Size distribution of NaK droplets released during RORSAT reactor core ejection

NaK droplets consist of eutectic sodium–potassium alloy and have been released during RORSAT reactor core ejections mostly on orbits close to 950 km altitude. They contributed to the space debris environment in the centimeter and millimeter regime. NaK droplets have been modeled before in ESAs MASTER Debris and Meteoroid Environment Model. The approach is currently revised for the MASTER 2005 upgrade. The new NaK model gives estimations of the parameters of the size distribution function, which are based on physical relations only. NASA radar observations confirm this physical approach. A bimodal size distribution is derived, which is based on the Rosin–Rammler equation. The Rosin–Rammler equation is an empirical volume distribution function. The number of parameters is limited to two. It is likely that the coolant system contains two types of orifice diameters. This makes it necessary to apply the Rosin–Rammler distribution twice, resulting in a bimodal size distribution with altogether four parameters. The comparison shows that the new NaK model is in good agreement with the NASA model, which is based on radar observations. Results of orbit propagation simulation runs are presented.     

Debris swarms seen by SMEI

The large 3° × 60° fields-of-view of the Solar Mass Ejection Imager (SMEI) instruments are oriented on the stabilized Coriolis satellite to image most of the sky each Sun-synchronous orbit. Besides observing coronal mass ejections, the SMEI mission objective, SMEI also has detected a plethora of Earth-orbiting satellites (resident space objects or RSOs) brighter than ∼8th magnitude at a rate of about 1 per minute. Occasionally, SMEI sees an RSO swarm: a sudden onset of a large number of RSOs, many more than the nominal rate, upto dozens detected in a 4-s frame. These swarms usually last for a few minutes. A sample of six such RSO ensembles is analyzed in this paper in which the distance and the direction of the velocity vector for individual objects are estimated. We present the observational evidence indicating that the swarms must be near-field objects traveling in orbits near that of Coriolis, and that the relatively speeds between the objects and Coriolis are low. Further, analyses indicate that the RSOs are quite close (<20 m) and are generally moving radially away from the satellite. The predicted encounter geometries for Coriolis passing through or near a small debris cloud is, generally, quite inconsistent with the observations. The most likely explanation consistent with the observations is that SMEI is seeing debris being ejected from the Coriolis spacecraft itself. An analysis of distance and brightness for a subset of the RSOs indicates that the median diameter of the debris particles is ∼80 μm.     

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.     

Highly Elliptical Orbits for Arctic observations: Assessment of ionizing radiation

The ionizing radiation environment was analyzed for a variety of potential Highly Elliptical Orbits (HEOs) with orbital periods ranging from 6 h to 24 h suitable to continuously monitor the Arctic region. Several models available from the ESA Space Environment Information System (SPENVIS) online tool were employed, including the new-generation AE9/AP9 model for trapped radiation. Results showed that the Total Ionizing Dose (TID) has a well-pronounced local minimum for the 14-h orbit, which is nearly identical to the overall minimum observed for the longest orbital period (24 h). The thickness of slab aluminum shielding required to keep the annual TID below 10, 5 and 3.33 krad (i.e. 150, 75 and 50 krad for 15 years of mission duration) for a 14-h orbit is 2.1, 2.7 and 3.1 mm respectively. The 16-h orbit requires an additional 0.5 mm of aluminum to achieve the same results, while the 24-h orbit requires less shielding in the order of 0.2–0.3 mm. Comparison between the AE8/AP8 and AE9/AP9 models was conducted for all selected orbits. Results demonstrated that differences ranged from −70% to +170% depending on orbit geometry.     

