The problem of how to optimally transfer between two planet-centered orbits using solar sails remains nearly unexplored. Most of the existing body of knowledge focuses on (blended) locally optimal control laws, often considers open-ended trajectories instead of orbital transfers, or tackles specific mission scenarios, leaving insight into the general transfer problem unexplored. In this work, we present the first step in the comprehensive study of optimal solar-sail transfers around planetary bodies by analyzing the simplest conceivable transfer, the planar circular-to-circular (C2C) transfer. The considered C2C transfer spans only one orbital revolution, which may constitute the future building block of more complex multi-revolution trajectories. The optimized control law maximizes the change in orbital radius within the C2C transfer, where the achieved radius change is used as the performance metric. The results show that the C2C performance (i.e., the ability of the solar sail to transfer) depends on the illumination conditions of the orbital plane and the ratio of the sail’s characteristic acceleration to the local gravitational acceleration. Maximum performance is achieved when the orbital plane is perpendicular to the Sun-planet line, where the transfer structure resembles that of a C2C transfer conducted with an ion drive. Furthermore, by using the ratio as the scaling parameter, the results presented in this paper allow 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.

Valuable insights into the thermospheric mass density and horizontal winds can be obtained from satellites equipped with accelerometers. To derive these quantities, radiation pressure must be accurately modeled and removed from the calibrated accelerometer measurements. However, the documented surface reflection and absorption coefficients, as well as the satellite’s thermal properties, are often inaccurate or, in some cases, even absent. This study presents a method for optimizing these parameters jointly with the accelerometer scale factors. Focusing on GRACE data from 2009, a case where radiation pressure was dominant over aerodynamic force, enabled us to refine the radiation pressure model without detrimental effects from errors in aerodynamic force modeling. We evaluated three variants of estimating the scale factor: estimating no accelerometer scale factors, only the y-axis scale factor, or both the y- and z-axis scale factors. We use the difference between the measured and modeled accelerations (the residual) as our target functional. Estimating both scale factors yielded the lowest residual for both GRACE satellites, even though the radiation pressure model was tuned using GRACE-A data only. After the optimization, we observed a systematic feature in the cross-track residuals within the geographical domain, which strongly correlates with the magnetic field vector experienced by the spacecraft. While its cause remains unknown, we introduced an empirical correction that effectively removed the feature and significantly increased consistency between GRACE-A and GRACE-B. Overall, we were able to reduce the RMS of the residuals by more than 13% in the cross-track direction and 32% in the radial direction, indicating a significant increase in modeling accuracy. The presented method provides a generalizable approach that can also be applied to future satellite missions with accelerometers.

The ESA GOCE satellite carried a gravity gradiometer consisting of three pairs of accelerometers on mutually orthogonal axes. For each accelerometer, bias and scale factors have been re-estimated by a dynamic precise orbit determination (POD) using improved gravity field modeling and standards. The kinematic orbit solution included in GPS-based Precise Science Orbit (PSO) product served as the baseline observables for 1210 daily arcs, covering the period from 1 November 2009 to 20 October 2013. Implementing improved force models almost completely resolved the deviations of the Y-axis scale factor obtained in earlier work (Visser and Ijssel 2016). A novel aspect is the verification by comparison with dynamic POD solutions based on SLR observations using 51 two-day orbital arcs. A high level of consistency was obtained between the kinematic PSO- and SLR-based accelerometer calibration parameters, e.g. within 0.01 nm/s2 for the X-axis pointing predominantly in the flight direction in terms of bias. One set of accelerometer scale factors was estimated for the entire mission. These were found to be consistent to within 0.005 for all accelerometer axes. The three-dimensional consistency between the dynamic orbits and the PSO reduced-dynamic orbit solutions has a mean Root-Mean-Square (RMS) of 4.5 and 10 cm, respectively, for the PSO reduced-dynamic and SLR-based dynamic orbit solutions. In addition, the one-dimensional RMS-of-fit of the PSO kinematic orbit solution improved significantly from 6.9 in Visser and Ijssel (2016) to 2.6 cm.

NASA's ACS3 mission aims to be the first Earth-bound solar sail to execute calibration steering laws for in-orbit estimation of solar-sail acceleration parameters. To maximise the mission's scientific return, this study identifies the physical effects to include in the dynamical model, the solar-sail acceleration parameters observable from flight data, and the uncertainties to consider during the orbit determination process. The sensitivity of the solar-sail dynamics to perturbations, model uncertainties, and sail-attitude errors is investigated by 1) comparing a reference orbit with modified orbits, each altered in a single dynamical aspect, and 2) evaluating the accuracy of modified models in reconstructing the reference orbit through iterative initial state adjustments. For the one-sigma 10-meter observation noise level of the ACS3 mission and a seven-day arc, results indicate that higher-order lunar perturbations, planetary third-body effects, and relativistic corrections can be omitted from the dynamical model. Additionally, the geopotential expansion may be limited to degree and order 32. In contrast, the dynamics should include the effects of solid Earth tides, account for the instantaneous Sun-sailcraft distance in the solar radiation pressure model, and assume imperfect reflection from the sail surface in the solar and planetary radiation pressure models. Furthermore, the analysis reveals varying levels of observability for the sail optical coefficients, with frontside reflectivity and specularity showing the strongest influence on the solar-sail dynamics. Finally, systematic attitude errors and uncertainties in atmospheric density and accommodation coefficients are the most challenging factors to absorb through initial state adjustment, potentially complicating the estimation of solar-sail acceleration parameters.

The Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite, which operated at an altitude of ∼250km, provided neutral thermosphere mass density and crosswind observations in the dawn-dusk sectors throughout most of its operational lifetime (2009–2013). As a result of its Sun-synchronous orbit, GOCE’s large solar panels remained at a near-perpendicular angle to the incoming solar radiation, leading to a significant radiation pressure acceleration. In this research, we focused on revisiting and reprocessing GOCE thermosphere mass density and crosswind data. We selected the coefficients describing the thermo-optical surface properties and employed a high-fidelity satellite geometry in a ray-racing simulation. Additionally, we distinguished between the solar flux in the visible and infrared bands and introduced a model for the satellite’s thermal emission. The availability of the in situ thermistor measurements allowed for the validation of the thermal model. Moreover, we replaced the Level-1b ion thruster data with raw telemetry, filling multiple data gaps. We analysed how incremental improvements in the radiation pressure modelling affected the observed crosswind speed. By replacing the panel model with the high-fidelity satellite geometry, the crosswind speed decreased up to 5 ms⁻¹. The biggest difference reduction of 40ms⁻¹resulted from introducing the thermal model. Splitting the solar flux further decreases the observed crosswind speed by up to 8ms⁻¹. The reduction in crosswind speed was most prominent during the first years of the mission when the solar activity was low. We compared the newly processed GOCE zonal wind data with respect to the most recent previous release. We observed a median absolute deviation decrease of 10 ms⁻¹around the south magnetic pole in the dawn sector. The yearly consistency of low-latitude zonal winds did not change significantly. The main obstacle in quantifying the improvement compared to the previous crosswind dataset stemmed from the fact that the previous and new datasets were generated with different crosswind estimation algorithms. The difference in thermosphere density compared to previously published datasets is minor since the effect of radiation pressure is most prominent in the cross-track direction. Finally, we verified the assumption about the energy accommodation coefficient of 0.82 and concluded that it remains valid after implementing the radiation pressure modelling improvements.

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.

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.

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.

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.