We present the first extensive analysis of K/Ka-band ranging post-fit residuals of an official Level-2 product, characterized as Line-of-Sight Gravity Differences (LGD), which exhibit and showcase interesting sub-monthly geophysical signals. These residuals, provided by Center for Space Research, were derived from the difference between spherical harmonic coefficient least-squares fits and reduced Level-1B range-rate observations. We classified the geophysical signals into four distinct categories: oceanic, meteorological, hydrological, and solid Earth, focusing primarily on the first three categories in this study. In our examination of oceanic processes, we identified notable mass anomalies in the Argentine basin, specifically within the Zapiola Rise, where persistent remnants of the rotating dipole-like modes are evident in the LGD post-fit residuals. Our analysis extended to the Gulf of Carpentaria and Australia during the 2013 Oswald cyclone, revealing significant LGD residual anomalies that correlate with cyclone tracking and precipitation data. Additionally, we investigated the monsoon seasons in Bangladesh, particularly from June–September 2007, where we observed peaks in sub-monthly variability. These findings were further validated by demonstrating high spatial and temporal correlations between gridded LGD residuals and ITSG-Grace2018 daily solutions. These identified anomalies are associated with significant mass change phenomena, underscoring the critical importance of these geophysical signals for future high-resolution studies of mass transport.

Estimates of Earth’s gravity temporal variations by GRACE(−FO) have catalyzed a wide range of scientific studies and discoveries. Although an increase in the satellite pairs would reduce the error and increase the temporal and spatial resolution, mission costs limit populating additional GRACE-like pairs. One viable solution is to reduce costs by miniaturizing the satellite. As a first step in reaching this objective, the Miniaturized Prototype for GRavity field Assessment using Distributed Earth-orbiting assets (uPGRADE) project aims to produce a CHAMP-like prototype gravimetry satellite that includes star trackers, GNSS and accelerometers in CubeSat size. As one of the primary payloads, the utility of high-precision Micro-Electro-Mechanical Systems (MEMS) accelerometer for gravimetric mission has not been considered. Here, we evaluated three, six and nine MEMS arrangements. We found that the six MEMS parallel arrangement can observe both the desired non-gravitational accelerations and additional absolute value of the angular velocity. We developed a measurement error model, associated with MEMS position and orientation errors, to guide the MEMS optimal design and assembly. Finally, we conducted uPGRADE mission simulations using appropriate observations and model errors. The impact of a 10 nm/s2MEMS accelerometer error on gravity recovery is very close to that of the 5 mm GNSS error. However, the accelerometer error degrades the low-degree coefficients more significantly, particularly (Formula presented) and (Formula presented). The simulations indicate that the temporal gravity can be estimated up to degree 15, albeit with some compromise in the low-degree coefficients. Recommendations are made to lower the projected noise floor of MEMS accelerometer to enhance the low-degree coefficients accuracy.

The aim of this paper is to present the concept of a dedicated gravity field mission for the planet Mars, the Mars Quantum Gravity Mission (MaQuIs). The mission is targeted at improving the data on the gravitational field of Mars, enabling studies on planetary dynamics, seasonal changes, and subsurface water reservoirs. MaQuIs follows well known mission scenarios, currently deployed for Earth, and includes state-of-the-art quantum technologies to enhance the gained scientific signal.

The Next Generation Gravity Mission (NGGM), currently in a feasibility study phase as a candidate Mission of Opportunity for ESA-NASA cooperation in the frame of the Mass Change and Geo-Sciences International Constellation (MAGIC), is designed to monitor mass transport in the Earth system by its variable gravity signature with increased spatial and temporal resolution. The NGGM will be composed by a constellation of two pairs of satellites, each providing the measurement of two quantities from which the map of Earth’s gravity field will be obtained: the variation of the distance between two satellites of each pair, measured by a laser interferometer with nanometer precision; and the relative non-gravitational acceleration between the centers of mass of each satellite pair, measured by ultra-sensitive accelerometers. This article highlights the importance of the second “observable” in the reconstruction of the lower harmonics of Earth’s gravity field, by highlighting the tight control requirements in linear and angular accelerations and angular rates, and the expectable performances from the drag-free, attitude, and orbit control system (DFAOCS) obtained through an end-to-end (E2E) simulator. The errors resulting from different mission scenarios with varying levels of drag-free control and pointing accuracy are then presented, demonstrating that a high-performance accelerometer alone is not sufficient to achieve the measurement quality necessary to achieve the mission objectives, if the spacecraft does not provide to this sensor a suitable drag-free environment and a precise and stable pointing. The consequences of these different mission scenarios on the gravity field retrieval accuracy, especially for the lower spherical harmonic degrees, are computed in order to quantitatively justify the rationale for these capabilities on the NGGM spacecraft.