Mars Phobos and Deimos Survey (M-PADS) – A martian Moons orbiter and Phobos lander

We describe a Mars ‘Micro Mission’ for detailed study of the martian satellites Phobos and Deimos. The mission involves two ∼330 kg spacecraft equipped with solar electric propulsion to reach Mars orbit. The two spacecraft are stacked for launch: an orbiter for remote investigation of the moons and in situ studies of their environment in Mars orbit, and another carrying a lander for in situ measurements on the surface of Phobos (or alternatively Deimos). Phobos and Deimos remain only partially studied, and Deimos less well than Phobos. Mars has almost always been the primary mission objective, while the more dedicated Phobos project (1988–89) failed to realise its full potential. Many questions remain concerning the moons’ origins, evolution, physical nature and composition. Current missions, such as Mars Express, are extending our knowledge of Phobos in some areas but largely neglect Deimos. The objectives of M-PADS focus on: origins and evolution, interactions with Mars, volatiles and interiors, surface features, and differences. The consequent measurement requirements imply both landed and remote sensing payloads. M-PADS is expected to accommodate a 60 kg orbital payload and a 16 kg lander payload. M-PADS resulted from a BNSC-funded study carried out in 2003 to define candidate Mars Micro Mission concepts for ESA’s Aurora programme.     

Bayesian linking of geosynchronous orbital debris tracks as seen by the Large Synoptic Survey Telescope

We describe a Bayesian sampling model for linking and constraining orbit models from angular observations of “streaks” in optical telescope images. Our algorithm is particularly suited to situations where the observation times are small fractions of the orbital periods of the observed objects or when there is significant confusion of objects in the observation field. We use Markov Chain Monte Carlo to sample from the joint posterior distribution of the parameters of multiple orbit models (up to the number of observed tracks) and parameters describing which tracks are linked with which orbit models. Using this algorithm, we forecast the constraints on geosynchronous (GEO) debris orbits achievable with the planned Large Synoptic Survey Telescope (LSST). Because of the short 15 s exposure times, preliminary orbit determinations of GEO objects from LSST will have large and degenerate errors on the orbital elements. Combined with the expected crowded fields of GEO debris it will be challenging to reliably link orbital tracks in LSST observations given the currently planned observing cadence.     

Solar and interplanetary precursors of geomagnetic storms in solar cycle 23

Estimating the magnetic storm effectiveness of solar and associated interplanetary phenomena is of practical importance for space weather modelling and prediction. This article presents results of a qualitative and quantitative analysis of the probable causes of geomagnetic storms during the 11-year period of solar cycle 23: 1996–2006. Potential solar causes of 229 magnetic storms (Dst ? −50 nT) were investigated with a particular focus on halo coronal mass ejections (CMEs). A 5-day time window prior to the storm onset was considered to track backward the Sun’s eruptions of halo CMEs using the SOHO/LASCO CMEs catalogue list. Solar and interplanetary (IP) properties associated with halo CMEs were investigated and correlated to the resulting geomagnetic storms (GMS). In addition, a comparative analysis between full and partial halo CME-driven storms is established. The results obtained show that about 83% of intense storms (Dst ? −100 nT) were associated with halo CMEs. For moderate storms (−100 nT < Dst ? −50 nT), only 54% had halo CME background, while the remaining 46% were assumed to be associated with corotating interaction regions (CIRs) or undetected frontside CMEs. It was observed in this study that intense storms were mostly associated with full halo CMEs, while partial halo CMEs were generally followed by moderate storms. This analysis indicates that up to 86% of intense storms were associated with interplanetary coronal mass ejections (ICMEs) at 1 AU, as compared to moderate storms with only 44% of ICME association. Many other quantitative results are presented in this paper, providing an estimate of solar and IP precursor properties of GMS within an average 11-year solar activity cycle. The results of this study constitute a key step towards improving space weather modelling and prediction.     

