The problem of how to solar sail around planets remains nearly unexplored. Most of the existing body of knowledge focuses on scape trajectories or locally optimal controls, not providing much insight into the inherent physical characteristics of the transfer problem. In this work, we present the first comprehensive study of solar-sail transfers around planetary bodies by analysing the simplest conceivable transfer, the planar Circular-to-Circular (C2C) transfer. The C2C transfer spans for only one orbital revolution, constituting the building block of more complex multi-revolution trajectories. By patching together a series of C2C transfers, a feasible initial guess for trajectory optimisation algorithms can be generated. The optimised control law maximises the orbital radius within the C2C transfer. The radius change is used as performance metric. The results suggest that the domain of the control variables can be substantially reduced, effectively enhancing convergence of the optimal control solver, and significantly reducing computational time. Furthermore, a dimensional analysis shows that the C2C performance only depends on one parameter: the ratio of the sail’s characteristic acceleration over the local gravitational acceleration. The scaled nature of the results allows to easily compute the C2C performance for a wide range of mission scenarios around any planetary body, providing a new tool for early mission design.@en

This study presents the first azimuth cutoff analysis in Synthetic Aperture Radar (SAR) altimetry, aiming to assess its applicability in characterizing sea-state dynamics. In SAR imaging, the azimuth cutoff serves as a proxy for the shortest waves, in terms of wavelength, that can be detected by the satellite under certain wind and wave conditions. The magnitude of this parameter is closely related to the wave orbital velocity variance, a key parameter for characterizing wind-wave systems. We exploit wave modulations exhibited in the tail of fully-focused SAR waveforms and extract the azimuth cutoff from the radar signal through the analysis of its along-track autocorrelation function. We showcase the capability of Sentinel-6A in deriving these two parameters based on analyses in the spatial and wavenumber domains, accompanied by a discussion of the limitations. We use Level-1A high-resolution Sentinel-6A data from one repeat cycle (10 days) globally to verify our findings against wave modeled data. In the spatial domain analysis, the estimation of azimuth cutoff involves fitting a Gaussian function to the along-track autocorrelation function. Results reveal pronounced dependencies on wind speed and significant wave height, factors primarily determining the magnitude of the velocity variance. In extreme sea states, the parameters are underestimated by the altimeter, while in relatively calm sea states and in the presence of swells, a substantial overestimation trend is observed. We introduce an alternative approach to extract the azimuth cutoff by identifying the fall-off wavenumber in the wavenumber domain. Results indicate effective mitigation of swell-induced errors, with some additional sensitivity to extreme sea states compared to the spatial domain approach.@en

Solar sailing is a propulsion method that uses solar radiation pressure (SRP) as main source of thrust and is therefore particularly suited for heliocentric flight regimes. However, the vast majority of sailcraft launched to date have flown around Earth, as will those scheduled for launch in the near future. Around the Earth, the dynamics of a solar sail are affected by the presence of eclipses and additional sources of acceleration apart from SRP, in particular, atmospheric drag and the Earth’s planetary radiation pressure (PRP). These accelerations can reach magnitudes in the order of (or even larger than) the SRP acceleration and, therefore, they can potentially be exploited to manoeuvre more effectively around the Earth. Nevertheless, the majority of research conducted on Earth-bound solar sailing either neglects these accelerations or treats them as uncontrollable sources of perturbation. In light of this, this paper presents a high-fidelity trajectory optimisation method which is then used to thoroughly characterise the manoeuvring capabilities of solar sails in the near-Earth environment. The optimisation algorithm is designed to change any orbital element in a locally optimal manner while accounting for the SRP, PRP, aerodynamic, and gravitational accelerations. To tune the optimiser, a first-order analysis of the accelerations achievable by sailcraft in proximity of the Earth is discussed. Then, the optimisation algorithm is exploited to fully characterise the manoeuvring capabilities of Earth-bound solar sails, taking NASA’s recently-launched ACS3 solar-sail mission as a baseline. Specifically, different parametric analyses are conducted to determine ACS3’s orbit-raising and inclination-changing capabilities for a large set of orbits, solar activities, and sailcraft characteristics. The results of this study not only enhance the understanding of ACS3’s performance but also provide valuable insights for the mission design of future Earth-bound solar-sail missions for a variety of mission applications, such as active-debris removal and in-orbit servicing. @en

