Cold Atom Interferometry for Enhancing the Radio Science Gravity Experiment: A Phobos Case Study

Interplanetary missions have typically relied on Radio Science (RS) to recover gravity fields by detecting their signatures on the spacecraft trajectory. The weak gravitational fields of small bodies, coupled with the prominent influence of confounding accelerations, hinder the efficacy of this method. Meanwhile, quantum sensors based on Cold Atom Interferometry (CAI) have demonstrated absolute measurements with inherent stability and repeatability, reaching the utmost accuracy in microgravity. This work addresses the potential of CAI-based Gradiometry (CG) as a means to strengthen the RS gravity experiment for small-body missions. Phobos represents an ideal science case as astronomic observations and recent flybys have conferred enough information to define a robust orbiting strategy, whilst promoting studies linking its geodetic observables to its origin. A covariance analysis was adopted to evaluate the contribution of RS and CG in the gravity field solution, for a coupled Phobos-spacecraft state estimation incorporating one week of data. The favourable observational geometry and the small characteristic period of the gravity signal add to the competitiveness of Doppler observables. Provided that empirical accelerations can be modelled below the nm/s 2 level, RS is able to infer the 6 × 6 spherical harmonic spectrum to an accuracy of 0.1–1% with respect to the homogeneous interior values. If this correlates to a density anomaly beneath the Stickney crater, RS would suffice to constrain Phobos’ origin. Yet, in event of a rubble pile or icy moon interior (or a combination thereof) CG remains imperative, enabling an accuracy below 0.1% for most of the 10 × 10 spectrum. Nevertheless, technological advancements will be needed to alleviate the current logistical challenges associated with CG operation. This work also reflects on the sensitivity of the candidate orbits with regard to dynamical model uncertainties, which are common in small-body environments. This brings confidence in the applicability of the identified geodetic estimation strategy for missions targeting other moons, particularly those of the giant planets, which are targets for robotic exploration in the coming decades. Astrodynamics & Space Mission

Dayside Upper-Thermospheric Density Fluctuations as Observed by GRACE and GRACE-FO at ∼500 km Height

We statistically investigate fluctuation amplitudes (normalized to the background values) of dayside low-/mid-latitude upper-thermospheric mass density as observed by the Gravity Recovery and Climate Experiment (GRACE) and GRACE-Follow-On (GRACE-FO) spacecraft at ∼500 km altitude between 2002 and 2022. There are three new findings in our results. First, the climatology closely replicates previous studies on stratospheric and upper-thermospheric gravity waves (GWs) below the GRACE(-FO) altitudes. For example, in low-latitude regions, the fluctuations are stronger above continents than in the oceanic area. Mid-latitude fluctuations prefer the local winter hemisphere to the summer, and the South American/Atlantic region in June solstice hosts stronger fluctuations than in any other low-/mid-latitude locations or seasons. Fluctuations are more intense under lower solar activity. The above-mentioned consistency of the GRACE(-FO) results with previous lower-altitude GW studies confirms that GWs can penetrate up to 500 km. Second, the anti-correlation of upper-thermospheric GW with solar activity, which has been earlier reported for multi-year time scales, can also be identified on the scale of the solar rotation period (∼27 days). Third, we demonstrate asymmetry between pre-noon and post-noon GWs. The former exhibits stronger GW activity, which may result from the colder thermosphere being more favorable for intense mass density fluctuations via secondary/tertiary GW generation.Astrodynamics & Space Mission

