasi-trapped proton fluxes below Earth’s radiation belt

The object of investigation is the phenomenon of proton (from tens keV to several MeV) flux enhancement in near-equatorial region (L < 1.15) at altitude up to ∼1300 km (the storm-time equatorial belt). These fluxes are quite small but the problem of their origin is more interesting than the possible damage they can produce. The well known sources of these protons are radiation belt and ring current. The mechanism of transport is the charge-exchange on neutral hydrogen of exosphere and the charge-exchange on oxygen of upper atmosphere. Therefore this belt is something like the ring current projection to low altitudes. Using the large set of satellites data we obtain the average energy spectrum, the approximation of spectrum using kappa-function, the flux dependence on L, B geomagnetic parameters. On the basis of more than 30 years of experimental observations we made the empiric model that extends model of proton fluxes below 100 keV in the region of small L-values (L < 1.15). The model was realized as the package of programs integrated into COSRAD system available via Internet. The model can be used for revision of estimation of dose that low-orbital space devices obtain.     

Onboard orbit determination using GPS observations based on the unscented Kalman filter

Spaceborne GPS receivers are used for real-time navigation by most low Earth orbit (LEO) satellites. In general, the position and velocity accuracy of GPS navigation solutions without a dynamic filter are 25 m (1σ) and 0.5 m/s (1σ), respectively. However, GPS navigation solutions, which consist of position, velocity, and GPS receiver clock bias, have many abnormal excursions from the normal error range for space operation. These excursions lessen the accuracy of attitude control and onboard time synchronization. In this research, a new onboard orbit determination algorithm designed with the unscented Kalman filter (UKF) was developed to improve the performance. Because the UKF is able to obtain the posterior mean and covariance accurately by using the second-order Taylor series expansion through the sampled sigma points that are propagated by using the true nonlinear system, its performance can be better than that of the extended Kalman filter (EKF), which uses the linearized state transition matrix to predict the covariance. The dynamic models for orbit propagation applied perturbations due to the 40 × 40 geo-potential, the gravity of the Sun and Moon, solar radiation pressure, and atmospheric drag. The 7(8)th-order Runge–Kutta numerical integration was applied for orbit propagation. Two types of observations, navigation solutions and C/A code pseudorange, can be used at the user’s discretion. The performances of the onboard orbit determination were verified using real GPS data of the CHAMP and KOMPSAT-2 satellites. The results of the orbit determination were compared with the precision orbit ephemeris (POE) of the CHAMP and KOMPSAT-2 satellites.     

Energetic neutral atom (ENA) and charged particle periodicities in Saturn’s magnetosphere

The Magnetospheric Imaging Instrument (MIMI) on the Cassini spacecraft has observed energetic neutral atoms (ENA) and charged particles at Saturn from mid-2004 to the present. The particles often but not always reveal striking periodic behavior that seems to depend on the type of particle and spacecraft location. When subjected to a Lomb periodogram analysis, energetic electrons (>150 keV) exhibited strong frequency peaks near 10.80 h (the nominal or “base” period of Saturn kilometric radiation) during 2006–2008, but essentially no periodicity during 2005. The electron periodograms also show pronounced “double” frequency peaks in 2007 and 2008. Energetic protons (3–26 keV) show strong peaks near the same period for 2005–2007, but none for 2008. Oxygen ions at the same energies display strong peaks for 2005 and 2006, but not for 2007 and 2008. By projecting the ENA images onto Saturn’s equatorial plane or onto a plane perpendicular to the equatorial plane and then summing the data in the appropriate dimension, “strip” images can be constructed from which a time history can be derived. These time histories of ENA emissions are also subjected to a Lomb periodogram analyses. The energetic hydrogen neutrals (20–50 keV) exhibited periodic behavior only during 2007, while energetic oxygen neutrals (64–144 keV) displayed a strong SKR-like period in 2005 and 2006 but not for 2007 or 2008. Some of this behavior may be due to changing spacecraft aspect relative to the ENA emissions, and some of it may be real. This periodic behavior may be consistent with a rotating anomaly that “flashes” brightly in the midnight-to-dawn sector once per 10.8 h, with the flash parameters depending on particle species and energy.     

Laser measurements to space debris from Graz SLR station

In order to test laser ranging possibilities to space debris objects, the Satellite Laser Ranging (SLR) Station Graz installed a frequency doubled Nd:YAG pulse laser with a 1 kHz repetition rate, a pulse width of 10 ns, and a pulse energy of 25 mJ at 532 nm (on loan from German Aerospace Center Stuttgart – DLR). We developed and built low-noise single-photon detection units to enable laser ranging to targets with inaccurate orbit predictions, and adapted our standard SLR software to include a few hundred space debris targets. With this configuration, we successfully tracked – within 13 early-evening sessions of each about 1.5 h – 85 passes of 43 different space debris targets, in distances between 600 km and up to more than 2500 km, with radar cross sections from >15 m² down to <0.3 m², and measured their distances with an average precision of about 0.7 m RMS.     

