Medium Earth Orbit dynamical survey and its use in passive debris removal

The Medium Earth Orbit (MEO) region hosts satellites for navigation, communication, and geodetic/space environmental science, among which are the Global Navigation Satellites Systems (GNSS). Safe and efficient removal of debris from MEO is problematic due to the high cost for maneuvers needed to directly reach the Earth (reentry orbits) and the relatively crowded GNSS neighborhood (graveyard orbits). Recent studies have highlighted the complicated secular dynamics in the MEO region, but also the possibility of exploiting these dynamics, for designing removal strategies. In this paper, we present our numerical exploration of the long-term dynamics in MEO, performed with the purpose of unveiling the set of reentry and graveyard solutions that could be reached with maneuvers of reasonable $\mathrm{\Delta }V$ cost. We simulated the dynamics over 120–200?years for an extended grid of millions of fictitious MEO satellites that covered all inclinations from 0 to 90°, using non-averaged equations of motion and a suitable dynamical model that accounted for the principal geopotential terms, 3rd-body perturbations and solar radiation pressure (SRP). We found a sizeable set of usable solutions with reentry times that exceed $～40$ years, mainly around three specific inclination values: 46°, 56°, and 68°; a result compatible with our understanding of MEO secular dynamics. For $\mathrm{\Delta }V?300$ m/s (i.e., achieved if you start from a typical GNSS orbit and target a disposal orbit with $e<0.3$), reentry times from GNSS altitudes exceed $～70$ years, while low-cost ($\mathrm{\Delta }V?5–35$ m/s) graveyard orbits, stable for at lest 200?years, are found for eccentricities up to $e\approx 0.018$. This investigation was carried out in the framework of the EC-funded “ReDSHIFT” project.     

Multi-instrument observations of large-scale atmospheric gravity waves/traveling ionospheric disturbances associated with enhanced auroral activity over Svalbard

This study reports on observations of large-scale atmospheric gravity waves/traveling ionospheric disturbances (AGWs/TIDs) using Global Positioning System (GPS) total electron content (TEC) and Fabry–Perot Interferometer’s (FPI’s) intensity of oxygen red line emission at 630?nm measurements over Svalbard on the night of 6 January 2014. TEC large-scale TIDs have primary periods ranging between 29 and 65?min and propagate at a mean horizontal velocity of $～$749–761?m/s with azimuth of $～$345–347$°$ (which corresponds to poleward propagation direction). On the other hand, FPI large-scale AGWs have larger periods of $～$42–142?min. These large-scale AGWs/TIDs were linked to enhanced auroral activity identified from co-located all-sky camera and IMAGE magnetometers. Similar periods, speed and poleward propagation were found for the all-sky camera ($～$60–97?min and $～$823?m/s) and the IMAGE magnetometers ($～$32–53?min and $～$708?m/s) observations. Joule heating or/and particle precipitation as a result of auroral energy injection were identified as likely generation mechanisms for these disturbances.     

Physical characterization of the deep-space debris WT1190F: A testbed for advanced SSA techniques

We report on extensive ${\mathit{BVR}}_c{I}_c$ photometry and low-resolution ($\lambda /\mathrm{\Delta }\lambda ～250$) spectroscopy of the deep-space debris WT1190F, which impacted Earth offshore from Sri Lanka, on 2015 November 13. In spite of its likely artificial origin (as a relic of some past lunar mission), the case offered important points of discussion for its suggestive connection with the envisaged scenario for a (potentially far more dangerous) natural impactor, like an asteroid or a comet.Our observations indicate for WT1190F an absolute magnitude $R_c={32.45}_{\pm 0.31}$, with a flat dependence of reflectance on the phase angle, such as ${\mathit{dR}}_c/d?～{0.007}_{\pm 2}$?mag?deg^?1. The detected short-timescale variability suggests that the body was likely spinning with a period twice the nominal figure of $P_{\mathrm{flash}}={1.4547}_{\pm 0.0005}\mathrm{s}$, as from the observed lightcurve. In the ${\mathit{BVR}}_c{I}_c$ color domain, WT1190F closely resembled the Planck deep-space probe. This match, together with a depressed reflectance around 4000 and 8500 Å may be suggestive of a “grey” (aluminized) surface texture.The spinning pattern remained in place also along the object fiery entry in the atmosphere, a feature that may have partly shielded the body along its fireball phase perhaps leading a large fraction of its mass to survive intact, now lying underwater along a tight ($～1\times 80$?km) strip of sea, at a depth of 1500?m or less.Under the assumption of Lambertian scatter, an inferred size of ${216}_{\pm 30}/\sqrt{\alpha /0.1}$?cm is obtained for WT1190F. By accounting for non-gravitational dynamical perturbations, the Area-to-Mass ratio of the body was in the range $(0.006?\mathit{AMR}?0.011)$?m²?kg^?1.Both these figures resulted compatible with the two prevailing candidates to WT1190F’s identity, namely the Athena II Trans-Lunar Injection Stage of the Lunar Prospector mission, and the ascent stage of the Apollo 10 lunar module, callsign “Snoopy”. Both candidates have been analyzed in some detail here through accurate 3D CAD design mockup modelling and BRDF reflectance rendering to derive the inherent photometric properties to be compared with the observations.     