Improving orbit prediction via thermospheric density calibration

The uncertainty on Thermospheric Mass Density (TMD), as derived from atmospheric models, can reach extremely high values. This effect is noteworthy in Low Earth Orbit (LEO), where atmospheric drag is the main perturbing force, as well as the most uncertain. LEO harbours almost 18,000 space objects at the end of 2021, around 60% of the total space debris population, and the rate of growth is increasing every year. Increasing the accuracy of TMD models, and thus the uncertainty characterisation, is important to ensure space environment sustainability in this congested and contested region. Accurate TMD modelling is a decisive factor in all space applications below the exopause, from LEO mission design to Space Situational Awareness (SSA) service provision: from conjunction assessment to re-entry and fragmentation analysis To enhance empirical TMD models, atmospheric density observations derived from satellite measurements are assimilated.This paper presents a novel approach for assimilating thermospheric density observations into atmospheric models to improve the accuracy of orbit predictions in short- to medium- term propagations. First, Global Navigation Satellite System (GNSS) derived density data from Swarm satellites are ingested from the publicly available Level 2 data products of the European Space Agency (ESA). In a second step, density data is assimilated into the empirical model NRMLSISE-00, using Principal Component Analysis (PCA) to decompose into the main temporal and spatial modes, providing useful physical insight into the main variables driving the model. Thirdly, the model is tested on several cases, whose data was not assimilated, such as LEO satellites that are well-tracked with GNSS-derived positions: Sentinel, and GRACE. The model is also tested with objects with less accurate reference trajectories, such as catalogued space debris in LEO. Finally, the orbits are propagated, using the improved drag model that includes the neutral density from the assimilation of the GNSS-derived observations into NLRMSISE-00. The accuracy of the method is assessed and compared to non-assimilated models. During the discussion of the results, other sources of uncertainty are analysed. To name a few, geomagnetic activity, solar radiation pressure coefficient, attitude knowledge, and spacecraft parameters such as mass, area, drag coefficient, and so on. The improvement on the state accuracy and uncertainty realism after a medium-term propagation is analysed and the application to catalogue maintenance discussed.Astrodynamics & Space Mission

CASSIOPE orbit and attitude determination using commercial off-the-shelf GPS receivers

As part of the “GPS Attitude, Positioning, and Profiling experiment (GAP)” of the Canadian CASSIOPE science and technology mission, a set of four geodetic GPS receivers connected to independent antennas on the top-panel of the spacecraft can be operated concurrently to collect dual-frequency code and phase measurements on both the L1 and L2 frequencies. The qualification of the commercial off-the-shelf (COTS) GPS receivers is discussed, and flight results of precise orbit and attitude determination are presented. Pseudorange and carrier phase errors amount to roughly 65 cm and 8 mm for the ionosphere-free dual-frequency combination, which compares favorably with other missions using fully qualified space GPS receivers and is mainly limited by choice of simple patch antennas without choke rings. Precise orbit determination of CASSIOPE using GPS observations can achieve decimeter-level accuracy during continued operations but suffers from onboard and mission restrictions that limit the typical data availability to less than 50% of each day and induce regular long-duration gaps of 4–10 h. Based on overlap analyses, daily peak orbit determination errors can, however, be confined to 1 m 3D on 84% of all days, which fulfills the mission needs for science data processing of other instruments. The attitude of CASSIOPE can be determined with a representative precision of about 0.2° in the individual axes using three GAP receivers and antennas. Availability of dual-frequency measurements is particularly beneficial and enables single-epoch ambiguity fixing in about 97% of all epochs. Overall, the GAP experiment demonstrates the feasibility of using COTS-based global navigation satellite system receivers in space and the benefits they can bring for small-scale science missions.Astrodynamics & Space Mission

ESA’s next-generation gravity mission concepts

The paper addresses the preparatory studies of future ESA mission concepts devoted to improve our understanding of the Earth’s mass change phenomena causing temporal variations in the gravity field, at different temporal and spatial scales, due to ice mass changes of ice sheets and glaciers, continental water cycles, ocean masses dynamics and solid-earth deformations.The ESA initiatives started in 2003 with a study on observation techniques for solid Earth missions and continued through several studies focusing on the satellite system, technology development for propulsion and distance metrology, preferred mission concepts, the attitude and orbit control system, as well as the optimization of the satellite constellation. These activities received precious inputs from the GOCE, GRACE and GRACE-FO missions. More recently, several studies related to new sensor concepts based on cold atom interferometry (CAI) were conducted, mainly focusing on technology development for different instrument configurations (GOCE-like and GRACE-like) and including validation activities, e.g. a first successful airborne survey with a CAI gravimeter.The latest results concerning the preferred satellite architectures and constellations, payload design and estimated science performance will be presented as well as remaining open issues for future concepts.Astrodynamics & Space Mission