Geostationary orbit determination using SATRE

A new strategy of precise orbit determination (POD) for GEO (Geostationary Earth Orbit) satellite using SATRE (SAtellite Time and Ranging Equipment) is presented. Two observation modes are proposed and different channels of the same instruments are used to construct different observation modes, one mode receiving time signals from their own station and the other mode receiving time signals from each other for two stations called pairs of combined observations. Using data from such a tracking network in China, the results for both modes are compared. The precise orbit determination for the Sino-1 satellite using the data from 6 June 2005 to 13 June 2005 has been carried out in this work. The RMS (Root-Mean-Square) of observing residuals for 3-day solutions with the former mode is better than 9.1 cm. The RMS of observing residuals for 3-day solutions with the latter mode is better than 4.8 cm, much better than the former mode. Orbital overlapping (3-day orbit solution with 1-day orbit overlap) tests show that the RMS of the orbit difference for the former mode is 0.16 m in the radial direction, 0.53 m in the along-track direction, 0.97 m in the cross-track direction and 1.12 m in the 3-dimension position and the RMS of the orbit difference for the latter mode is 0.36 m in the radial direction, 0.89 m in the along-track direction, 1.18 m in the cross-track direction and 1.52 m in the 3-dimension position, almost the same as the former mode. All the experiments indicate that a meter-level accuracy of orbit determination for geostationary satellite is achievable.     

Solar proton enhancements in different energy channels and coronal mass ejections during the last solar cycle

The main properties of 11622 coronal mass ejections (CMEs) observed by the Solar and Heliospheric Observatory (SOHO) mission’s Large Angle and Spectrometric Coronagraph (LASCO-C2) from January 1996 through December 2006 are considered. Moreover, the extended database of solar proton enhancements (SPEs) with proton flux >0.1 pfu at energy >10 MeV measured at the Earth’s orbit is also studied. A comparison of these databases gives new results concerning the sources and acceleration mechanisms of solar energetic particles. Specifically, coronal mass ejections with width >180° (wide) and linear speed >800 km/s (fast) seem they have the best correlation with solar proton enhancements. The study of some specific solar parameters, such as soft X-ray flares, sunspot numbers, solar flare index etc. has showed that the soft X-ray flares with importance >M5 may provide a reasonable proxy index for the SPE production rate. From this work, it is outlined that the good relation of the fast and wide coronal mass ejections to proton enhancements seems to lead to a similar conclusion. In spite of the fact that in the case of CMEs the statistics cover only the last solar cycle, while the measurements of SXR flares are extended over three solar cycles, it is obvious for the studied period that the coronal mass ejections can also provide a good index for the solar proton production.     

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.     

Synergistic approach of asteroid exploitation and planetary protection

The asteroid and cometary impact hazard has long been recognised as an important issue requiring risk assessment and contingency planning. At the same time asteroids have also been acknowledged as possible sources of raw materials for future large-scale space engineering ventures. This paper explores possible synergies between these two apparently opposed views; planetary protection and space resource exploitation. In particular, the paper assumes a 5 tonne low-thrust spacecraft as a baseline for asteroid deflection and capture (or resource transport) missions. The system is assumed to land on the asteroid and provide a continuous thrust able to modify the orbit of the asteroid according to the mission objective. The paper analyses the capability of such a near-term system to provide both planetary protection and asteroid resources to Earth. Results show that a 5 tonne spacecraft could provide a high level of protection for modest impact hazards: airburst and local damage events (caused by 15–170 m diameter objects). At the same time, the same spacecraft could also be used to transport to bound Earth orbits significant quantities of material through judicious use of orbital dynamics and passively safe aero-capture manoeuvres or low energy ballistic capture. As will be shown, a 5 tonne low-thrust spacecraft could potentially transport between 12 and 350 times its own mass of asteroid resources by means of ballistic capture or aero-capture trajectories that pose very low dynamical pressures on the object.     

