Non-gravitational Perturbations Research Articles

Comet 81P/Wild 2: Changes in the spin axis orientation during the last five apparitions

Comet 81P/Wild 2 is characterized by the presence of a prominent fan-shaped dust emission originating from an active source at high latitude on the nucleus, whose axis is assumed to coincide with the comet's rotation axis. Therefore, several authors estimated the spin axis orientation of 81P in past apparitions based on the polar jet model.By measuring the PAs of the fan on CCD images taken with different telescopes during the 2009–10 and 2022–23 apparitions, we estimated a position of the comet's spin axis at RA = 295.0° ± 7.5°, Dec = 14.5° ± 4.0° for the 2009–10 apparition and at RA = 296.7 ± 2.0°, Dec = 17.3 ± 2.5° for the 2022–23 apparition. Despite some degree of uncertainty of the estimate for the 2009–10 apparition, we interpolated the estimate for 2009–10 and 2022–23 with the published data of the previous apparition of 1997, to assess the presence and the extent of a drift of the pole since the 1997 passage.The analysis over a long time span of five consecutive apparitions confirms previous observations that the spin axis of comet 81P is subject to a slow drift with variable rate, probably connected to outgassing-induced jet forces and the related non-gravitational perturbations of its orbital period.

Influence of non-gravitational forces on the co-orbital motion

ABSTRACT In the Solar system, there exist many non-gravitational perturbations for co-orbital objects, such as the solar radiation pressure, Yarkovsky effect, and so forth. Their effects play important roles in the dynamics of co-orbital objects as they lead to long-term perturbations accumulating. The motivation of this paper is to investigate the general mechanism of the non-gravitational force on the co-orbital motion in the circular restricted three-body problem. We propose an effective method for perturbed co-orbital motions by analysing the locus of the co-orbital objects in a two-dimensional map. Several expressions derived uncover how the non-gravitational force acts on orbital parameters. Taking the Sun–Jupiter system as an example, we implement numerical computations to demonstrate the validity of our results. Numerical computation shows that most of loci of co-orbital motions are in agreement with our conclusions. Some interesting phenomena of perturbed co-orbital motion, such as the co-orbital transition and escape, are found and explained. The results obtained from this paper provide an efficient approach to analyse the evolution of perturbed co-orbital motions.

A Study of Solar Radiation Pressure Model in BDS-3 Precise Orbit Determination

For the BDS (BeiDou Navigation Satellite System) satellites, the solar radiation pressure is the major non-gravitational perturbation the satellites suffer. Due to the influence of multiple factors, accurate modeling the solar radiation pressure acting on these satellites is difficult to accomplish. The solar radiation pressure perturbation is an essential source of error in the precise orbit determination (POD) and orbit prediction processes of the BDS satellites. As the ECOMC (Empirical CODE Orbit Model 1 and 2 Combined) model adopts the advantageous features of the ECOM1 (Empirical CODE Orbit Model 1) model and the ECOM2 (Empirical CODE Orbit Model 2) model, a greater number of parameters have been introduced into the model, leading to strong correlation between the ECOMC model parameters. In response to the deficiency of the ECOMC model, the authors collected the BDS-3 satellite precise ephemeris data that were provided by Wuhan University (WHU) from January 2019 to April 2022. And by these ephemeris data, the ECOMC model’s 13 parameters were obtained through the dynamic orbit fitting method. By conducting these time sequence diagrams analysis of the ECOMC model parameters, this thesis affords the selection strategies of the solar radiation pressure parameters of the ECOMC model for BDS-3 inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellite. And the rationality of the selection strategies of the solar radiation pressure parameters for the ECOMC model was verified by orbit fitting and orbit prediction experiments. The results show that using the improved ECOMC model gains the best orbit fitting effects for BDS-3 IGSO and MEO satellite, and can also enhance the accuracy of medium and long-term orbit prediction of BDS-3 IGSO and MEO satellite.