NASA’s ACS3 mission will be the first Earth-bound solar-sail mission to fly so-called calibration steering laws. These steering laws are designed to expose the sailcraft to a variety of dynamical conditions to isolate the effects of different parameters on the dynamics, thereby facilitating the estimation of these parameters. This paper presents the set of candidate calibration steering laws of ACS3, highlighting their operational challenges and impact on the estimation of the sail’s reflectivity and specularity. The results show that, for a conservative GPS position accuracy of 10 m, accurate estimation of the reflectivity and specularity with uncertainties in the order of 10−4 − 10−3 can be achieved by flying any of the proposed calibration laws. However, ACS3’s calibration steering laws were also found to introduce operational challenges that may hinder their implementation for extended periods of time. In particular, the decreased power generation capability of solar arrays was found to be the most severe operational challenge for two out of the five ACS3’s calibration laws analysed. @en

This study investigates the influence of ocean currents on wave modeling and satellite observations using in situ wave measurements from the One Ocean Expedition 2021–2023. In January 2023, six OpenMetBuoy drifters were deployed in the Agulhas Current region. Their high immersion ratio minimized wind effects, allowing them to follow the current and return to the Indian Ocean by the Agulhas retroflection, collecting data for about 2 months. Comparing surface current velocities from both the Mercator model and Globcurrent product with drifter data reveals underestimation for velocities over (Formula presented.) with Mercator showing greater variability. Significant wave height and Stokes drift parameters from MFWAM and ERA5 were also evaluated against drifters. Both models tend to overestimate Stokes drift more noticeable in ERA5, indicating sensitivity to wind seas. For significant wave height, both models agree well with drifter measurements with correlations of 0.90 for MFWAM and 0.83 for ERA5. However, ERA5's lack of surface current data combined with its coarse resolution (0.5 (Formula presented.)) lead to underestimation of wave heights exceeding 2.5 m. MFWAM products including and excluding currents exhibit root mean square errors of 0.39 and 0.45 m, respectively, when compared to drifter measurements. This confirms that neglecting currents introduces additional errors particularly in areas with sharp current gradients. Analyzing MFWAM wave spectra, including and excluding currents, reveals wave energy transfer attributed to wave-current interactions. The spatial extent of these interactions is captured by satellite altimeters, revealing wave modulations with considerable wave height variations when waves cross eddies and the current core.

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In the coming decade, JUICE and Europa Clipper radio-science will yield the most accurate estimation to date of the Galilean moons’ physical parameters and ephemerides. JUICE's PRIDE (Planetary Radio Interferometry and Doppler Experiment) will help achieve such a solution by providing VLBI (Very Long Baseline Interferometry) observations of the spacecraft's lateral position, complementing nominal radio-science measurements. In this paper, we quantify how PRIDE VLBI can contribute to the moons’ ephemerides determination, in terms of attainable solution improvement and validation opportunities. To this end, we simulated VLBI data for JUICE, but also investigated the possibility to perform simultaneous tracking of JUICE and Europa Clipper, thus ultimately generating both single- and dual-spacecraft VLBI. We considered various tracking and data quality scenarios for both VLBI types, and compared the formal uncertainties provided by covariance analyses with and without VLBI. These analyses were performed for both global and local (i.e. per-flyby) estimations of the moons’ states, as eventually achieving a global solution first requires proceeding arc-per-arc. We showed that both single- and multi-spacecraft VLBI measurements only bring limited improvement to the global state estimation, but significantly contribute to the moons’ normal points (i.e. local states at flyby times), most notably in the out-of-plane direction. Additionally, we designed a validation plan exploiting PRIDE VLBI to progressively validate the classical radio-science solution, whose robustness and statistical realism is sensitive to modelling inconsistencies. By improving the local state estimations and offering various validation opportunities, PRIDE will be invaluable in overcoming possible dynamical challenges. It can therefore play a key role in reconstructing a global solution for the Galilean moons’ dynamics with the uncertainty levels promised by JUICE-Europa Clipper analyses. This, in turn, is critical to the accurate characterisation of tidal dissipation in the Jovian system, holding the key to the long-term evolution of the Galilean moons.