Heliotropic dust rings for Earth climate engineering

This paper examines the concept of a Sun-pointing elliptical Earth ring comprised of dust grains to offset global warming. A new family of non-Keplerian periodic orbits, under the effects of solar radiation pressure and the Earth’s J₂ oblateness perturbation, is used to increase the lifetime of the passive cloud of particles and, thus, increase the efficiency of this geoengineering strategy. An analytical model is used to predict the orbit evolution of the dust ring due to solar-radiation pressure and the J₂ effect. The attenuation of the solar radiation can then be calculated from the ring model. In comparison to circular orbits, eccentric orbits yield a more stable environment for small grain sizes and therefore achieve higher efficiencies when the orbit decay of the material is considered. Moreover, the novel orbital dynamics experienced by high area-to-mass ratio objects, influenced by solar radiation pressure and the J₂ effect, ensure the ring will maintain a permanent heliotropic shape, with dust spending the largest portion of time on the Sun facing side of the orbit. It is envisaged that small dust grains can be released from a circular generator orbit with an initial impulse to enter an eccentric orbit with Sun-facing apogee. Finally, a lowest estimate of 1 × 10¹² kg of material is computed as the total mass required to offset the effects of global warming.     

Modeling of LEO orbital debris populations for ORDEM2008

The NASA Orbital Debris Engineering Model, ORDEM2000, is in the process of being updated to a new version: ORDEM2008. The data-driven ORDEM covers a spectrum of object size from 10 μm to greater than 1 m, and ranging from LEO (low Earth orbit) to GEO (geosynchronous orbit) altitude regimes. ORDEM2008 centimeter-sized populations are statistically derived from Haystack and HAX (the Haystack Auxiliary) radar data, while micron-sized populations are estimated from shuttle impact records. Each of the model populations consists of a large number of orbits with specified orbital elements, the number of objects on each orbit (with corresponding uncertainty), and the size, type, and material assignment for each object. This paper describes the general methodology and procedure commonly used in the statistical inference of the ORDEM2008 LEO debris populations. Major steps in the population derivations include data analysis, reference-population construction, definition of model parameters in terms of reference populations, linking model parameters with data, seeking best estimates for the model parameters, uncertainty analysis, and assessment of the outcomes. To demonstrate the population-derivation process and to validate the Bayesian statistical model applied in the population derivations throughout, this paper uses illustrative examples for the special cases of large-size (>1 m, >32 cm, and >10 cm) populations that are tracked by SSN (the Space Surveillance Network) and also monitored by Haystack and HAX radars operating in a staring mode.     

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.     

The fast debris evolution model

The ‘particles-in-a-box’ (PIB) model introduced by Talent [Talent, D.L. Analytic model for orbital debris environmental management. J. Spacecraft Rocket, 29 (4), 508–513, 1992.] removed the need for computer-intensive Monte Carlo simulation to predict the gross characteristics of an evolving debris environment. The PIB model was described using a differential equation that allows the stability of the low Earth orbit (LEO) environment to be tested by a straightforward analysis of the equation’s coefficients. As part of an ongoing research effort to investigate more efficient approaches to evolutionary modelling and to develop a suite of educational tools, a new PIB model has been developed. The model, entitled Fast Debris Evolution (FADE), employs a first-order differential equation to describe the rate at which new objects ?10 cm are added and removed from the environment. Whilst Talent [Talent, D.L. Analytic model for orbital debris environmental management. J. Spacecraft Rocket, 29 (4), 508–513, 1992.] based the collision theory for the PIB approach on collisions between gas particles and adopted specific values for the parameters of the model from a number of references, the form and coefficients of the FADE model equations can be inferred from the outputs of future projections produced by high-fidelity models, such as the DAMAGE model.     

Relativistic electrons high doses at International Space Station and Foton M2/M3 satellites

The paper presents observation of relativistic electrons. Data are collected by the Radiation Risk Radiometer-Dosimeters (R3D) B2/B3 modifications during the flights of Foton M2/M3 satellites in 2005 and 2007 as well as by the R3DE instrument at the European Technology Exposure Facility (EuTEF) on the Columbus External Payload Adaptor at the International Space Station (ISS) in the period February 20 – April 28, 2008. On the Foton M2/M3 satellites relativistic electrons are observed more frequently than on the ISS because of higher (62.8°) inclination of the orbit. At both Foton satellites the usual duration of the observations are a few minutes long. On the ISS the duration usually is about 1 min or less. The places of observations of high doses due to relativistic electrons are distributed mainly at latitudes above 50° geographic latitude in both hemispheres on Foton M2/M3 satellites. A very high maximum is found in the southern hemisphere at longitudinal range 0°–60°E. At the ISS the maximums are observed between 45° and 52° geographic latitude in both hemispheres mainly at longitudes equatorward from the magnetic poles. The measured absolute maximums of dose rates generated by relativistic electrons are found to be as follows: 304 μGy h⁻¹ behind 1.75 g cm⁻² shielding at Foton M2, 2314 μGy h⁻¹ behind 0.71 g cm⁻² shielding at Foton M3 and 19,195 μGy h⁻¹ (Flux is 8363 cm⁻² s⁻¹) behind les than 0.4 g cm⁻² shielding at ISS.     

