Real-time spacecraft intercept strategy on J2-perturbed orbits

A real-time intercept strategy for spacecraft under the non-uniform gravitational perturbation of Earth is addressed in this paper. To intercept a target spacecraft on general conic sections, an interceptor considered in this work makes use of a thruster propelling the constant thrust which is comparable to unrealistic impulse-type thrust. The $J_2$ perturbation introduces critical dynamic variations of spacecraft orbiting the Earth, which results in a considerable amount of position error of the interceptor at the final intercept point. In order to release the burden of $J_2$ disturbance and make the miss distance between the target and interceptor small, a real-time intercept technique with an optimal intercept algorithm is suggested. The strategy proposed is to obtain an optimized output iteratively for a given time interval with previously obtained optimal values. These parameters are evaluated by the optimal intercept algorithm suggested. Once the optimal velocity change is obtained to satisfy intercept requirements, although the orbital system is perturbed, it is easy to regenerate a new solution by setting the previous solution as new initial guesses. This strategy is employed iteratively until the interceptor meets the target. Several numerical simulations are performed to highlight the proposed real-time strategy for spacecraft intercept missions.     

Variation of hmF2 and NmF2 deduced from DPS-4 over Multan (Pakistan) and their comparisons with IRI-2012 & IRI-2016 during the deep solar minimum between cycles 23 & 24

We report the results of ionospheric measurements from DPS-4 installed at Multan (Geog coord. 30.18°N, 71.48°E, dip 47.4°). The variations in F2-layer maximum electron density NmF2 and its peak height hmF2 are studied during the deep solar minimum between cycles 23 & 24 i.e 2008–2009 with comparisons conducted with the International Reference Ionosphere (IRI) versions 2012 & 2016. We find that the hmF2 observations peak around the pre-sunrise and sunrise hours depending on the month. Seasonally, the daytime variation of NmF2 is higher in the Equinox and Summer, while daytime hmF2 are slightly higher in the Equinox and Winter. High values of hmF2 around midnight are caused by an increase of upward drifts produced by meridional winds. The ionosphere over Multan, which lies at the verge of low and mid latitude, is affected by both $E\times B$ drifts and thermospheric winds as evident from mid-night peaks and near-sunrise dips in hmF2. The results of the comparison of the observed NmF2 and hmF2 for the year 2008–2009 with the IRI-2012 (both NmF2 and hmF2) and IRI-2016 (only hmF2) estimates indicate that for NmF2, IRI-2012 with Consultative Committee International Radio (CCIR) option produces values in better agreement with observed data. Whereas, for hmF2, IRI-2016 with both International Union of Radio Science (URSI) and CCIR SHU-2015 options, predicts well for nighttime hours throughout the year. However, the IRI-2012 with CCIR option produces better agreement with data during daytime hours. Furthermore, IRI-2012 with CCIR option gives better results during Equinox months, whereas, IRI-2016 with both URSI and CCIR SHU-2015 options predict well for Winter and Summer.     

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.     

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.     

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).     

Simulation-based evaluation of a cold atom interferometry gradiometer concept for gravity field recovery

The prospects of future satellite gravimetry missions to sustain a continuous and improved observation of the gravitational field have stimulated studies of new concepts of space inertial sensors with potentially improved precision and stability. This is in particular the case for cold-atom interferometry (CAI) gradiometry which is the object of this paper. The performance of a specific CAI gradiometer design is studied here in terms of quality of the recovered gravity field through a closed-loop numerical simulation of the measurement and processing workflow. First we show that mapping the time-variable field on a monthly basis would require a noise level below $5\text{mE}/\sqrt{\text{Hz}}$. The mission scenarios are therefore focused on the static field, like GOCE. Second, the stringent requirement on the angular velocity of a one-arm gradiometer, which must not exceed ${10}^{-6}$?rad/s, leads to two possible modes of operation of the CAI gradiometer: the nadir and the quasi-inertial mode. In the nadir mode, which corresponds to the usual Earth-pointing satellite attitude, only the gradient $V_{\mathit{yy}}$, along the cross-track direction, is measured. In the quasi-inertial mode, the satellite attitude is approximately constant in the inertial reference frame and the 3 diagonal gradients $V_{\mathit{xx}}\text{,}{V}_{\mathit{yy}}$ and $V_{\mathit{zz}}$ are measured. Both modes are successively simulated for a 239?km altitude orbit and the error on the recovered gravity models eventually compared to GOCE solutions. We conclude that for the specific CAI gradiometer design assumed in this paper, only the quasi-inertial mode scenario would be able to significantly outperform GOCE results at the cost of technically challenging requirements on the orbit and attitude control.     