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Thermosphere mass density and crosswind can be derived from accelerometer and GNSS tracking data. However, present datasets are often provided without comprehensive uncertainty specifications. We present a newly developed method that propagates measurement noise and errors in the satellite specification, thermosphere models, and radiation flux data to density observations to quantify their uncertainty. We focus specifically on density observations derived only from GNSS tracking data, which are limited in resolution along the orbit due to unavoidable smoothing. While the method can be applied to simulated and real data, making it useful for existing datasets and mission design, we demonstrated it using data from the GRACE B satellite. First, we compare the aerodynamic acceleration derived separately from the accelerometer and GNSS tracking data, highlighting the role of two significant noise sources: noise due to the differentiation of the positions and noise from the evaluation of the gravity vector at a noisy position. Averaging substantially reduces the noise in the aerodynamic acceleration as long as the differentiation noise dominates, which is the case at frequencies higher than the orbital frequency. Below, gravity vector evaluation noise becomes the dominating noise source, and consequently, averaging over longer periods leads to only marginal uncertainty reduction. Further, we investigate the uncertainty in the radiation pressure acceleration and demonstrate that averaging over one orbit substantially reduces the uncertainty in the along-track radiation pressure acceleration. We show that the uncertainty of density observations derived from the accelerometer data is about 4% of the density for data from 2003 when the GRACE B satellite was at 490km altitude during high solar activity. In 2008, solar activity was very low, and the altitude was still 476km, resulting in an uncertainty of 5%–20% because GNSS tracking noise and radiation pressure modeling errors play a much larger role as the aerodynamic acceleration becomes smaller. In the case of density observations derived only from GNSS tracking data, the uncertainty is about 5% in 2003 and 20%–50% in 2008 when averaging over one-third orbit. In 2008, GNSS tracking noise explains nearly all uncertainty in the density observation. Averaging over one orbit reduces the uncertainty to 4% and 5% in 2003 and 2008, respectively.@en

Uncertainties in radiation pressure modelling play a significant role in the thermospheric density and crosswind observations derived from the GRACE-FO accelerometer, especially during low solar activity. Under such conditions, the radiation pressure acceleration matches the magnitude of the aerodynamic acceleration along the track and exceeds it in the cross-track direction. The GRACE-FO mission has been operating for several years at such high altitudes during both low and rising solar activity, providing a perfect opportunity to study the effects of radiation pressure. This research uses ray tracing based on a high-fidelity satellite geometry model to calculate the radiation pressure acceleration. We numerically fine-tuned the coefficients describing the thermo-optical surface properties to obtain more accurate radiation pressure accelerations than those specified in the GRACE-FO mission manual. We also used in situ temperature measurements from thermistors on the solar arrays to model the satellite's thermal emission. These temperature measurements allowed a realistic setup of the thermal model, extended by the parameter describing the efficiency of the solar cells, and reproduced the acceleration of the thermal emission with an accuracy of RMS 0.148 nms⁻². The combination of the updated thermal model and the fine-tuning of the surface coefficients improved the accuracy of the crosswind acceleration to an RMS of 0.55 nms⁻², compared to an RMS of 4.22 nms⁻² when using panel models and instantaneous thermal radiation. We compared the observed crosswind with two models: HWM14 and TIE-GCM. While both models capture most of the salient features of the observed crosswind, HWM14 shows particularly good agreement at high latitudes. Compared to the previously employed radiation pressure model, the crosswind observations have been improved in low and mid-latitudes, especially during periods of higher solar activity. Since the effect of radiation pressure is most significant in the crosswind direction, the effect on density was small compared to previously published datasets.