Feasibility of performing space surveillance tasks with a proposed space-based optical architecture

Under ESA contract an industrial consortium including Aboa Space Research Oy (ASRO), the Astronomical Institute of the University of Bern (AIUB), and the Dutch National Aerospace Laboratory (NLR), proposed the observation concept, developed a suitable sensor architecture, and assessed the performance of a space-based optical (SBO) telescope in 2005. The goal of the SBO study was to analyse how the existing knowledge gap in the space debris population in the millimetre and centimetre regime may be closed by means of a passive optical instrument. The SBO instrument was requested to provide statistical information on the space debris population in terms of number of objects and size distribution. The SBO instrument was considered to be a cost-efficient with 20 cm aperture and 6° field-of-view and having flexible integration requirements. It should be possible to integrate the SBO instrument easily as a secondary payload on satellites launched into low-Earth orbits (LEO), or into geostationary orbit (GEO). Thus the selected mission concept only allowed for fix-mounted telescopes, and the pointing direction could be requested freely. Since 2007 ESA focuses space surveillance and tracking activities in the Space Situational Awareness (SSA) preparatory program. Ground-based radars and optical telescopes are studied for the build-up and maintenance of a catalogue of objects. In this paper we analyse how the proposed SBO architecture could contribute to the space surveillance tasks survey and tracking. We assume that the SBO instrumentation is placed into a circular sun-synchronous orbit at 800 km altitude. We discuss the observation conditions of objects at higher altitude, and select an orbit close to the terminator plane. A pointing of the sensor orthogonal to the orbital plane with optimal elevation slightly in positive direction (0° and +5°) is found optimal for accessing the entire GEO regime within one day, implying a very good coverage of controlled objects in GEO, too. Simulations using ESA’s Program for Radar and Optical Observation Forecasting (PROOF) in the version 2005 and a GEO reference population extracted from DISCOS revealed that the proposed pointing scenario provides low phase angles together with low angular velocities of the objects crossing the field-of-view. Radiometric simulations show that the optimal exposure time is 1–2 s, and that spherical objects in GEO with a diameter of below 1 m can be detected. The GEO population can be covered under proper illumination nearly completely, but seasonal drops of the coverage are possible. Subsequent observations of objects are on average at least every 1.5 days, not exceeding 3 days at maximum. A single observation arc spans 3° to 5° on average. Using a simulation environment that connects PROOF to AIUB’s program system CelMech we verify the consistency of the initial orbit determination for five selected test objects on subsequent days as a function of realistic astrometric noise levels. The initial orbit determination is possible. We define requirements for a correlator process essential for catalogue build-up and maintenance. Each single observation should provide an astrometric accuracy of at least 1”–1.5” so that the initially determined orbits are consistent within a few hundred kilometres for the semi-major axis, 0.01 for the eccentricity, and 0.1° for the inclination.     

Viewing radiation signatures of solar energetic particles in interplanetary space

A current serious limitation on the studies of solar energetic particle (SEP) events is that their properties in the inner heliosphere are studied only through in situ spacecraft observations. Our understanding of spatial distributions and temporal variations of SEP events has come through statistical studies of many such events over several solar cycles. In contrast, flare SEPs in the solar corona can be imaged through their radiative and collisional interactions with solar fields and particles. We suggest that the heliospheric SEPs may also interact with heliospheric particles and fields to produce signatures which can be remotely observed and imaged. A challenge with any such candidate signature is to separate it from that of flare SEPs. The optimum case for imaging high-energy (E > 100 MeV) heliospheric protons may be the emission of π⁰-decay γ-rays following proton collisions with solar wind (SW) ions. In the case of E > 1 MeV electrons, gyrosynchrotron radio emission may be the most readily detectible remote signal. In both cases we may already have observed one or two such events. Another radiative signature from nonthermal particles may be resonant transition radiation, which has likely already been observed from solar flare electrons. We discuss energetic neutrons as another possible remote signature, but we rule out γ-ray line and 0.511 MeV positron annihilation emission as observable signatures of heliospheric energetic ions. We are already acquiring global signatures of large inner-heliospheric SW density features and of heliosheath interactions between the SW and interstellar neutral ions. By finding an appropriate observable signature of remote heliospheric SEPs, we could supplement the in situ observations with global maps of energetic SEP events to provide a comprehensive view of SEP events.     

Dynamical evolution of high area-to-mass ratio debris released into GPS orbits

A large set of simulations, including all the relevant perturbations, was carried out to investigate the long-term dynamical evolution of fictitious high area-to-mass ratio (A/M) objects released, with a negligible velocity variation, in each of the six orbital planes used by Global Positioning System (GPS) satellites. As with similar objects discovered in near synchronous trajectories, long lifetime orbits, with mean motions of about 2 revolutions per day, were found possible for debris characterized by extremely high area-to-mass ratios. Often the lifetime exceeds 100 years up to A/M ∼ 45 m²/kg, decreasing rapidly to a few months above such a threshold. However, the details of the evolution, which are conditioned by the complex interplay of solar radiation pressure and geopotential plus luni-solar resonances, depend on the initial conditions. Different behaviors are thus possible. In any case, objects like those discovered in synchronous orbits, with A/M as high as 20–40 m²/kg, could also survive in this orbital regime, with semi-major axes close to the semi-synchronous values, with maximum eccentricities between 0.3 and 0.7, and with significant orbit pole precessions (faster and wider for increasing values of A/M), leading to inclinations between 30° and more than 90°.