First solar observations with ALMA

The Atacama Large Millimeter-Submillimeter Array (ALMA) has opened a new window for studying the Sun via high-resolution high-sensitivity imaging at millimeter wavelengths. In this contribution I review the capabilities of the instrument for solar observing and describe the extensive effort taken to bring the possibility of solar observing with ALMA to the scientific community. The first solar ALMA observations were carried out during 2014 and 2015 in two ALMA bands, Band 3 ($\lambda =3$?mm) and Band 6 ($\lambda =1.3$?mm), in single-dish and interferometric modes, using single pointing and mosaicing observing techniques, with spatial resolution up to $～$2″ and $～$1″ in the two bands, respectively. I overview several recently published studies which made use of the first solar ALMA observations, describe current status of solar observing with ALMA and briefly discuss the future capabilities of the instrument.     

A combination method using evolutionary algorithms in initial orbit determination for too short arc

With the combination of two evolutionary algorithms EDA and DE, a new method of initial orbit determination for satellites based on ground-based too-short-arc is established. Compared with other algorithms, the proposed method focuses on the most densely populated region in the solution space rather than the individual with best fitness value. Both the global information and local information are well fused in the search of optimum. In the method $(a,e,M)$ are treated as variables of the optimization, and the optimization procedure is carried out as a two-stage hierarchical optimization problem which has three variables for each stage. Kernel density estimation is applied to build the probability distribution model without any assumptions of the specified distribution, accompanied by handling semi-major axis and eccentricity as a pair of dependent variables in the construction of the probability for the correlation between them in the practice. Numerical experiments with real ground-based observations show that the proposed method is applicable to too-short-arc with even 3?s, and the result of bias in several kilometers can be achieved with $5^{″}$ error added to angular measurements.     

Vertical and radial metallicity gradients in high latitude galactic fields with SDSS

We used the ugr magnitudes of 1437467 F-G type main-sequence stars with metal abundance $-2?[\mathrm{Fe}/\mathrm{H}]?+0.2$ dex and estimated radial and vertical metallicity gradients for high Galactic-latitude fields, $50°<b?90°$ and $0°<l?360°$, of the Milky Way Galaxy. The radial metallicity gradient $d[\mathrm{Fe}/\mathrm{H}]/\mathit{dR}=-0.042\pm 0.011$ dex kpc^?1 estimated for the stars with $1.31<z\le 1.74$ kpc is attributed to the thin-disc population. While, the radial gradients evaluated for stars at higher vertical distances are close to zero indicating that the thick disc and halo have not undergone a radial collapse phase at least at high Galactic latitudes. The vertical metallicity gradients estimated for stars with three different Galactic latitudes, $50°<b?65°,65°<b?80°$ and $80°<b?90°$ do not show a strong indication for Galactic latitude dependence of our gradients. The thin disc, $0.5<z?2$ kpc, with a vertical metallicity gradient $d\left[\mathrm{Fe}/\mathrm{H}\right]/\mathit{dz}=-0.308\pm 0.018$ dex kpc^?1, is dominant only in galactocentric distance interval $6<R?10$ kpc, while the thick disc ($2<z?5$ kpc) could be observed in the intervals $6<R?10$ and $10<R?15$ kpc with compatible vertical metallicity gradients, i.e. $d\left[\mathrm{Fe}/\mathrm{H}\right]/\mathit{dz}=-0.164\pm 0.014$ dex kpc^?1 and $d\left[\mathrm{Fe}/\mathrm{H}\right]/\mathit{dz}=-0.172\pm 0.016$ dex kpc^?1. Five vertical metallicity gradients are estimated for the halo ($z>5$ kpc) in three galactocentric distance intervals, $6<R?10,10<R?15$ and $15<R?20$ kpc. The first one corresponding to the interval $6<R?10$ kpc is equal to $d\left[\mathrm{Fe}/\mathrm{H}\right]/\mathit{dz}=-0.023\pm 0.006$ dex kpc^?1, while the others at larger galactocentric distances are close to zero. We derived synthetic vertical metallicity gradients for 2,230,167 stars and compared them with the observed ones. There is a good agreement between the two sets of vertical metallicity gradients for the thin disc, while they are different for the thick disc. For the halo, the conspicuous difference corresponds to the galactocentric distance interval $6<R?10$ kpc, while they are compatible at higher galactocentric distance intervals.     