Millimeter accuracy SLR bias determination using independent multi-LEO DORIS and GPS-based precise orbits

Satellite Laser Ranging (SLR) has become an invaluable core technique in numerous geodetic applications. SLR measurements to passive spherical satellites essentially contribute to the determination of geocenter coordinates and global scale in the International Terrestrial Reference Frame (ITRF) realizations. In addition, SLR measurements to active satellites in Low Earth Orbit (LEO) are up to now mostly used for an independent validation of orbit solutions, usually derived by microwave tracking techniques based on Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) or Global Navigation Satellite Systems (GNSS). This allows for the analysis of systematic orbit errors (e.g., originating from poorly known non-gravitational perturbations or sensor offsets) not only in the radial direction (key to satellite altimetry missions), but in three dimensions.Major obstacles to reach the millimeter accuracy and stability goals of 0.1mm/y (at decadal time scales) of the Global Geodetic Observing System (GGOS) are station-satellite measurement biases and on-ground/board coordinate offsets. Among the observatories of the International Laser Ranging Service (ILRS) a large diversity of measurement qualities exists, and the calibration of station-dependent errors is now necessary to further exploit SLR data for present and future climate-driven needs.We demonstrate that the analysis of SLR data to active LEO satellites equipped with DORIS or GNSS receivers is a promising means to characterize SLR biases and their stability. Using two independent selections of Earth observation missions in LEOs (consisting of six altimetry, three magnetic field and two gravity field satellites) with three different analysis software packages (Bernese, ZOOM, Napeos), we estimate SLR range biases for all involved tracking stations on a yearly basis. We find that for many of the stations independently estimated sets of biases agree on a few-mm level and that the inclusion of satellites from multiple missions allows rendering the bias estimation more robust and in particular less prone to geographically correlated orbit errors. This shows that microwave-derived orbits of active LEO satellites, nowadays of very high quality due to numerous advances in modeling and analysis techniques, can serve as interesting sources for SLR station calibration in demanding climate applications.

Calibration of ISA accelerometer sensing axes for the BepiColombo mission

ISA is a three-axis accelerometer embarked on-board BepiColombo, a joint ESA/JAXA space mission launched on the 19th of October 2018 ​at 22.45 (local time) and devoted to put two spacecraft (MPO and MMO) around Mercury (2025), for a deeper investigation of the planet and its environment. ISA aims at measuring, directly and not by modelling, first time for a planet other than Earth, the non-gravitational perturbations the MPO will undergo during its stay around Mercury. Such data will be used within the frame of the Radio-Science Experiments to reconstruct, a posteriori and with very high accuracy, the true gravitational orbit of the spacecraft and, at last, the gravity field of Mercury. Three single accelerometers, each one characterised by its own sensing axis, i.e. the direction along which it is sensitive to accelerations, collect the non-gravitational perturbations encountered by the MPO. The arrangement of sensing axes, whose knowledge is essential to reconstruct the sensed accelerations, was measured with very high accuracy by the Experimental Gravitation group at IAPS/INAF in Rome, which manages ISA and holds the PI-ship. The group developed a calibration procedure to identify on-ground the direction of ISA sensing axes with respect to an optical reference frame. An experimental facility was designed and assembled to accomplish the measurement. In November 2015, the calibration was performed on the ISA Flight Model, currently in cruise phase towards Mercury. Results of the measurement campaign are reported and prove the determination of ISA sensing axes with an accuracy within 20–30 arcseconds per single axis, well below the 100 arcseconds required by the Radio-Science needs.

STORM: A semi-analytical orbit propagator for assessing the compliance with Mars Planetary Protection Requirements

STORM is a general semi-analytical propagation code developed at Airbus Defence and Space and originally designed to perform long-term Mars orbit simulations, for mission analysis purposes. Since the 1960’s, humans have sent 18 spacecraft to study the Red Planet, 8 of which are active as of February 2021. While space-debris surveillance and mitigation have been gathering momentum in the past decades in the case of Earth, the issue of artificial objects left in orbit around Mars is another cause for concern in view of the Committee of Space Research’s Planetary Protection Policy. In that perspective, STORM is introduced as a potential tool for assessing the compliance of spacecraft with orbital lifetime requirements. The programme makes it possible to study the evolution of orbits over several decades by propagating a set of mean equinoctial orbital elements, with a comprehensive set of gravitational and non-gravitational perturbations. Particular emphasis is laid on atmospheric entry cases as the programme is interfaced with the European Mars Climate Database, which is the current best knowledge of the state of the Martian atmosphere. This work is focused on the semi-analytical propagator’s implementation and its actual use for predicting entry dates. A sensitivity analysis is conducted to ascertain the influence of atmosphere modelling and initial conditions, providing insight into how to account for uncertainties in a probabilistic way.