A new weighted mean temperature model in China

The Global Positioning System (GPS) has been applied in meteorology to monitor the change of Precipitable Water Vapor (PWV) in atmosphere, transformed from Zenith Wet Delay (ZWD). A key factor in converting the ZWD into the PWV is the weighted mean temperature ($T_m$), which has a direct impact on the accuracy of the transformation. A number of Bevis-type models, like $T_m-T_s$ and $T_m-T_s\text{,}{P}_s$ type models, have been developed by statistics approaches, and are not able to clearly depict the relationship between $T_m$ and the surface temperature, $T_s$. A new model for $T_m$, called weighted mean temperature norm model (abbreviated as norm model), is derived as a function of $T_s$, the lapse rate of temperature, δ, the tropopause height, $h_{\mathit{trop}}$, and the radiosonde station height, $h_s$. It is found that $T_m$ is better related to $T_s$ through an intermediate temperature. The small effects of lapse rate can be ignored and the tropopause height be obtained from an empirical model. Then the norm model is reduced to a simplified form, which causes fewer loss of accuracy and needs two inputs, $T_s$ and $h_s$. In site-specific fittings, the norm model performs much better, with RMS values reduced averagely by 0.45 K and the Mean of Absolute Differences (MAD) values by 0.2 K. The norm model is also found more appropriate than the linear models to fit $T_m$ in a large area, not only with the RMS value reduced from 4.3 K to 3.80 K, correlation coefficient $R^2$ increased from 0.84 to 0.88, and MAD decreased from 3.24 K to 2.90 K, but also with the distribution of simplified model values to be more reasonable. The RMS and MAD values of the differences between reference and computed PWVs are reduced by on average 16.3% and 14.27%, respectively, when using the new norm models instead of the linear model.     

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.     

Time-varying solar radiation pressure on Ajisai in comparison with LAGEOS satellites

This study aims to investigate solar radiation pressure acting on the spherical geodetic satellites, Ajisai, LAGEOS-1, and LAGEOS-2. The solar radiation pressure coefficients ($C_R$) are derived in two independent ways: (a) through precise orbit determination (POD) using satellite laser ranging (SLR) data, and (b) through modeling using the optical properties of the satellite surface material. The average $C_R$ value of Ajisai (1.039), as calculated from the time series of $C_R$ POD estimates every 15?days, is consistently smaller than those of LAGEOS-1 (1.140) and LAGEOS-2 (1.103). This difference can be explained by the fact that the surface of Ajisai is mostly covered by mirrors. The Ajisai $C_R$ values estimated by POD show remarkable semi-annual variation, which disagrees with the results of a previous study (Sengoku et al., 1995) predicting that the $C_R$ of Ajisai varies almost annually. We attribute this semi-annual variation to two physical reasons: the non-spherical additional cross-sectional area due to the “attached fitting ring” and the low reflectivity of the surface material in the polar regions. Furthermore, the solar radiation pressure acting on Ajisai varies annually in a direction perpendicular to the sun-satellite vector. Finally, the two independent $C_R$ values of Ajisai agree more when we assume a total solar irradiance of 1361?W/m², whereas the value 1367?W/m² has been commonly used in POD.     

