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.     

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.     

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.     

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.     

Effects of dust polarity and nonextensive electrons on the dust-ion acoustic solitons and double layers in earth atmosphere

Propagation of dustion acoustic solitary waves (DIASWs) and double layers is discussed in earth atmosphere, using the Sagdeev potential method. The best model for distribution function of electrons in earth atmosphere is found by fitting available data on different distribution functions. The nonextensive function with parameter $q=0.58$ provides the best fit on observations. Thus we analyze the propagation of localized waves in an unmagnetized plasma containing nonextensive electrons, inertial ions, and negatively/positively charged stationary dust. It is found that both compressive and rarefactive solitons as well as double layers exist depending on the sign (and the value) of dust polarity. Characters of propagated waves are described using the presented model.     

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.     

A robust semi-analytic method to solve the minimum ΔV two-impulse rendezvous problem

A novel semi-analytic approach is developed to determine the minimum $\mathrm{\Delta }V$ for a two-impulse rendezvous and validated both empirically and analytically. A previously published closed-form $\mathrm{\Delta }V$ estimate and the Lambert minimum energy transfer is used to establish upper and lower bounds of the minimum $\mathrm{\Delta }V$ transfer between two orbits. These bounds, in conjunction with the bisection method, operate on a nonlinear radical cost function to guarantee linear convergence. This approach has several real world applications including a low earth orbit (LEO) to highly elliptical orbit (HEO), and a HEO to retrograde geosynchronous orbit transfer. The minimum $\mathrm{\Delta }V$ estimates are better than those reported in the existing literature, while run times improved as much as two orders of magnitude over a fixed time Lambert solver. All singularity cases were addressed such that any orbital geometry, including Hohmann and radial elliptic transfers, converged to the global minimum $\mathrm{\Delta }V$. This approach will work for both coplanar and non-coplanar 3D geometries for any orbit type.     

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.     

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.     

Roto-orbital dynamics of a triaxial rigid body around a sphere. Relative equilibria and stability

We study the roto-orbital motion of a triaxial rigid body around a sphere, which is assumed to be much more massive than the triaxial body. The associated dynamics of this system, which consists of a normalized Hamiltonian with respect to the fast angles (partial averaging), is investigated making use of variables referred to the total angular momentum. The first order approximation of this model is integrable. We carry out the analysis of the relative equilibria, which hinges principally in the dihedral angle between the orbital and rotational planes and the ratio among the moments of inertia $\rho =(B-A)/(2C-B-A)$. In particular, the dynamics of the body frame, though formally given by the classical Euler equations, experiences changes of stability in the principal directions related to the roto-orbital coupling. When $\rho =1/3$, we find a family of relative equilibria connected to the unstable equilibria of the free rigid body.     

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.     

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).     

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.