Solar and interplanetary origins of the November 2004 superstorms

During the first half of November 2004, many solar flares and coronal mass ejections (CMEs) were associated with solar active region (AR) 10696. This paper attempts to identify the solar and interplanetary origins of two superstorms which occurred on 8 and 10 November with peak intensities of Dst = −373 nT and −289 nT, respectively. Southward interplanetary magnetic fields within a magnetic cloud (MC), and a sheath + MC were the causes of these two superstorms, respectively. Two different CME propagation models [Gopalswamy, N., Yashiro, S., Kaiser, M.L. et al. Predicting the 1-AU arrival times of coronal mass ejections. J. Geophys. Res. 106, 29207–29219, 2001; Gopalswamy, N.S., Lara, A., Manoharan, P.K. et al. An empirical model to predict the 1-AU arrival of interplanetary shocks. Adv. Space Res. 36, 2289–2294, 2005] were employed to attempt to identify the solar sources. It is found that the models identify several potential CMEs as possible sources for each of the superstorms. The two Gopalswamy et al. models give the possible sources for the first superstorm as CMEs on 2330 UT 4 November 2004 or on 1454 UT 5 November 2004. For the second superstorm, the possible solar source was a CME that on 0754 UT 5 November 2004 or one that occurred on 1206 UT 5 November 2004. We note that other propagation models sometimes agree and other times disagree with the above results. It is concluded that during high solar/interplanetary activity intervals such as this one, the exact solar source is difficult to identify. More refined propagation models are needed.     

Comparison analyses on the 150 × 150 lunar gravity field models by gravity/topography admittance,correlation and precision orbit determination

We analyzed the 150 × 150 lunar gravity field models, LP150Q, GLGM-3 and SGM150, using the power spectrum on the lunar nearside and farside, the lunar global and localized gravity/topography admittance and correlation, and Chang’E-2 precision orbit determination to investigate which model is a more effective tool to estimate geophysical parameters and determine the lunar satellite precision orbit. Results indicate that all gravity field models can be used to estimate the lunar geophysical parameters of the nearside of the Moon. However, SGM150 is better in such computation of the farside. Additionally, SGM150 is shown to be the most useful model for determining the lunar satellite orbit.     

Impact of GPS antenna phase center variations on precise orbits of the GOCE satellite

The first European Space Agency Earth explorer core mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) has been launched on March 17, 2009. The 12-channel dual-frequency Global Positioning System receiver delivers 1 Hz data and provides the basis for precise orbit determination (POD) on the few cm-level for such a very low orbiting satellite (254.9 km). As a member of the European GOCE Gravity Consortium, which is responsible for the GOCE High-level Processing Facility (HPF), the Astronomical Institute of the University of Bern (AIUB) provides the Precise Science Orbit (PSO) product for the GOCE satellite. The mission requirement for 1-dimensional POD accuracy is 2 cm. The use of in-flight determined antenna phase center variations (PCVs) is necessary to meet this requirement. The PCVs are determined from 154 days of data and the magnitude is up to 3-4 cm. The impact of the PCVs on the orbit determination is significant. The cross-track direction benefits most of the PCVs. The improvement is clearly seen in the orbit overlap analysis and in the validation with independent Satellite Laser Ranging (SLR) measurements. It is the first time that SLR could validate the cross-track component of a LEO orbit.