GRACE observations revealed that rapid mass loss in the West Antarctic Ice Sheet (WAIS) abruptly paused in 2015, followed by a much lower rate of mass loss ((Formula presented.) Gt yr⁻¹) until the decommissioning of GRACE in 2017. The critical 1-year GRACE intermission data gap raises the question of whether the reduced mass loss rate persists. The Swarm gravimetry data, which have a lower resolution, show good agreement with GRACE/GRACE-FO observations during the overlapping period, i.e., high correlation (0.78) and consistent trend estimates. Swarm data efficiently bridge the GRACE/GRACE-FO data gap and reveal that WAIS has returned to the rapid mass loss state ((Formula presented.) Gt yr⁻¹) that prevailed prior to 2015 during the GRACE intermission data gap. The changes in precipitation patterns, driven by the climate cycles, further explain and confirm the dramatic shifts in the WAIS mass loss regime implied by the Swarm observations.

Although the knowledge of the gravity of the Earth has improved considerably with CHAMP, GRACE, and GOCE (see appendices for a list of abbreviations) satellite missions, the geophysical community has identified the need for the continued monitoring of the time-variable component with the purpose of estimating the hydrological and glaciological yearly cycles and long-term trends. Currently, the GRACE-FO satellites are the sole dedicated provider of these data, while previously the GRACE mission fulfilled that role for 15 years. There is a data gap spanning from July 2017 to May 2018 between the end of the GRACE mission and start the of GRACE-FO, while the Swarm satellites have collected gravimetric data with their GPS receivers since December 2013. We present high-quality gravity field models (GFMs) from Swarm data that constitute an alternative and independent source of gravimetric data, which could help alleviate the consequences of the 10-month gap between GRACE and GRACE-FO, as well as the short gaps in the existing GRACE and GRACE-FO monthly time series. The geodetic community has realized that the combination of different gravity field solutions is superior to any individual model and set up the Combination Service of Time-variable Gravity Fields (COST-G) under the umbrella of the International Gravity Field Service (IGFS), part of the International Association of Geodesy (IAG). We exploit this fact and deliver the highest-quality monthly GFMs, resulting from the combination of four different gravity field estimation approaches. All solutions are unconstrained and estimated independently from month to month. We tested the added value of including kinematic baselines (KBs) in our estimation of GFMs and conclude that there is no significant improvement. The non-gravitational accelerations measured by the accelerometer on board Swarm C were also included in our processing to determine if this would improve the quality of the GFMs, but we observed that is only the case when the amplitude of the non-gravitational accelerations is higher than during the current quiet period in solar activity Using GRACE data for comparison, we demonstrate that the geophysical signal in the Swarm GFMs is largely restricted to spherical harmonic degrees below 12. A 750 km smoothing radius is suitable to retrieve the temporal variations in Earth's gravity field over land areas since mid-2015 with roughly 4 cm equivalent water height (EWH) agreement with respect to GRACE. Over ocean areas, we illustrate that a more intense smoothing with 3000 km radius is necessary to resolve large-scale gravity variations, which agree with GRACE roughly at the level of 1 cm EWH, while at these spatial scales the GRACE observes variations with amplitudes between 0.3 and 1 cm EWH. The agreement with GRACE and GRACE-FO over nine selected large basins under analysis is 0.91 cm, 0.76 cm yr-1, and 0.79 in terms of temporal mean, trend, and correlation coefficient, respectively. The Swarm monthly models are distributed on a quarterly basis at ESA's Earth Swarm Data Access (at https://swarm-diss.eo.esa.int/, last access: 5 June 2020, follow Level2longterm and then EGF) and at the International Centre for Global Earth Models (http://icgem.gfz-potsdam.de/series/02_COST-G/Swarm, last access: 5 June 2020), as well as identified with the DOI https://doi.org/10.5880/ICGEM.2019.006 (Encarnacao et al., 2019).