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Solar sailing is a propulsion method that takes advantage of solar radiation pressure to generate thrust. Although most of near-future solar-sail missions will fly in low Earth orbit, where planetary radiation pressure can be as large as 20% of solar radiation pressure, studies on the accelerations produced by the Earth’s albedo and blackbody radiation have only been conducted to a very limited first-order extent. This paper therefore provides a novel, detailed analytical model for these perturbing accelerations, valid for perfectly reflecting solar sails. The full derivation of the model is described, and a thorough analysis of the blackbody and albedo radiation pressure accelerations is conducted for different orbital conditions. Then, to determine the model’s accuracy, a comparison with the state of the art (the finite-disk radiation source model and a high-fidelity numerical model) is provided. Ultimately, different analyses to quantify the effect of planetary radiation pressure acceleration on the solar-sail maneuvering capabilities are presented, using NASA’s upcoming ACS3 mission as reference scenario. The results highlight the nonnegligible effect of uncontrolled planetary radiation pressure acceleration, which can reduce the sailcraft’s achievable altitude and inclination gains to 76 and 80%, respectively, of the gains obtained when planetary radiation pressure is not accounted for.@en

Planetary Radio Interferometry and Doppler Experiment (PRIDE) is a multi-purpose experimental technique aimed at enhancing the science return of planetary missions. The technique exploits the science payload and spacecraft service systems without requiring a dedicated onboard instrumentation or imposing on the existing instrumentation any special for PRIDE requirements. PRIDE is based on the near-field phase-referencing Very Long Baseline Interferometry (VLBI) and evaluation of the Doppler shift of the radio signal transmitted by spacecraft by observing it with multiple Earth-based radio telescopes. The methodology of PRIDE has been developed initially at the Joint Institute for VLBI ERIC (JIVE) for tracking the ESA’s Huygens Probe during its descent in the atmosphere of Titan in 2005. From that point on, the technique has been demonstrated for various planetary and other space science missions. The estimates of lateral position of the target spacecraft are done using the phase-referencing VLBI technique. Together with radial Doppler estimates, these observables can be used for a variety of applications, including improving the knowledge of the spacecraft state vector. The PRIDE measurements can be applied to a broad scope of research fields including studies of atmospheres through the use of radio occultations, the improvement of planetary and satellite ephemerides, as well as gravity field parameters and other geodetic properties of interest, and estimations of interplanetary plasma properties. This paper presents the implementation of PRIDE as a component of the ESA’s Jupiter Icy Moons Explorer (JUICE) mission.

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ESA’s Earth explorer mission CryoSat-2 has an ice-monitoring objective, but it has proven to also be a valuable source of observations for measuring impacts of climate change over oceans. In this paper, we report on our long-term ocean data analysis and validation and give our final words on CryoSat-2’s Geophysical Ocean Products (GOP) Baseline-C. The validation is based on a cross comparison with concurrent altimetry and with in situ tide gauges. The highlights of our findings include GOP Baseline-C showing issues with the ionosphere and pole tide correction. The latter gives rise to an east–west pattern in range bias. Between Synthetic Aperture Radar (SAR) and Low-Resolution Mode (LRM), a 1.4 cm jump in range bias is explained by a 0.5 cm jump in sea state bias, which relates to a significant wave height SAR-LRM jump of 10.5 cm. The remaining 0.9 cm is due to a range bias between ascending and descending passes, exhibiting a clear north–south pattern and ascribed to a timing bias of +0.367 ms, affecting both time-tag and elevation. The overall range bias of GOP Baseline-C is established at −2.9 cm, referenced to all calibrated concurrent altimeter missions. The bias drift does not exceed 0.2 mm/yr, leading to the conclusion that GOP Baseline-C is substantially stable and measures up to the altimeter reference missions. This is confirmed by tide gauge comparison with a selected set of 309 PSMSL tide gauges over 2010–2022: we determined a correlation of R = 0.82, a mean standard deviation of (Formula presented.) cm (common reference and GIA corrected), and a drift of 0.17 mm/yr. In conclusion, the quality, continuity, and reference of GOP Baseline-C is exceptionally good and stable over time, and no proof of any deterioration or platform aging has been found. Any improvements for the next CryoSat-2 Baselines could come from sea state bias optimization, ionosphere and pole tide correction improvement, and applying a calibrated value for any timing biases.