Next Generation Gravity Mission Elements of the Mass Change and Geoscience International Constellation: From Orbit Selection to Instrument and Mission Design

ESA’s Next Generation Gravity Mission (NGGM) is a candidate Mission of Opportunity for ESA–NASA cooperation in the frame of the Mass Change and Geosciences International Constellation (MAGIC). The mission aims at enabling long-term monitoring of the temporal variations of Earth’s gravity field at relatively high temporal (down to 3 days) and increased spatial resolutions (up to 100 km) at longer time intervals. This implies also that time series of GRACE and GRACE-FO can be extended towards a climate series. Such variations carry information about mass change induced by the water cycle and the related mass exchange among atmosphere, oceans, cryosphere, land and solid Earth and will complete our picture of global and climate change. The main observable is the variation of the distance between two satellites measured by a ranging instrument. This is complemented by accelerometers that measure the nongravitational accelerations, which need to be reduced from ranging measurements to obtain the gravity signal. The preferred satellite constellation comprises one satellite pair in a near-polar and another in an inclined circular orbit. The paper focuses on the orbit selection methods for optimizing the spatial sampling for multiple temporal resolutions and then on the methodology for deriving the engineering requirements for the space segment, together with a discussion on the main mission parameters.Astrodynamics & Space Mission

Bandwidth correction of Swarm GPS carrier phase observations for improved orbit and gravity field determination

Gravity fields derived from GPS tracking of the three Swarm satellites have shown artifacts near the geomagnetic equator, where the carrier phase tracking on the L2 frequency is unable to follow rapid ionospheric path delay changes due to a limited tracking loop bandwidth of only 0.25 Hz in the early years of the mission. Based on the knowledge of the loop filter design, an analytical approach is developed to recover the original L2 signal from the observed carrier phase through inversion of the loop transfer function. Precise orbit determination and gravity field solutions are used to assess the quality of the correction. We show that the a posteriori RMS of the ionosphere-free GPS phase observations for a reduced-dynamic orbit determination can be reduced from 3 to 2 mm while keeping up to 7% more data in the outlier screening compared to uncorrected observations. We also show that artifacts in the kinematic orbit and gravity field solution near the geomagnetic equator can be substantially reduced. The analytical correction is able to mitigate the equatorial artifacts. However, the analytical correction is not as successful compared to the down-weighting of problematic GPS data used in earlier studies. In contrast to the weighting approaches, up to 9–10% more kinematic positions can be retained for the heavily disturbed month March 2015 and also stronger signals for gravity field estimation in the equatorial regions are obtained, as can be seen in the reduced error degree variances of the gravity field estimation. The presented approach may also be applied to other low earth orbit missions, provided that the GPS receivers offer a sufficiently high data rate compared to the tracking loop bandwidth, and provided that the basic loop-filter parameters are known.Astrodynamics & Space Mission

Thermosphere densities derived from Swarm GPS observations

After the detection of many anomalies in the Swarm accelerometer data, an alternative method has been developed to determine thermospheric densities for the three-satellite mission. Using a precise orbit determination approach, non-gravitational and aerodynamic-only accelerations are estimated from the high-quality Swarm GPS data. The GPS-derived non-gravitational accelerations serve as a baseline for the correction of the Swarm-C along-track accelerometer data. The aerodynamic accelerations are converted directly into thermospheric densities for all Swarm satellites, albeit at a much lower temporal resolution than the accelerometers would have been able to deliver. The resulting density and acceleration data sets are part of the European Space Agency Level 2 Swarm products. To improve the Swarm densities, two modifications have recently been added to our original processing scheme. They consist of a more refined handling of radiation pressure accelerations and the use of a high-fidelity satellite geometry and improved aerodynamic model. These modifications lead to a better agreement between estimated Swarm densities and NRLMSISE-00 model densities. The GPS-derived Swarm densities show variations due to solar and geomagnetic activity, as well as seasonal, latitudinal and diurnal variations. For low solar activity, however, the aerodynamic signal experienced by the Swarm satellites is very small, and therefore it is more difficult to accurately resolve latitudinal density variability using GPS data, especially for the higher-flying Swarm-B satellite. Therefore, mean orbit densities are also included in the Swarm density product.Astrodynamics & Space Mission