In preparation for the Center for Space Research Release 6 of Gravity Recovery and Climate Experiment (GRACE) data, 32 accelerometer parameterization schemes are analyzed, which combine skew-symmetric, symmetric, and full-scale matrices with four different bias parameterizations inspired on those used on Release 5. After three selection stages, it has been determined that the daily full-scale matrix parameterization combined with the daily bias and linear drift improved the quality of the degree 60 GRACE spherical harmonic solutions by reducing the amplitude of north–south elongated artifacts by nearly 1 mm geoid height in some months. The improvements are largest during the period of 2002–2005 and after 2011. From 2007 to 2010, this parameterization scheme slightly degrades the GRACE solutions (limited under 0.1 mm geoid height increase in the intensities of north–south artifacts), but it has been demonstrated that this effect is limited to small areas and is barely visually noticeable. As a result of the proposed parameterization scheme, throughout the complete GRACE data period, the discrepancy of the C2,0 coefficient relative to satellite laser ranging data has been reduced by a factor of 2.

The Swarm satellites carry accelerometers as part of their scientific payload. These instruments measure the non-gravitational acceleration due to forces like drag or radiation pressure acting on the spacecraft, from which thermospheric neutral densities and potentially winds can be derived. Unfortunately, the acceleration measurements suffer from a variety of perturbations, the most prominent being slow temperature-induced bias variations and sudden bias changes. Other less prominent perturbation includes spikes and artificial periodic signals. Though all perturbation are visible in the measurements of all Swarm accelerometers, their severity is much different for the three Swarm satellites. In this presentation, we illustrate all known disturbances and assess their severity for scientific exploitation of the accelerometer data separately for each Swarm satellite.

The Swarm satellite mission provides important information regarding the temporal changes of Earth’s gravity field. Several European institutes routinely process Swarm GPS data to produce kinematic orbits, which forms the basis for the estimation of monthly gravity fields. Each institute follows a different gravity field estimation approach and all together they provide complementary advantages. As a result, the combined gravity field model is superior to any individual contribution, improving the accuracy of the measurement of mass transport processes. These models are an integral part of the European Gravity Service for Improved Emergency Management project (http://egsiem.eu), thus providing independent input, in additional to dedicated geodetic data. We illustrate the agreement of the Swarm models with the much more accurate GRACE solutions, at 1666km wavelength and over most of the Swarm mission lifetime. We additionally highlight large surface mass transport processes represented by the Swarm GPS data.

The Swarm satellites carry accelerometers and GPS receivers as part of their scientific payload. The GPS receivers are not only used for locating the position and time of the magnetic measurements, but also for determining non-gravitational forces like drag and radiation pressure acting on the spacecraft. The accelerometers measure these forces directly, at much finer resolution than the GPS receivers, from which thermospheric neutral densities and potentially winds can be derived. Unfortunately, the acceleration measurements suffer from a variety of disturbances, the most prominent being slow temperature-induced bias variations and sudden bias changes. These disturbances required significant changes to the processing algorithms, which as a side effect caused a significant delay of the accelerometer data release. In this presentation, we describe the new processing that is required for transforming the disturbed acceleration measurements into scientifically valuable thermospheric neutral densities. In the first stage, the sudden bias changes in the acceleration measurements are removed using a dedicated software tools. We present a new option of automated step detection and correction, which should speed up the accelerometer data release. The second stage is the calibration of the accelerometer measurements against the nongravitational accelerations derived from the GPS receiver, which includes the correction for the slow temperature-induced bias variations. The identification of validity periods for calibration and correction parameters is part of the second stage. In the third stage, the calibrated and corrected accelerations a merged with the non-gravitational accelerations derived from the GPS receiver by a weighted average in the spectral domain, where the weights depend on the frequency. The fourth stage consists of transforming the corrected and calibrated accelerations into thermospheric neutral densities. We describe the methods used in each stage, highlight the difficulties encountered, and comment on the quality of the thermospheric neutral density data set.

ESA’s SWARM constellation of three near-polar satellites was launched on 22 November 2013, with the primary scientific objective to map the Earth’s magnetic field and its variations. Although not among its primary scientific objectives, the specific orbital formation geometry of the three identical SWARM accelerometer-equipped satellites allows recovery for more accurate low-degree temporal gravity field. Equipped with satellite laser ranging retro-reflectors, accelerometers and geodetic-quality GPS receivers, data from the SWARM satellites have been used to estimate low-degree temporal gravity field based on the acceleration, short-arc, and celestial mechanics approaches, with geopotential solutions complete to degree and order 15. Here we will use the improved formulation for the energy balance approach (EBA) to estimate the temporal gravity field using data from the SWARM satellites. The improved energy balance approach to generate in situ geopotential difference measurements using the GRACE KBR data has achieved the measurement accuracy by more than 3 orders of magnitude compared to previous studies. Specifically, we will: (1) assess the accuracy of SWARM temporal gravity field EBA solutions by comparing with solutions using other approaches and versus GRACE solutions using GPS and using KBR; (2) assess the impact on lowdegree temporal gravity field EBA solutions using kinematic or dynamic SWARM GPS orbits; (3) evaluate low-degree temporal gravity solutions with or without accelerometer-corrections for data from individual SWARM satellite or from the combined constellation of SWARM satellites; (4) evaluate and confirm the maximum achievable degree and order of temporal gravity field model using data from the SWARM constellation of satellites, and (5) investigate the fidelity of the estimated SWARM second degree zonal geopotential coefficients and other approaches, as well as the solutions using other data, including SLR, other GPS, and GRACE KBR solutions.