GRACE accelerometer calibration by high precision non-gravitational force modeling

The precise modeling and knowledge of non-gravitational forces acting on satellites is of big interest to many scientific tasks and missions. Since 2002, the twin GRACE satellites have measured these forces in a low Earth orbit with highly precise accelerometers, for about 15?years. Besides the significance for the GRACE mission, these measurement data allow the evaluation of modeling approaches and the improvement of force models. Unfortunately, before any scientific usage, the accelerometer measurements need to be calibrated, namely scale factor and bias have to be regularly estimated.In this study we demonstrate an accelerometer calibration approach, solely based on high precision non-gravitational force modeling without any use of empirically or stochastically estimated parameters, using our in-house developed satellite simulation tool XHPS. The aim of this work is twofold, first we use the accelerometer data and the residuals resulting from the calibration to quantitatively analyze and validate different non-gravitational force model approaches. In a second step, we compare the calibration results to three different calibration methods from different authors, based on gravity field recovery, GPS-based precise orbit determination, and based on modeled accelerations.We consider atmospheric drag forces and winds, as well as radiation forces due to solar radiation pressure, albedo, Earth infrared and thermal radiation (TRP) of the satellite itself. For TRP, we investigate different transient temperature calculation approaches for the satellite surfaces with absorbed power from the aforementioned radiation sources. A detailed finite element model of the satellite is utilized for every force, considering orientation, material properties and shadowing conditions for each element.For cross-track and radial direction, which are mainly affected by the radiative forces, our calibration residuals are quite small when drag is not super dominant (1–3?$\text{nm}/{\text{s}}^2$ for total accelerations around $\pm$50?$\text{nm}/{\text{s}}^2$). For these directions the calibration seems to perform better than the other compared methods, where some bigger differences were found. For the drag dominated along-track direction it is vice versa, here our method is not sensitive enough because the difference between modeled and measured drag is bigger (e.g. residuals around 10?$\text{nm}/{\text{s}}^2$ for total accelerations around $\pm$70?$\text{nm}/{\text{s}}^2$ for low solar activity). In along-track direction the orbit determination based methods are more sensitive and produce more reliable results. Results for the complete GRACE mission time span from 2003 to 2017 are shown, covering different seasonal environmental conditions.     

Modelling ionospheric vertical drifts over Africa low latitudes using Empirical Orthogonal functions and comparison with climatological model

For the first time, empirical model of daytime vertical $\mathbf{E}\times \mathbf{B}$ drift based on Empirical Orthogonal functions (EOF) decomposition technique is presented. Day-to-day variability of $\mathbf{E}\times \mathbf{B}$ drift inferred from horizontal (H) geomagnetic field data around dip latitude for the period of 2008–2013 is used to both develop and validate the model. Results show that the EOF technique is promising with modelled values and data giving correlation coefficient values of at least 0.90 for geomagnetic conditions of both $K_p?3$ and $K_p>3$ within 2008–2013. Independent model validation shows that in situ $\mathbf{E}\times \mathbf{B}$ values from ion velocity meter (IVM) instrument on-board C/NOFS satellite are closer to model $\mathbf{E}\times \mathbf{B}$ estimates than the climatological Scherliess-Fejer (SF) model incorporated within the International Reference Ionosphere (IRI).     