A Comparative Study on the Solar Radiation Pressure Modeling in GPS Precise Orbit Determination

For Global Positioning System (GPS) precise orbit determination (POD), the solar radiation pressure (SRP) is the dominant nongravitational perturbation force. Among the current SRP models, the ECOM and box-wing models are widely used in the International GNSS Service (IGS) community. However, the performance of different models varies over different GPS satellites. In this study, we investigate the performances of different SRP models, including the box-wing and adjustable box-wing as a priori models, and ECOM1 and ECOM2 as parameterization models, in the GPS POD solution from 2017 to 2019. Moreover, we pay special attention to the handling of the shadow factor in the SRP modeling for eclipsing satellites, which is critical to achieve high-precision POD solutions but has not yet been fully investigated. We demonstrate that, as an a priori SRP model, the adjustable box-wing has better performance than the box-wing model by up to 5 mm in the orbit day boundary discontinuity (DBD) statistics, with the largest improvement observed on the BLOCK IIR satellites using the ECOM1 as a parameterization SRP model. The box-wing model shows an insignificant orbit improvement serving as the a priori SRP model. For the eclipsing satellites, the three-dimensional (3D) root mean square (RMS) values of orbit DBD are improved when the shadow factor is applied only in the D direction (pointing toward to Sun) than that in the three directions (D, Y, and B) in the satellite frame. Different SRP models have comparable performance in terms of the Earth rotation parameter (ERP) agreement with the IERS EOP 14C04 product, whereas the magnitude of the length of day (LoD) annual signal is reduced when the shadow factor is applied in the D direction than in the three directions. This study clarifies how the shadow factor should be applied in the GPS POD solution and demonstrates that the a priori adjustable box-wing model combined with ECOM1 is more suitable for high-precision GPS POD solutions, which is useful for the further GNSS data analysis.

Impact of non-gravitational effects on chaotic properties of retrograde orbits

Context. Dynamical studies of asteroid populations in retrograde orbits, that is with orbital inclinations greater than 90 degrees, are interesting because the origin of such orbits is still unexplained. Generally, the population of retrograde asteroids includes mostly Centaurs and transneptunian objects. A special case is the near-Earth object (343158) 2009 HC82 from the Apollo group. Another interesting object is the comet 333P/LINEAR, which for several years was considered the second retrograde object approaching Earth. Another comet in retrograde orbit, 161P Hartley/IRAS appears to be an object of similar type. Thanks to the large amount of observational data for these two comets, we tested various models of cometary non-gravitational forces applied to their dynamics. Aims. The goal was to estimate which of non-gravitational perturbations could affect the stability of retrograde bodies. In principle, we study the local stability by measuring the divergence of nearby orbits. Methods. We numerically determined Lyapunov characteristic indicators and the associated Lyapunov times (LT). This time, our calculations of these parameters were extended by more advanced models of non-gravitational perturbations (i.e. Yarkovsky drift and in selected cases cometary forces). This allowed us to estimate chaos in the Lyapunov sense. Results. We found that the Yarkovsky effect for obliquities of γ = 0° and γ = 180° can change the LT substantially. In most cases, for the prograde rotation, we received more stable solutions. Moreover, we confirmed the role of retrograde resonances in this process. Additionally, the studied cometary effects also significantly influence the long-term behaviour of the selected comets. The LT can reach values from 100 to over 1000 yr. Conclusions. All of our results indicate that the use of models with non-gravitational effects for retrograde bodies is clearly justified.

Enhanced solar radiation pressure model for GPS satellites considering various physical effects