Highlights about the performances of storm-time TEC modelling techniques for low/equatorial and mid-latitude locations

A statistical evaluation of storm-time total electron content (TEC) modelling techniques over various latitudes of the African sector and surrounding areas is presented. The source of observational TEC data used in this study is the Global Navigation Satellite Systems (GNSS), specifically the Global Positioning Systems (GPS) receiver networks. For each selected receiver station, three different storm-time models based on empirical orthogonal functions (EOF) analysis, non-linear regression analysis (NLRA) and Artificial neural networks (ANN), were implemented. Storm-time GPS TEC data used for both development and validation of the models was selected based on the storm criterion of $\mathit{Dst}?-50$ nT or $K_p?4$ to take into account both coronal mass ejections (CMEs) and co-rotating interaction regions (CIRs) driven storms, respectively. To make an independent test of the models, storm periods considered for validation were excluded from datasets used during the implementation of the models and results are compared with observations, monthly median values, and International Reference Ionosphere (IRI-2016) predictions. Considering GPS TEC as reference, a statistical analysis performed over six storm periods reserved for validation revealed that ANN model is about 10%, 26%, and 58% more accurate than EOF, NLRA, and IRI models, respectively. It was further found that, EOF model performs 15%, and 44% better than NLRA, and IRI models, respectively, while NLRA is 25% better than IRI. On the other hand, results are also discussed referring to the background ionosphere represented by monthly median TEC (MM TEC) and statistics are provided. Moreover, strengths and weaknesses of each model are highlighted.     

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.     

The influence of the spatial and temporal collocation windows on the comparisons of the ionospheric characteristic parameters derived from COSMIC radio occultation and digisondes

GPS radio occultation (RO) ionospheric products obtained by Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) mission during the year of 2014 and the observations from 3 digisonde stations which are located at different latitudes are used to study the influence of different time and space collocation windows on the comparisons of the ionospheric characteristic parameters (ICPs), including the peak density and peak height, derived from the two techniques. The results show that the correlation coefficients (CC) and the standard deviation of the absolute biases (SDAB) between the ICPs derived from the two techniques vary distinctly under different spatial and time collocation windows. Generally, the CC (SDAB) of the ICPs decrease (increase) as the size of the collocation window increases in time dimension or in space dimension. The rate of change of the statistic parameters with the increase in the size of the collocation window in time dimension and space dimension is analyzed for each digisonde station. It is found that within the collocation window of $\left(60\mathrm{m}\mathrm{i}\mathrm{n},{20}^{°},{20}^{°}\right)$, the influence of the increase of $1^{°}$ in the space window on the statistical comparison is much more significant than that of the increase of 1?min in the time window, and it is suggested that there can be appropriate relaxation on the time window within the threshold of 60?min to get a balance between the quality of the comparison results and the number of the matched pairs. In addition, it is found that the same variations in the longitude window and in the latitude window may have different influences on the comparison results when the horizontal gradients in electron density are distinctly different along different directions at the digisonde station, and strict space collocation window is preferred when comparing the observations from COSMIC RO with those from the digisonde station in such cases.     

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.     

An attempt to inverse the ionospheric sporadic-E layer critical frequency based on the COSMIC radio occultation data

Ionospheric sporadic E layer refers to localized thin irregularity with enhanced plasma density appearing in the height range of ionospheric E layer (～90–130?km). The much higher electron density in the sporadic E layer than the background ionosphere would cause sudden TEC enhancement in the occultation TEC profile. A wavelet decomposition and reconstruction method is applied to extract the TEC fluctuation in this paper, and then $S_{\text{max}}$ index is defined to represent the intensity of the sudden TEC enhancement. $S_{\text{max}}$ index is compared with sporadic E critical frequency ($\mathit{foEs}$) observed by the ionosonde. The results show a well linear correlation between them with mean correlation coefficient about 0.7. Thus, an empirical linear model is established to inverse the $\mathit{foEs}$. The monthly/hourly mean values and global distribution of sporadic E intensity and occurrence ratio are calculated using this method based on the COSMIC occultation data from 2007 to 2011. The statistical analysis results indicate that it is feasible to inverse the $\mathit{foEs}$ based on the occultation TEC profile data and the inversion results can be applied to the long-term global variations of sporadic E investigations.     