Near-infrared study of open clusters Teutsch 10 and Teutsch 25

The astrophysical parameters have been estimated for two unstudied open star clusters Teutsch 10 and Teutsch 25 using the Two Micron All Sky Survey ($2\mathit{MASS}$) database. Radius is estimated as 4.5 arcmin for both clusters using radial density profiles. We have estimated proper motion values in both RA and DEC directions as $2.28\pm 0.3$ and $-0.38\pm 0.11$?mas?yr^?1 for Teutsch 10 and $0.48\pm 0.3$ and $3.35\pm 0.16$?mas?yr^?1 for Teutsch 25 using $\mathit{PPMXL}$¹ catalog. By estimating the stellar membership probabilities, we have identified 30 and 28 most likely members for Teutsch 10 and Teutsch 25 respectively. We have estimated the reddening as $E(B-V)=0.96\pm 0.3$?mag for Teutsch 10 and $0.58\pm 0.2$?mag for Teutsch 25, while the corresponding distances are $2.4\pm 0.2$ and $1.9\pm 0.1$?kpc. Ages of $70\pm 10$?Myr for Teutsch 10 and $900\pm 100$?Myr for Teutsch 25 are estimated using the theoretical isochrones of metallicity Z?=?0.019. The mass function slopes are derived as $1.23\pm 0.30$ and $1.09\pm 0.35$ for Teutsch 10 and Teutsch 25 respectively. Estimated mass function slope for both the clusters are close to the Salpeter value ($x=1.35$) within the errors. Estimated values of dynamical relaxation time are found to be less than cluster’s age for these objects. This concludes that both objects are dynamically relaxed. The possible reason for relaxation may be due to dynamical evolution or imprint of star formation or both.     

An analytical model of prominence dynamics

Solar prominences are magnetic structures incarcerating cool and dense gas in an otherwise hot solar corona. Prominences can be categorized as quiescent and active. Their origin and the presence of cool gas ($～{10}^4$?K) within the hot ($～{10}^6\text{K}$) solar corona remains poorly understood. The structure and dynamics of solar prominences was investigated in a large number of observational and theoretical (both analytical and numerical) studies. In this paper, an analytic model of quiescent solar prominence is developed and used to demonstrate that the prominence velocity increases exponentially, which means that some gas falls downward towards the solar surface, and that Alfvén waves are naturally present in the solar prominences. These theoretical predictions are consistent with the current observational data of solar quiescent prominences.     

Velocity shear Kelvin-Helmholtz instability with inhomogeneous DC electric field in the magnetosphere of Saturn

In this paper parallel flow velocity shear Kelvin-Helmholtz instability has been studied in two different extended regions of the inner magnetosphere of Saturn. The method of the characteristic solution and kinetic approach has been used in the mathematical calculation of dispersion relation and growth rate of K-H waves. Effect of magnetic field (B), inhomogeneity (P/a), velocity shear scale length ($A_i$), temperature anisotropy ($T_{\perp }/T_{||}$), electric field (E), ratio of electron to ion temperature ($T_e/T_i$), density gradient (${\epsilon }_n{\rho }_i$) and angle of propagation ($\theta$) on the dimensionless growth rate of K-H waves in the inner magnetosphere of Saturn has been observed with respect to $k_{\perp }{\rho }_i$. Calculations of this theoretical analysis have been done taking the data from the Cassini in the inner magnetosphere of Saturn in the two extended regions of Rs ～4.60–4.01 and Rs ～4.82–5.0. In our study velocity shear, temperature anisotropy and magnitude of the electric field are observed to be the major sources of free energy for the K-H instability in both the regions considered. The inhomogeneity of electric field, electron-ion temperature ratio, and density gradient have been observed playing stabilizing effect on K-H instability. This study also indicates the effect of the vicinity of icy moon Enceladus on the growth of K-H instability.     