Solar radiation pressure (SRP) is the dominant non-gravitational perturbation for GPS satellites. In the IGS (International GNSS Service), this perturbation is modeled differently by individual analysis centers (ACs). The two most widely used methods are the Empirical CODE orbit Model (ECOM, ECOM2) and the JPL GSPM model. When using ECOM models, a box-wing model or other a priori models, as well as stochastic pulses at noon or midnight, are optionally adopted by some ACs to compensate for the deficiencies of the ECOM or ECOM2 model. However, both box-wing and GSPM parameters were published many years ago. There could be an aging effect going with time. Also, optical properties and GSPM parameters of GPS Block IIF satellites are currently not yet published. In this contribution, we first determine Block-specific optical parameters of GPS satellites using GPS code and phase measurements of 6 years. Various physical effects, such as yaw bias, radiator emission in the satellite body-fixed − X and Y directions and the thermal radiation of solar panels, are considered as additional constant parameters in the optical parameter adjustment. With all the adjusted parameters, we form an enhanced box-wing model adding all the modeled physical effects. In addition, we determine Block-specific GSPM parameters by using the same GPS measurements. The enhanced box-wing model and the GSPM model are then taken as a priori model and are jointly used with ECOM and ECOM2 model, respectively. We find that the enhanced box-wing model performs similarly to the GSPM model outside eclipse seasons. RMSs of all the ECOM and ECOM2 parameters are reduced by 30% compared to results without the a priori model. Orbit misclosures and orbit predictions are improved by combining the enhanced box-wing model with ECOM and ECOM2 models. In particular, the improvement in orbit misclosures for the eclipsing Block IIR and IIF satellites, as well as the non-eclipsing IIA satellites, is about 25%, 10% and 10%, respectively, for the ECOM model. Therefore, the enhanced box-wing model is recommended as an a priori model in GPS satellite orbit determination.

High-fidelity comet 67P ephemeris and predictions based on Rosetta data

Because of observational biases and outgassing, comets are notoriously challenging in terms of trajectory estimation and ephemeris predictions. We used tracking data collected by ESA's Rosetta mission at 67P/Churyumov-Gerasimenko to derive 10-m level constraints on the distance between the Earth and 67P in 2014 and 2016, which, together with high-quality ground-based astrometry, provide unprecedented information on a comet's trajectory. Based on these data, we reconstruct the trajectory of 67P from 2012 to 2018 by modeling nongravitational perturbations with a rotating jet model, informed by measured physical properties of the comet. Using this trajectory reconstruction as reference, we characterize the astrometric error of publicly available optical observations of 67P and show how their quality significantly degrades with brightness and proximity to the Sun. Moreover, we assessed the accuracy of predictions made with different nongravitational perturbation models and data treatments. While each comet is unique and it is difficult to provide a general recipe, the reliability of an ephemeris can benefit from the availability of high-quality data with quantified uncertainties and can be gauged by comparing different ephemeris solutions and tracking a solution's stability and predictive performance as new observations are added to the fit.

Characterization of Temporarily Captured Minimoon 2020 CD3 by Keck Time-resolved Spectrophotometry

Abstract We present time-resolved visible spectrophotometry of 2020 CD3, the second known minimoon. The spectrophotometry was taken with the Keck I/Low Resolution Imaging Spectrometer between wavelengths 434 and 912 nm in the B, g, V, R, I, and RG850 filters as it was leaving the Earth–Moon system on 2020 March 23 UTC. The spectrum of 2020 CD3 resembles V-type asteroids and some lunar rock samples with a 434–761 nm reddish slope of ∼18%/100 nm (g–r = 0.62 ± 0.08 and r–i = 0.21 ± 0.06) with an absorption band at ∼900 nm corresponding to i–z = −0.54 ± 0.10. Combining our measured H of 31.9 ± 0.1 with an albedo of 0.35 typical for V-type asteroids, we determine 2020 CD3's diameter to be ∼0.9 ± 0.1 m, making it the first minimoon and one of the smallest asteroids to be spectrally studied. We use our time-series photometry to detect significant periodic light-curve variations with a period of ∼573 s and amplitude of ∼1. In addition, we extend the observational arc of 2020 CD3 to 37 days, to 2020 March 23 UTC. From the improved orbital solution for 2020 CD3, we estimate the likely duration of its capture to be ∼2 yr and the nongravitational perturbation on its orbit due to radiation pressure with an area-to-mass ratio of (6.9 ± 2.4) × 10−4 m2 kg−1 implying a density of 2.3 ± 0.8 g cm−3, broadly compatible with other meter-scale asteroids and lunar rock. We searched for prediscovery detections of 2020 CD3 in the Zwicky Transient Facility archive as far back as 2018 October but were unable to locate any positive detections.