Gas-surface interactions modelling influence on satellite aerodynamics and thermosphere mass density

The satellite acceleration data from the CHAMP, GRACE, GOCE, and Swarm missions provide detailed information on the thermosphere density over the last two decades. Recent work on reducing errors in modelling the spacecraft geometry has greatly reduced scale differences between the thermosphere data sets from these missions. However, residual inconsistencies between the data sets and between data and models are still present. To a large extent, these differences originate in the modelling of the gas-surface interactions (GSI), which is part of the satellite aerodynamic modelling used in the acceleration to density data processing. Physics-based GSI models require in-situ atmospheric composition and temperature data that are not measured by any of the above-mentioned satellites and, as a consequence, rely on thermosphere models for these inputs. To reduce the dependence on existing thermosphere models, we choose a GSI model with a constant energy accommodation coefficient per mission, which we optimize exploiting particular attitude manoeuvres and wind analyses to increase the self-consistency of the multi-mission thermosphere mass density data sets. We compare our results with those based on variable energy accommodation obtained by different studies and semi-empirical models to show the principal differences. The presented comparisons provide novel opportunity to quantify the discrepancies between current GSI models. Among the presented data, density variations with variable accommodation are within ±10%, and peaks can reach up to 15% at the poles. The largest differences occur during low solar activity periods. In addition, we utilize a series of attitude manoeuvres performed in May 2014 by the Swarm A and C satellites, which are flying in close proximity, to evaluate the residual inconsistency of the density observations as a function of the energy accommodation coefficient. Our analysis demonstrates that an energy accommodation coefficient of 0.85 maximizes the consistency of the Swarm density observations during the attitude manoeuvres. Using such coefficient, for Swarm A and Swarm C, the new density would be lower in magnitude with a 4-5% difference. In recent studies, similar energy accommodation coefficients were retrieved for the CHAMP and GOCE missions by investigating thermospheric winds. These new values for the energy accommodation coefficient provide a higher consistency among different missions and models. A comparison of neutral densities between current thermosphere models and observations indicates that semi-empirical models such as NRLMSISE-00 and DTM-2013 significantly overestimate the density, and that an overall higher consistency between the observations from the different missions can be achieved with the presented assumptions. The new densities from this work provide consistencies of 4.13% and 3.65% between the minimum and maximum mean ratios among the selected missions with NRLMSISE-00 and DTM-2013, respectively. A comparison with the WACCM-X general circulation model is also performed. Similar to the other models, WACCM-X seems to provide higher estimates of mass density especially under high and moderate solar activities. This work has the objective to guide density data users over the multiple data sets and highlight the remaining uncertainties associated with different GSI models. Astrodynamics & Space MissionsSpace Engineerin

Interhemispheric Asymmetry of the Thermospheric Neutral Density Response to the 7–9 September 2017 Geomagnetic Storms

The thermospheric neutral density response to the 7–9 September 2017 storms is investigated based on the Swarm satellite observations and the thermosphere-ionosphere-electrodynamic general circulation model (TIEGCM) simulation. The Swarm data depicted a prominent interhemispheric asymmetry (IHA) in the afternoon sector during the second storm, a feature that was yet explained. Driven by realistic high-latitude electric potential and electron precipitation patterns, the TIEGCM is able to reproduce the observed storm-time neutral density response. The TIEGCM simulation reveals that the differences in the traveling atmospheric disturbances (TADs) is largely responsible for the observed IHA in the neutral mass density response at low and middle latitudes, whereas the difference in mean molecular mass between the two hemispheres may contribute to the IHA in neutral density at higher latitudes. The IHAs in TADs and mean molecular mass are attributed to the IHA in Joule heating dissipation on the night and dawn sides.Astrodynamics & Space Mission