An estimation of Envisat’s rotational state accounting for the precession of its rotational axis caused by gravity-gradient torque

The rotational state of Envisat is re-estimated using the specular glint times in optical observation data obtained from 2013 to 2015. The model is simplified to a uniaxial symmetric model with the first order variation of its angular momentum subject to a gravity-gradient torque causing precession around the normal of the orbital plane. The sense of Envisat’s rotation can be derived from observational data, and is found to be opposite to the sense of its orbital motion. The rotational period is estimated to be $(120.674\pm 0.068)·\exp \left((4.5095\pm 0.0096)\times {10}^{-4}·t\right)\text{s}$, where t is measured in days from the beginning of 2013. The standard deviation is 0.760?s, making this the best fit obtained for Envisat in the literature to date. The results demonstrate that the angle between the angular momentum vector and the negative normal of the orbital plane librates around a mean value of $8.53°\pm 0.42°$ with an amplitude from about $0.7°$ (in 2013) to $0.5°$ (in 2015), with the libration period equal to the precession period of the angular momentum, from about 4.8?days (in 2013) to 3.4?days (in 2015). The ratio of the minimum to maximum principal moments of inertia is estimated to be $0.0818\pm 0.0011$, and the initial longitude of the angular momentum in the orbital coordinate system is $40.5°\pm 9.3°$. The direction of the rotation axis derived from our results at September 23, 2013, UTC 20:57 is similar to the results obtained from satellite laser ranging data but about $20°$ closer to the negative normal of the orbital plane.     

On the practical exploitation of perturbative effects in low Earth orbit for space debris mitigation

This paper presents the results of a numerical evaluation of the natural lifetime reduction in low Earth orbit, due to dynamical perturbations. The study considers two values for the area-to-mass ratio, a nominal ratio which resembles a typical value of spacecraft in orbit today, and an enhanced ratio which covers the surface augmentation. The results were obtained with two orbit propagators, one of a semi-analytical nature and the second one using non-averaged equations of motion. The simulations for both propagators were set up similarly to allow comparison. They both use the solar radiation pressure and the secular terms of the geopotential ($J_2,J_4$ and $J_6$). The atmospheric drag was turned on and off in both propagators to alternatively study the eccentricity build up and the residual lifetime. The non-averaging case also covers a validation with the full 6?×?6 geopotential. The results confirm the findings in previous publications, that is, the possibility for de-orbiting from altitudes above the residual atmosphere if a solar sail is deployed at the end-of-life, due to the combined effect of solar radiation pressure and the oblateness of the Earth. At near polar inclinations, shadowing effects can be exploited to the same end. The results obtained with the full, non-averaging propagator revealed additional de-orbiting corridors associated with solar radiation pressure which were not found by previous work on space debris mitigation. The results of both tools are compared for specific initial conditions. For nominal values of area-to-mass ratio, instead, it is confirmed that this resonance effect is negligible.The paper then puts the findings in the perspective of the current satellite catalogue. It identifies space missions which are currently close to a resonance corridor and shows the orbit evolution within the resonances with a significantly shorter residual orbital lifetime. The paper finishes with a discussion on the exploitation of these effects with regards to the long-term simulation of the space debris environment and a flux and collision probability comparison.     

Effects of space weather on the ionosphere and LEO satellites’ orbital trajectory in equatorial,low and middle latitude

We study the effects of space weather on the ionosphere and low Earth orbit (LEO) satellites’ orbital trajectory in equatorial, low- and mid-latitude (EQL, LLT and MLT) regions during (and around) the notable storms of October/November, 2003. We briefly review space weather effects on the thermosphere and ionosphere to demonstrate that such effects are also latitude-dependent and well established. Following the review we simulate the trend in variation of satellite’s orbital radius (r), mean height (h) and orbit decay rate (ODR) during 15 October–14 November 2003 in EQL, LLT and MLT. Nominal atmospheric drag on LEO satellite is usually enhanced by space weather or solar-induced variations in thermospheric temperature and density profile. To separate nominal orbit decay from solar-induced accelerated orbit decay, we compute $r\text{,}h$ and ODR in three regimes viz. (i) excluding solar indices (or effect), where $r=r_0\text{,}h=h_0$ and $\mathit{ODR}={\mathit{ODR}}_0$ (ii) with mean value of solar indices for the interval, where $r=r_m\text{,}h=h_m$ and $\mathit{ODR}={\mathit{ODR}}_m$ and (iii) with actual daily values of solar indices for the interval ($r\text{,}h$ and ODR). For a typical LEO satellite at h?=?450?km, we show that the total decay in r during the period is about 4.20?km, 3.90?km and 3.20?km in EQL, LLT and MLT respectively; the respective nominal decay ($r_0$) is 0.40?km, 0.34?km and 0.22?km, while solar-induced orbital decay ($r_m$) is about 3.80?km, 3.55?km and 2.95?km. h also varied in like manner. The respective nominal ${\mathit{ODR}}_0$ is about 13.5?m/day, 11.2?m/day and 7.2?m/day, while solar-induced ${\mathit{ODR}}_m$ is about 124.3?m/day, 116.9?m/day and 97.3?m/day. We also show that severe geomagnetic storms can increase ODR by up to 117% (from daily mean value). However, the extent of space weather effects on LEO Satellite’s trajectory significantly depends on the ballistic co-efficient and orbit of the satellite, and phase of solar cycles, intensity and duration of driving (or influencing) solar event.     