An application of the weighted horizontal magnetic gradient to solar compact and eruptive events

We propose to apply the weighted horizontal magnetic gradient (${\mathit{WG}}_M$), introduced in Korsós et al., 2015, for analysing the pre-flare and pre-CME behaviour and evolution of Active Regions (ARs) using the SDO/HMI-Debrecen Data catalogue. To demonstrate the power of investigative capabilities of the ${\mathit{WG}}_M$ method, in terms of flare and CME eruptions, we studied two typical ARs, namely, AR 12158 and AR 12192. The choice of ARs represent canonical cases. AR 12158 produced an X1.6 flare with fast “halo” CME ($v_{\mathit{linear}}$ = 1267 $\text{km}{\text{s}}^{-1}$) while in AR 12192 there occurred a range of powerful X-class eruptions, i.e. X1.1, X1.6, X3.1, X1.0, X2.0 and X2.0-class energetic flares, interestingly, none with an accompanying CME. The value itself and temporal variation of ${\mathit{WG}}_M$ is found to possess potentially important diagnostic information about the intensity of the expected flare class. Furthermore, we have also estimated the flare onset time from the relationship of duration of converging and diverging motions of the area-weighted barycenters of two subgroups of opposite magnetic polarities. This test turns out not only to provide information about the intensity of the expected flare-class and the flare onset time but may also indicate whether a flare will occur with/without fast CME. We have also found that, in the case when the negative polarity barycenter has moved around and the positive one “remained” at the same coordinates preceding eruption, the flare occurred with fast “halo” CME. Otherwise, when both the negative and the positive polarity barycenters have moved around, the AR produced flares without CME. If these properties found for the movement of the barycenters are generic pre-cursors of CME eruption (or lack of it), identifying them may serve as an excellent pre-condition for refining the forecast of the lift-off of CMEs.     

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.     

Hierarchical Bayesian modeling of ionospheric TEC disturbances as non-stationary processes

We model regular and irregular variation of ionospheric total electron content as stationary and non-stationary processes, respectively. We apply the method developed to SCINDA GPS data set observed at Bahir Dar, Ethiopia $\left(11.6°\text{N,}37.4°\text{E}\right)$. We use hierarchical Bayesian inversion with Gaussian Markov random process priors, and we model the prior parameters in the hyperprior. We use Matérn priors via stochastic partial differential equations, and use scaled $\text{Inv}-{\chi }^2$ hyperpriors for the hyperparameters. For drawing posterior estimates, we use Markov Chain Monte Carlo methods: Gibbs sampling and Metropolis-within-Gibbs for parameter and hyperparameter estimations, respectively. This allows us to quantify model parameter estimation uncertainties as well. We demonstrate the applicability of the method proposed using a synthetic test case. Finally, we apply the method to real GPS data set, which we decompose to regular and irregular variation components. The result shows that the approach can be used as an accurate ionospheric disturbance characterization technique that quantifies the total electron content variability with corresponding error uncertainties.     

Constraining the mass of the black hole GX 339-4 using spectro-temporal analysis of multiple outbursts

We carried out spectro-temporal analysis of the archived data from multiple outbursts spanning over the last two decades from the black hole X-ray binary GX 339-4. In this paper, the mass of the compact object in the X-ray binary system GX 339-4 is constrained based on three indirect methods. The first method uses broadband spectral modelling with a two component flow structure of the accretion around the black hole. The broadband data are obtained from RXTE (Rossi X-ray Timing Explorer) in the range 3.0 to 150.0?keV and from Swift and NuSTAR (Nuclear Spectroscopic Telescope Array) simultaneously in the range 0.5 to 79.0?keV. In the second method, we model the time evolution of Quasi-periodic Oscillation (QPO) frequencies, considering it to be the result of an oscillating shock that radially propagates towards or away from the compact object. The third method is based on scaling a mass dependent parameter from an empirical model of the photon index ($\mathrm{\Gamma }$) – QPO ($\nu$) correlation. We compare the results at 90 percent confidence from the three methods and summarize the mass estimate of the central object to be in the range $8.28–11.89M_{\odot }$.