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This manuscript aims to present and evaluate the applicability of combining optical line-of-sight (LoS) navigation with crosslink radiometric navigation for deep-space cruising distributed space systems. To do so, a set of four distributed space systems architectures is presented, and for each of those, the applicability of the combination is evaluated, comparing it to the baseline solutions, which are based on only optical navigation. The comparison is done by studying the performance in a circular heliocentric orbit in seven different time intervals (ranging from 2024 to 2032) and exploiting the observation of all the pairs of planets from Mercury to Saturn. The distance between spacecraft is kept around 200 km. Later, a NEA mission test case is generated in order to explore the applicability to a more realistic case. This analysis shows that the technique can also cope with a variable inter-satellite distance, and the best performance is obtained when the spacecraft get closer to each other.

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We present new neutral mass density and crosswind observations for the CHAMP, GRACE, and GRACE-FO missions, filling the last gaps in our database of accelerometer-derived thermosphere observations. For consistency, we processed the data over the entire lifetime of these missions, noting that the results for GRACE in 2011- 2017 and GRACE-FO are entirely new. All accelerometer data are newly calibrated. We modeled the temperature-induced bias variations for the GRACE accelerometer data to counter the detrimental effects of the accelerometer thermal control deactivation in April 2011. Further, we developed a new radiation pressure model, which uses ray tracing to account for shadowing and multiple reflections and calculates the satellitea's thermal emissions based on the illumination history. The advances in calibration and radiation pressure modeling are essential when the radiation pressure acceleration is significant compared to the aerodynamic one above 450 km altitude during low solar activity, where the GRACE and GRACE-FO satellites spent a considerable fraction of their mission lifetime. The mean of the new density observations changes only marginally, but their standard deviation shows a substantial reduction compared to thermosphere models, up to 15% for GRACE in 2009. The mean and standard deviation of the new GRACE-FO density observations are in good agreement with the GRACE observations. The GRACE and CHAMP crosswind observations agree well with the physics-based TIE-GCM winds, particularly the polar wind patterns. The mean observed crosswind is a few tens of m·s-1 larger than the model one, which we attribute primarily to the crosswind errors being positive by the definition of the retrieval algorithm. The correlation between observed and model crosswind is about 60%, except for GRACE in 2004- 2011 when the signal was too small to retrieve crosswinds reliably.

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In this paper we review the precision orbit determination (POD) performance of the CryoSat-2 mission where we used all tracking data between June-2010 and Jan-2023; with station and beacon coordinates provided in the ITRF2020 reference system, we use a mean gravity model, and we use spacecraft specific models for modeling drag and radiation pressure. To model time variable gravity (TVG) we distinguish between two components, there is a short term oceanic and atmospheric part for which we use the AOD1B model; for the longer term part we employ GRACE and GRACE-FO monthly potential coefficient solutions. Our experience is that adding TVG information is not necessarily successful during POD, and that attention must be paid to the proper processing of the GRACE and GRACE-FO data. To demonstrate this property we define four runs where we gradually implement TVG information. An evaluation criterion is the level of POD tracking residuals, the level of the empirical accelerations, and a comparison to precision orbit ephemeris provided by the Centre National d'Etudes Spatiales (CNES). Unexplained empirical accelerations found during POD are on the level of 3 nm/s ² for the along-track component and 13 nm/s ² for the cross-track component. The laser residuals converge at approximately 1.02 cm and the Doppler residuals are on the level of 0.406 mm/s, the radial orbit difference to the CNES POE-F (Precision Orbit Ephemeris version F) orbits narrows to 6.5 mm. Tracking residuals are not evenly distributed for DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite) beacons, the South Atlantic Anomaly effect is for instance clearly visible in the first empirical orthogonal function EOF mode of monthly binned DORIS residuals. After consideration of all possible TVG approaches our conclusion is that 3 hourly AOD1B model fields result in a small but visible improvement. The addition of TVG from GRACE and GRACE-FO is implemented in two different ways from which we can select a version that does lead to a reduction in the Doppler tracking residuals and which does reduce the level of solved for empirical accelerations.