A 1% Measurement of the Gravitomagnetic Field of the Earth with Laser-Tracked Satellites

A new measurement of the gravitomagnetic field of the Earth is presented. The measurement has been obtained through the careful evaluation of the Lense-Thirring (LT) precession on the combined orbits of three passive geodetic satellites, LAGEOS, LAGEOS II, and LARES, tracked by the Satellite Laser Ranging (SLR) technique. This general relativity precession, also known as frame-dragging, is a manifestation of spacetime curvature generated by mass-currents, a peculiarity of Einstein’s theory of gravitation. The measurement stands out, compared to previous measurements in the same context, for its precision (≃7.4×10−3, at a 95% confidence level) and accuracy (≃16×10−3), i.e., for a reliable and robust evaluation of the systematic sources of error due to both gravitational and non-gravitational perturbations. To achieve this measurement, we have largely exploited the results of the GRACE (Gravity Recovery And Climate Experiment) mission in order to significantly improve the description of the Earth’s gravitational field, also modeling its dependence on time. In this way, we strongly reduced the systematic errors due to the uncertainty in the knowledge of the Earth even zonal harmonics and, at the same time, avoided a possible bias of the final result and, consequently, of the precision of the measurement, linked to a non-reliable handling of the unmodeled and mismodeled periodic effects.

Numerical Modelling of Satellite Downlink Signals in a Finslerian-Perturbed Schwarzschild Spacetime

The work presented in this paper aims to contribute to the problem of testing Finsler gravity theories by means of experiments and observations in the solar system. Within a class of spherically symmetric static Finsler spacetimes we consider a satellite with an on-board atomic clock, orbiting in the Finslerian-perturbed gravitational field of the earth, whose time signal is transmitted to a ground station, where its receive time and frequency are measured with respect to another atomic clock. This configuration is realized by the Galileo 5 and 6 satellites that have gone astray and are now on non-circular orbits. Our method consists in the numerical integration of the satellite’s orbit, followed by an iterative procedure which provides the numerically integrated signals, i.e., null geodesics, from the satellite to the ground station. One of our main findings is that for orbits that are considerably more eccentric than the Galileo 5 and 6 satellite orbits, Finslerian effects can be separated from effects of perturbations of the Schwarzschild spacetime within the Lorentzian geometry. We also discuss the separation from effects of non-gravitational perturbations. This leads us to the conclusion that observations of this kind combined with appropriate numerical modelling can provide suitable tests of Finslerian modifications of general relativity.

A HERO for General Relativity

HERO (Highly Eccentric Relativity Orbiter) is a space-based mission concept aimed to perform several tests of post-Newtonian gravity around the Earth with a preferably drag-free spacecraft moving along a highly elliptical path fixed in its plane undergoing a relatively fast secular precession. We considered two possible scenarios—a fast, 4-h orbit with high perigee height of 1047 km and a slow, 21-h path with a low perigee height of 642 km . HERO may detect, for the first time, the post-Newtonian orbital effects induced by the mass quadrupole moment J 2 of the Earth which, among other things, affects the semimajor axis a via a secular trend of ≃4–12 cm yr − 1 , depending on the orbital configuration. Recently, the secular decay of the semimajor axis of the passive satellite LARES was measured with an error as little as 0 . 7 cm yr − 1 . Also the post-Newtonian spin dipole (Lense-Thirring) and mass monopole (Schwarzschild) effects could be tested to a high accuracy depending on the level of compensation of the non-gravitational perturbations, not treated here. Moreover, the large eccentricity of the orbit would allow one to constrain several long-range modified models of gravity and accurately measure the gravitational red-shift as well. Each of the six Keplerian orbital elements could be individually monitored to extract the G J 2 / c 2 signature, or they could be suitably combined in order to disentangle the post-Newtonian effect(s) of interest from the competing mismodeled Newtonian secular precessions induced by the zonal harmonic multipoles J ℓ of the geopotential. In the latter case, the systematic uncertainty due to the current formal errors σ J ℓ of a recent global Earth’s gravity field model are better than 1 % for all the post-Newtonian effects considered, with a peak of ≃ 10 − 7 for the Schwarzschild-like shifts. Instead, the gravitomagnetic spin octupole precessions are too small to be detectable.