Since 2002 Gravity Recovery and Climate Experiment (GRACE) provides monthly gravity fields from K-band ranging (KBR) between two GRACE satellites. These KBR gravity monthlies have enabled the global observation of time-varying Earth mass signal at a regional scale (about 400 km resolution). Apart from KBR, monthly gravity solutions can be computed from onboard GPS data. The newly reprocessed GPS monthlies from 13 yr of GRACE data are shown to yield correct time-variable gravity signal (seasonality, trends, interannual variations) at a spatial resolution of 1300 km (harmonic degree 15). We show that GPS fields from new Swarm mission are of similar quality as GRACE GPS monthlies. Thus, Swarm GPS monthlies represent new and independent source of information on time-variable gravity, and, although with lower resolution and accuracy, they can be used for its monitoring, particularly if GRACE KBR/GPS data become unavailable before GRACE Follow-On is launched (2017 August).

It is of great interest to numerous geophysical studies that the time series of global gravity field models derived from Gravity Recovery and Climate Experiment (GRACE) data remains uninterrupted after the end of this mission. With this in mind, some institutes have been spending efforts to estimate gravity field models from alternative sources of gravimetric data. This study focuses on the gravity field solutions estimated from Swarm global positioning system (GPS) data, produced by the Astronomical Institute of the University of Bern, the Astronomical Institute (ASU, Czech Academy of Sciences) and Institute of Geodesy (IfG, Graz University of Technology). The three sets of solutions are based on different approaches, namely the celestial mechanics approach, the acceleration approach and the short-arc approach, respectively. We derive the maximum spatial resolution of the time-varying gravity signal in the Swarm gravity field models to be degree 12, in comparison with the more accurate models obtained from K-band ranging data of GRACE. We demonstrate that the combination of the GPS-driven models produced with the three different approaches improves the accuracy in all analysed monthly solutions, with respect to any of them. In other words, the combined gravity field model consistently benefits from the individual strengths of each separate solution. The improved accuracy of the combined model is expected to bring benefits to the geophysical studies during the period when no dedicated gravimetric mission is operational.

The Swarm satellites were launched on November 22, 2013, and carry accelerometers and GPS receivers as part of their scientific payload. The GPS receivers do not only provide the position and time for the magnetic field measurements, but are also used for determining non-gravitational forces like drag and radiation pressure acting on the spacecraft. The accelerometers measure these forces directly, at much finer resolution than the GPS receivers, from which thermospheric neutral densities can be derived. Unfortunately, the acceleration measurements suffer from a variety of disturbances, the most prominent being slow temperature-induced bias variations and sudden bias changes. In this paper, we describe the new, improved four-stage processing that is applied for transforming the disturbed acceleration measurements into scientifically valuable thermospheric neutral densities. In the first stage, the sudden bias changes in the acceleration measurements are manually removed using a dedicated software tool. The second stage is the calibration of the accelerometer measurements against the non-gravitational accelerations derived from the GPS receiver, which includes the correction for the slow temperature-induced bias variations. The identification of validity periods for calibration and correction parameters is part of the second stage. In the third stage, the calibrated and corrected accelerations are merged with the non-gravitational accelerations derived from the observations of the GPS receiver by a weighted average in the spectral domain, where the weights depend on the frequency. The fourth stage consists of transforming the corrected and calibrated accelerations into thermospheric neutral densities. We present the first results of the processing of Swarm C acceleration measurements from June 2014 to May 2015. We started with Swarm C because its acceleration measurements contain much less disturbances than those of Swarm A and have a higher signal-to-noise ratio than those of Swarm B. The latter is caused by the higher altitude of Swarm B as well as larger noise in the acceleration measurements of Swarm B. We show the results of each processing stage, highlight the difficulties encountered, and comment on the quality of the thermospheric neutral density data set.