Impact analysis of the transponder time delay on radio-tracking observables

Accurate tracking of probes is one of the key points of space exploration. Range and Doppler techniques are the most commonly used. In this paper we analyze the impact of the transponder delay, $i.e$. the processing time between reception and re-emission of a two-way tracking link at the satellite, on tracking observables and on spacecraft orbits. We show that this term, only partially accounted for in the standard formulation of computed space observables, can actually be relevant for future missions with high nominal tracking accuracies or for the re-processing of old missions. We present several applications of our formulation to Earth flybys, the NASA GRAIL and the ESA BepiColombo missions.     

Impact of rogue active regions on hemispheric asymmetry

The solar dipole moment at activity minimum is a good predictor of the strength of the subsequent solar cycle. Through a systematic analysis using a state-of-the-art $2\times 2$D solar dynamo model, we found that bipolar magnetic regions (BMR) with atypical characteristics can modify the strength of the next cycle via their impact on the buildup of the dipole moment as a sunspot cycle unfolds. In addition to summarizing these results, we present further effects of such “rogue” BMRs. These have the ability to generate hemispheric asymmetry in the subsequent sunspot cycle, since they modify the polar cap flux asymmetry of the ongoing cycle. We found strong correlation between the polar cap flux asymmetry of cycle i and the total pseudo sunspot number asymmetry of cycle $i+1$. Good correlation also appears in the case of the time lag of the hemispheres of cycle $i+1$.     

Fast solar radiation pressure modelling with ray tracing and multiple reflections

Physics based SRP (Solar Radiation Pressure) models using ray tracing methods are powerful tools when modelling the forces on complex real world space vehicles. Currently high resolution (1?mm) ray tracing with secondary intersections is done on high performance computers at UCL (University College London). This study introduces the BVH (Bounding Volume Hierarchy) into the ray tracing approach for physics based SRP modelling and makes it possible to run high resolution analysis on personal computers. The ray tracer is both general and efficient enough to cope with the complex shape of satellites and multiple reflections (three or more, with no upper limit). In this study, the traditional ray tracing technique is introduced in the first place and then the BVH is integrated into the ray tracing. Four aspects of the ray tracer were tested for investigating the performance including runtime, accuracy, the effects of multiple reflections and the effects of pixel array resolution.Test results in runtime on GPS IIR and Galileo IOV (In Orbit Validation) satellites show that the BVH can make the force model computation 30–50 times faster. The ray tracer has an absolute accuracy of several nanonewtons by comparing the test results for spheres and planes with the analytical computations. The multiple reflection effects are investigated both in the intersection number and acceleration on GPS IIR, Galileo IOV and Sentinel-1 spacecraft. Considering the number of intersections, the 3rd reflection can capture $99.12\%\text{,}99.14\%$, and $91.34\%$ of the total reflections for GPS IIR, Galileo IOV satellite bus and the Sentinel-1 spacecraft respectively. In terms of the multiple reflection effects on the acceleration, the secondary reflection effect for Galileo IOV satellite and Sentinel-1 can reach 0.2?$\text{nm}/{\text{s}}^2$ and 0.4?$\text{nm}/{\text{s}}^2$ respectively. The error percentage in the accelerations magnitude results show that the 3rd reflection should be considered in order to make it less than $0.035\%$. The pixel array resolution tests show that the dimensions of the components have to be considered when choosing the spacing of the pixel in order not to miss some components of the satellite in ray tracing. This paper presents the first systematic and quantitative study of the secondary and higher order intersection effects. It shows conclusively the effect is non-negligible for certain classes of misson.