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Daedalus MASE (Mission Assessment through Simulation Exercise) is an open-source package of scientific analysis tools aimed at research in the Lower Thermosphere-Ionosphere (LTI). It was created with the purpose to assess the performance and demonstrate closure of the mission objectives of Daedalus, a mission concept targeting to perform in-situ measurements in the LTI. However, through its successful usage as a mission-simulator toolset, Daedalus MASE has evolved to encompass numerous capabilities related to LTI science and modeling. Inputs are geophysical observables in the LTI, which can be obtained either through in-situ measurements from spacecraft and rockets, or through Global Circulation Models (GCM). These include ion, neutral and electron densities, ion and neutral composition, ion, electron and neutral temperatures, ion drifts, neutral winds, electric field, and magnetic field. In the examples presented, these geophysical observables are obtained through NCAR’s Thermosphere-Ionosphere-Electrodynamics General Circulation Model. Capabilities of Daedalus MASE include: 1) Calculations of products that are derived from the above geophysical observables, such as Joule heating, energy transfer rates between species, electrical currents, electrical conductivity, ion-neutral collision frequencies between all combinations of species, as well as height-integrations of derived products. 2) Calculation and cross-comparison of collision frequencies and estimates of the effect of using different models of collision frequencies into derived products. 3) Calculation of the uncertainties of derived products based on the uncertainties of the geophysical observables, due to instrument errors or to uncertainties in measurement techniques. 4) Routines for the along-orbit interpolation within gridded datasets of GCMs. 5) Routines for the calculation of the global coverage of an in situ mission in regions of interest and for various conditions of solar and geomagnetic activity. 6) Calculations of the statistical significance of obtaining the primary and derived products throughout an in situ mission’s lifetime. 7) Routines for the visualization of 3D datasets of GCMs and of measurements along orbit. Daedalus MASE code is accompanied by a set of Jupyter Notebooks, incorporating all required theory, references, codes and plotting in a user-friendly environment. Daedalus MASE is developed and maintained at the Department for Electrical and Computer Engineering of the Democritus University of Thrace, with key contributions from several partner institutions.

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Solar sailing is a propellantless propulsion method that exploits solar radiation pressure to generate thrust. In recent years, several solar sails have been launched into Earth-bound orbit to demonstrate this technology’s potential. Because planetary radiation pressure can reach magnitudes comparable to that of solar radiation pressure in proximity of the Earth, it cannot automatically be neglected in near-Earth solar-sail mission design studies. Nevertheless, its effect on the solar-sail dynamics has been investigated only to a very limited, first-order extent, and every study considered an “ideal” – i.e., perfectly reflecting – sail model. Although employing the ideal sail model proves useful for preliminary orbital analyses, its limited fidelity prevents more in-depth research into the near-Earth solar-sail dynamics and trajectory optimization. In light of this, this paper provides a new planetary radiation pressure acceleration model for optical solar sails. This model forms an extension of the “spherical” planetary radiation pressure acceleration model for ideal solar sails devised by Carzana et al. in Reference [1]. In the current paper, the underlying assumptions and full derivation of the newly devised optical model are presented. Subsequently, the accuracy of the optical model is analyzed through a comparison with the ideal model, using NASA’s upcoming ACS3 mission as reference scenario. @en

This paper aims to investigate the capabilities of exploiting optical line-of-sight navigation using star trackers. First, a synthetic image simulator is developed to generate realistic images, which is later exploited to test the star tracker's performance. Then, generic considerations regarding attitude estimation are drawn, highlighting how the camera's characteristics influence the accuracy of the estimation. The full attitude estimation chain is designed and analyzed in order to maximize the performance in a deep-space cruising scenario. After that, the focus is shifted to the actual planet-centroiding algorithm, with particular emphasis on the illumination compensation routine, which is shown to be fundamental to achieving the required navigation accuracy. The influence of the center of the planet within the singular pixel is investigated, showing howthis uncontrollable parameter can lower performance. Finally, the complete algorithm chain is tested with the synthetic image simulator in a wide range of scenarios. The final promising results show that with the selected hardware, even in the higher noise condition, it is possible to achieve a direction's azimuth and elevation angle error in the order of 1-2 arc sec for Venus, and below 1 arc sec for Jupiter, for a spacecraft placed at 1 AU from the Sun. These values finally allow for a positioning error below 1000 km, which is in line with the current non-autonomous navigation state-of-the-art.