Spectral analysis of data noise is performed in the context of gravity field recovery from inter-satellite ranging measurements acquired by the satellite gravimetry mission GRACE. The motivation of the study is two-fold: (i) to promote a further improvement of GRACE data processing techniques and (ii) to assist designing GRACE follow-on missions. The analyzed noise realizations are produced as the difference between the actual GRACE inter-satellite range measurements and the predictions based on state-of-the-art force models. The exploited functional model is based on the so-called “range combinations,” which can be understood as a finite-difference analog of inter-satellite accelerations projected onto the line-of-sight connecting the satellites. It is shown that low-frequency noise is caused by limited accuracy of the computed GRACE orbits. In the first instance, it leads to an inaccurate estimation of the radial component of the inter-satellite velocities. A large impact of this component stems from the fact that it is directly related to centrifugal accelerations, which have to be taken into account when the measured range-accelerations are linked with inter-satellite accelerations. Another effect of orbit inaccuracies is a miscalculation of forces acting on the satellites (particularly, the one described by the zero-degree term of the Earth’s gravitational field). The major contributors to the noise budget at high frequencies (above 9 mHz) are (i) ranging sensor errors and (ii) limited knowledge of the Earth’s static gravity field at high degrees. Importantly, we show that updating the model of the static field on the basis of the available data must be performed with a caution as the result may not be physical due to a non-unique recovery of high-degree coefficients. The source of noise in the range of intermediate frequencies (1–9 mHz), which is particularly critical for an accurate gravity field recovery, is not fully understood yet. We show, however, that it cannot be explained by inaccuracies in background models of time-varying gravity field. It is stressed that most of the obtained results can be treated as sufficiently general (i.e., applicable in the context of a statistically optimal estimation based on any functional model).

Spectral analysis of data noise is performed in the context of gravity field recovery from inter-satellite ranging measurements acquired by the satellite gravimetry mission GRACE. The motivation of the study is two-fold: (i) to promote a further improvement of GRACE data processing techniques and (ii) to assist designing GRACE follow-on missions. The analyzed noise realizations are produced as the difference between the actual GRACE inter-satellite range measurements and the predictions based on state-of-the-art force models. The exploited functional model is based on the so-called “range combinations,” which can be understood as a finite-difference analog of inter-satellite accelerations projected onto the line-of-sight connecting the satellites. It is shown that low-frequency noise is caused by limited accuracy of the computed GRACE orbits. In the first instance, it leads to an inaccurate estimation of the radial component of the inter-satellite velocities. A large impact of this component stems from the fact that it is directly related to centrifugal accelerations, which have to be taken into account when the measured range-accelerations are linked with inter-satellite accelerations. Another effect of orbit inaccuracies is a miscalculation of forces acting on the satellites (particularly, the one described by the zero-degree term of the Earth’s gravitational field). The major contributors to the noise budget at high frequencies (above 9 mHz) are (i) ranging sensor errors and (ii) limited knowledge of the Earth’s static gravity field at high degrees. Importantly, we show that updating the model of the static field on the basis of the available data must be performed with a caution as the result may not be physical due to a non-unique recovery of high-degree coefficients. The source of noise in the range of intermediate frequencies (1–9 mHz), which is particularly critical for an accurate gravity field recovery, is not fully understood yet. We show, however, that it cannot be explained by inaccuracies in background models of time-varying gravity field. It is stressed that most of the obtained results can be treated as sufficiently general (i.e., applicable in the context of a statistically optimal estimation based on any functional model).

A thermal laser thruster depends on introduction of a high energy laser beam, absorption by the fluid propellant, confinement of the hot propellant gas with minimal losses, and conversion of thermal to kinetic energy in the nozzle. Based on thermodynamic constraints, efficient energy conversion is possible in either the subsonic Laser Supported Combustion (LSC) wave in a converging diverging nozzle or the supersonic Laser Supported Detonation (LSD) wave in a diverging nozzle configuration. A short discussion of both mechanisms is presented. Thruster modeling was performed. The results of steady laser heated LSD flows using LiH as propellant assuming finite rate chemistry are presented.

Ground to orbit launch using laser propulsion requires a thermal system. Physically allowed thermal concepts are discussed and compared. It is argued that the laser supported detonation (LSD) mechanism presents a number of advantages over the alternatives. Numerical simulations of ascent trajectories for a system based on the LSD mechanism were performed to gain insight into the mechanics of laser propulsion and the influence of the most relevant mission parameters. Comparison with the Lightcraft flight data was made and it is shown that the 70 meter height limit is due to excessive laser diffraction. A hypothetical 10 km Lightcraft simulation employing existing technology is presented.