General Relativity Measurements in the Field of Earth with Laser-Ranged Satellites: State of the Art and Perspectives

Recent results of the LARASE research program in terms of model improvements and relativistic measurements are presented. In particular, the results regarding the development of new models for the non-gravitational perturbations that affect the orbit of the LAGEOS and LARES satellites are described and discussed. These are subtle and complex effects that need a deep knowledge of the structure and the physical characteristics of the satellites in order to be correctly accounted for. In the field of gravitational measurements, we present a new measurement of the relativistic Lense-Thirring precession with a 0.5 % precision. In this measurement, together with the relativistic effect we also estimated two even zonal harmonics coefficients. The uncertainties of the even zonal harmonics of the gravitational field of the Earth have been responsible, until now, of the larger systematic uncertainty in the error budget of this kind of measurements. For this reason, the role of the errors related to the model used for the gravitational field of the Earth in these measurements is discussed. In particular, emphasis is given to GRACE temporal models, that strongly help to reduce this kind of systematic errors.

Analysis of Orbit Accuracy for Non-cooperative Earth-Orbiting Objects

Abstract The atmospheric resistance and solar radiation pressure are the main sources of non-gravitational perturbations in orbit determination and prediction of non-cooperative earth-orbiting objects. The calculation of both perturbation accelerations involves the satellite’s surface-mass ratio. Another factor affecting the accuracy of orbit determination and prediction is the sparse observation. In this paper, we examine the sensitivity of orbit prediction accuracy and orbit decay rate relative to surface-mass ratio. The influence of the space-based angle data to orbit determination was also analyzed. The results show that the error of orbit prediction is multiplied by the change of surface–mass ratio. The orbital error determined by using 7-minutes single-station ground-based radar data and 15-minutes double-space-based angle measurements is 63.77 m lower than that only determined by using single-station ground-based radar data. The space-based angle information greatly improves the observation geometry of the non-cooperative target and improves the precision of orbit determination. The position error of the inclined geosynchronous satellite determined by 3-days ground-based radar data is 323.49 m and the prediction error of 1-7 days is less than 1.0 km. Using 3-days ground-based radar data and single spaced-based angle measurement to determine the orbit of the medium-orbit satellite with an altitude of about 1000 km, the orbital accuracy is 14.66 m and the prediction error of 1-7 days is less than 50.00 m. To determine the orbit of the 280 km height satellite with, 1.5-days ground-based radar data and single space-based angle data, the position error is 270.37 m and the prediction error of 1-day is 1.70 km.

Measuring the De Sitter precession with a new Earth\u2019s satellite to the simeq 10^{-5} level: a proposal

The inclination I of an Earth’s satellite in polar orbit undergoes a secular De Sitter precession of -,7.6 milliarcseconds per year for a suitable choice of the initial value of its non-circulating node Omega . The competing long-periodic harmonic rates of change of I due to the even and odd zonal harmonics of the geopotential vanish for either a circular or polar orbit, while no secular rates occur at all. This may open up, in principle, the possibility of measuring the geodesic precession in the weak-field limit with an accurately tracked satellite by improving the current bound of 9times 10^{-4} from Lunar Laser Ranging, which, on the other hand, may be even rather optimistic, by one order of magnitude, or, perhaps, even better. The most insidious competing effects are due to the solid and ocean components of the K_1 tide since their perturbations have nominal huge amplitudes and the same temporal pattern of the De Sitter signature. They vanish for polar orbits. Departures of simeq {10^{-5}}^circ mathrm{to} {10^{-3}}^circ from the ideal polar geometry allow to keep the K_1 tidal perturbations to a sufficiently small level. Most of the other gravitational and non-gravitational perturbations vanish for the proposed orbital configuration, while the non-vanishing ones either have different temporal signatures with respect to the De Sitter effect or can be modeled with sufficient accuracy. In order to meet the proposed goal, the measurement accuracy of I should be better than simeq 35~text {microarcseconds}=0.034~text {milliarcseconds} over, say, 5 year.