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Solar sailing is a spacecraft propulsion method relying solely on solar radiation pressure to provide thrust and is therefore propellantless by nature. Although it represents a practical and promising propulsion system particularly suited for heliocentric flight regimes, the majority of sailcraft missions flown to date have remained Earth-bound and more Earth-bound missions are scheduled for the near future. However, the fundamental dynamics and trajectory optimization of a solar sail around the Earth have only been investigated to a limited extent, often neglecting the effect of non-negligible perturbations in the dynamics and the optimal control problem. Among these perturbations are the effect of eclipses, non-spherical gravity, and aerodynamic drag. Their magnitude can be comparable to, or even exceed that of solar radiation pressure and their effect on the solar-sail dynamics should be investigated to ensure the sailcraft's transfer capabilities and controllability. This article does so by including these perturbations in the dynamics and by considering aerodynamic drag in the optimal control problem. Using this formulation, it is shown that the optimal control problem is independent of the solar-sail loading parameter and that, by solving it, locally optimal steering laws can be derived to effectively change individual orbital elements. These newly derived steering laws form an extension to the laws found by McInnes for unperturbed solar-sail Earth-bound motion. By accounting for the perturbations in the derivation of the steering laws, it is possible to characterize how the perturbations affect the solar-sail maneuvering capabilities. This is quantified based on the established increase of the targeted orbital element. Furthermore, a range of different starting orbits will be considered to analyze the effects of perturbations in different orbital regimes. As demonstration of the real need for this investigation, NASA's Advanced Composite Solar Sail System (ACS3) mission will be considered as real-case scenario. This mission is scheduled for launch in mid-2022 and may benefit from the steering laws derived in this article to prove the maneuverability of solar sails in Earth orbit.

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Copernicus Sentinel–1 is a C-Band Synthetic Aperture Radar (SAR) satellite mission within the European Copernicus Programme. The two satellites Sentinel-1A and -1B were launched in April 2014 and 2016, respectively. The Copernicus POD (Precise Orbit Determination) Service is responsible for the determination of orbital and auxiliary products required by the Payload Data Ground Segment (PDGS). Precise orbits are determined based on the dual-frequency GPS (Global Positioning System) data delivered by dedicated geodetic-grade GPS receivers on-board the satellites. Several updates in the operational orbit determination were done during the years including an update of the GPS antenna reference point coordinates. The switch to GPS carrier phase ambiguity-fixing was a major improvement. A reprocessing of the entire mission span of both satellites became necessary to provide a consistent orbit time series for the mission based on state-of-the-art models and processing settings. Due to the lack of independent observation techniques, the Sentinel-1 orbit quality has been assessed by analysing processing metrics, orbit overlaps and orbit comparisons. For this purpose, members of the Copernicus POD Quality Working Group (QWG) provided reprocessed Sentinel-1 orbit time series based on their software packages and their orbit determination settings. A weighted average of all five delivered solutions - a combined orbit - serves as reference for the comparisons. The quality and reliability of this reference orbit depends among others on the number of available orbit solutions and whether a manoeuvre has been performed during the processed day or not. The mean orbit consistency between all orbit solutions is below 1 cm in 3D RMS for the entire mission time interval for both satellites. Only few days show inferior quality due to data gaps or orbit manoeuvres. Following this sophisticated validation process, the reprocessed Sentinel-1 orbits from the Copernicus POD Service have been made available to the user community.

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The MICROSCOPE mission was designed to test the weak equivalence principle (WEP), stating the equality between the inertial and the gravitational masses, with a precision of 10-15 in terms of the Eötvös ratio η. Its experimental test consisted of comparing the accelerations undergone by two collocated test masses of different compositions as they orbited the Earth, by measuring the electrostatic forces required to keep them in equilibrium. This was done with ultrasensitive differential electrostatic accelerometers onboard a drag-free satellite. The mission lasted two and a half years, cumulating five months worth of science free-fall data, two-thirds with a pair of test masses of different compositions - titanium and platinum alloys - and the last third with a reference pair of test masses of the same composition - platinum. We summarize the data analysis, with an emphasis on the characterization of the systematic uncertainties due to thermal instabilities and on the correction of short-lived events which could mimic a WEP violation signal. We found no violation of the WEP, with the Eötvös parameter of the titanium and platinum pair constrained to η(Ti,Pt)=[-1.5±2.3(stat)±1.5(syst)]×10-15 at 1σ in statistical errors.

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