The adjusted optical properties for Galileo/BeiDou-2/QZS-1 satellites and initial results on BeiDou-3e and QZS-2 satellites

Solar Radiation Pressure (SRP) is the dominant non-gravitational perturbation for GNSS (Global Navigation Satellite System) satellites. In the absence of precise surface models, the Empirical CODE Orbit Models (ECOM, ECOM2) are widely used in GNSS satellite orbit determination. Based on previous studies, the use of an a priori box-wing model enhances the ECOM model, especially if the spacecraft is a stretched body satellite. However, so far not all the GNSS system providers have published their metadata. To ensure a precise use of the a priori box-wing model, we estimate the optical parameters of all the Galileo, BeiDou-2, and QZS-1 (Quasi Zenith Satellite System) satellites based on the physical processes from SRP to acceleration. Validation using orbit prediction proves that the adjusted parameters of Galileo and QZS-1 satellites exhibit almost the same performance as the corresponding published and “best guess” values. Whereas, the estimated parameters of BeiDou-2 satellites demonstrate an improvement of more than 60% over the initial “guess” values. The resulting optical parameters of all the satellites are introduced into an a priori box-wing model, which is jointly used with ECOM and ECOM2 model in the orbit determination. Results show that the pure ECOM2 model exhibits better performance than the pure ECOM model for Galileo, BeiDou-2 GEO and QZS-1 orbits. Combined with the a priori box-wing model the ECOM model (ECOM+BW) results in the best Galileo, BeiDou-2 GEO and QZS-1 orbits. The standard deviation (STD) of satellite laser ranging residuals reduce by about 20% and 5% with respect to the pure ECOM2 model for Galileo and BeiDou-2 GEO orbits, while the reductions are about 40% and 60% for QZS-1 orbits in yaw-steering and orbit-normal mode respectively. BeiDou-2 IGSO and MEO satellite orbits do not benefit much from the a priori box-wing model. In summary, we suggest setting up a unified SRP model of ECOM+BW for Galileo, QZS-1, and BeiDou-2 orbits based on the adjusted metadata. In addition, we estimate the optical parameters of BeiDou-3e and QZS-2 satellites using a limited number of tracking stations. Results regarding the unified SRP model indicate the same advantages, the STD of satellite laser ranging residuals reduces by about 30% and 20% for QZS-2 and BeiDou-3e orbits respectively over orbit products without a priori model. The estimation procedure is effective and easy to apply to the new emerging satellites in the future.

Dynamical cartography of Earth satellite orbits

We have carried out a numerical investigation of the coupled gravitational and non-gravitational perturbations acting on Earth satellite orbits in an extensive grid, covering the whole circumterrestrial space, using an appropriately modified version of the SWIFT symplectic integrator, which is suitable for long-term (∼120 years) integrations of the non-averaged equations of motion. Hence, we characterize the long-term dynamics and the phase-space structure of the Earth-orbiter environment, starting from low altitudes (∼400 km) and going up to the GEO region and beyond. This investigation was done in the framework of the EC-funded “ReDSHIFT” project, with the purpose of enabling the definition of passive debris removal strategies, based on the use of physical mechanisms inherent in the complex dynamics of the problem (i.e., resonances). Accordingly, the complicated interactions among resonances, generated by different perturbing forces (i.e., lunisolar gravity, solar radiation pressure, tesseral harmonics in the geopotential) are accurately depicted in our results, where we can identify the regions of phase space where the motion is regular and long-term stable and regions for which eccentricity growth and even instability due to chaotic behavior can emerge. The results are presented in an “atlas” of dynamical stability maps for different orbital zones, with a particular focus on the (drag-free) range of semimajor axes, where the perturbing effects of the Earth’s oblateness and lunisolar gravity are of comparable order. In some regions, the overlapping of the predominant lunisolar secular and semi-secular resonances furnish a number of interesting disposal hatches at moderate to low eccentricity orbits. All computations were repeated for an increased area-to-mass ratio, simulating the case of a satellite equipped with an on-board, area-augmenting device. We find that this would generally promote the deorbiting process, particularly at the transition region between LEO and MEO. Although direct reentry from very low eccentricities is very unlikely in most cases of interest, we find that a modest “delta-v” (ΔV) budget would be enough for satellites to be steered into a relatively short-lived resonance and achieve reentry into the Earth’s atmosphere within reasonable timescales (∼50 years).

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

We report on extensive BVRcIc photometry and low-resolution (λ/Δλ∼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 Rc=32.45±0.31, with a flat dependence of reflectance on the phase angle, such as dRc/dϕ∼0.007±2 mag deg−1. The detected short-timescale variability suggests that the body was likely spinning with a period twice the nominal figure of Pflash=1.4547±0.0005s, as from the observed lightcurve. In the BVRcIc 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 (∼1×80 km) strip of sea, at a depth of 1500 m or less.Under the assumption of Lambertian scatter, an inferred size of 216±30/α/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⩽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.