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The Earth masses reside in a near-hydrostatic equilibrium, while the deviations are, for example, manifested in the geoid, which is nowadays well determined by satellite gravimetry. Recent progress in estimating the density distribution of the Earth allows us to examine individual Earth layers and to directly see how the sum approaches the observed anomalous gravitational field. This study evaluates contributions from the crust and the upper mantle taken from the LITHO1.0 model and quantifies the gravitational spectra of the density structure to the depth of 435 km. This is done without isostatic adjustments to see what can be revealed with models like LITHO1.0 alone. At the resolution of 290 km (spherical harmonic degree 70), the crustal contribution starts to dominate over the upper mantle and at about 150 km (degree 130) the upper mantle contribution is nearly negligible. At the spatial resolution $$

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite, launched on 17 March 2009, is designed to measure the Earth’s mean gravity field with unprecedented accuracy at spatial resolutions down to 100 km. The accurate calibration of the gravity gradiometer on-board GOCE is of utmost importance for achieving the mission goals. ESA’s baseline method for the calibration uses star sensor and accelerometer data of a dedicated calibration procedure, which is executed every 2 months. In this paper, we describe a method for monitoring the evolution of calibration parameter during that time. The method works with star sensor and accelerometer data and does not require gravity field models, which distinguishes it from other existing methods. We present time series of calibration parameters estimated from GOCE data from 1 November 2009 to 17 May 2010. The time series confirm drifts in the calibration parameters that are present in the results of other methods, including ESA’s baseline method. Although these drifts are very small, they degrade the gravity gradients, leading to the conclusion that the calibration parameters of the ESA’s baseline method need to be linearly interpolated. Further, we find a correction of −36 × 10−6 for one calibration parameter (in-line differential scale factor of the cross-track gradiometer arm), which improves the gravity gradient performance. The results are validated by investigating the trace of the calibrated gravity gradients and comparing calibrated gravity gradients with reference gradients computed along the GOCE orbit using the ITG-Grace-2010s gravity field model.

This paper describes the upgrade of the GOCE Level 1b gradiometer processing as part of ESA’s Payload Data Segment (PDS). Four processing steps have been identified which can be improved: 1. The optimal determination of the angular rates of the satellite, based on a combination of star sensor and gradiometer data. This is the so-called angular rate reconstruction. 2. The optimal determination of the spacecraft’s attitude, again based on a combination of star sensor and gradiometer data. 3. The combination of data of all simultaneously available star sensors. And, 4. the calibration of the measured accelerations is improved by taking the time dependence of selected calibration parameters into account. In this paper the complete upgrade of the gradiometer Level 1b processing is described, and the expected improvement of the gravity gradients as well as the gravity field solutions is quantified. The largest overall improvements are due to the new method for angular rate reconstruction, mainly at the low to medium frequencies and at the harmonics of the orbital revolution frequency. In addition, spurious artifacts in the gravity gradient V yy , which are caused by non-perfect common mode rejection, can be reduced significantly by the improved calibration approach. We show that the standard deviation of the gravity gradient tensor trace can be reduced by about 90 percent for the frequencies below the gradiometer measurement band (i.e. below 5 mHz) and by about 4 percent within the measurement band (from 5 to 100 mHz). The geoid error of satellite gravity gradiometry solutions based on 61 days of data is reduced from 3.0 to 2.2 cm between spherical harmonic degree 20 and 150. The corresponding gravity anomaly error, between the same degrees, is reduced from 0.7 to 0.5 mGal.

The European Space Agency’s Gravity field and steady-state ocean circulation explorer mission (GOCE) was launched on 17 March 2009. As the first of the Earth Explorer family of satellites within the Agency’s Living Planet Programme, it is aiming at a better understanding of the Earth system. The mission objective of GOCE is the determination of the Earth’s gravity field and geoid with high accuracy and maximum spatial resolution. The geoid, combined with the de facto mean ocean surface derived from twenty-odd years of satellite radar altimetry, yields the global dynamic ocean topography. It serves ocean circulation and ocean transport studies and sea level research. GOCE geoid heights allow the conversion of global positioning system (GPS) heights to high precision heights above sea level. Gravity anomalies and also gravity gradients from GOCE are used for gravity-to-density inversion and in particular for studies of the Earth’s lithosphere and upper mantle. GOCE is the first-ever satellite to carry a gravitational gradiometer, and in order to achieve its challenging mission objectives the satellite embarks a number of world-first technologies. In essence the spacecraft together with its sensors can be regarded as a spaceborne gravimeter. In this work, we describe the mission and the way it is operated and exploited in order to make available the best-possible measurements of the Earth gravity field. The main lessons learned from the first 19 months in orbit are also provided, in as far as they affect the quality of the science data products and therefore are of specific interest for GOCE data users.

With the launch of the Gravity field and Ocean Circulation Explorer (GOCE) in 2009 the science in gravity got another boost. After the time-lapse and long-wavelength studies from Gravity Recovery and Climate Experiment (GRACE) a new sensor was available for determination of the Earth's gravity field and geoid with high accuracy and spatial resolution. Equipped with a 6-component gradiometer and flying at an altitude of 260 km and less GOCE provides the most detailed measurements of Earth's gravity from space ever. On top, GOCE also provides gravity gradients, i.e., the three-dimensional second derivatives of the gravitational potential. This paper provides a review of the results presented at the ‘GOCE solid Earth workshop’ at the University of Twente, The Netherlands (2012), where an overview was given of the present status of the data models, and applications with GOCE which form the basis for this special issue and the review in this paper. An introduction will be given to the GOCE satellite followed by an overview of GOCE data and gravity models. The present state of GOCE related research in geodesy, oceanography and solid Earth sciences indicates the first steps taken to integrate GOCE in the different application fields. For all three fields an overview is given on the most recent scientific results and developments, and first results specifically focusing on these studies where GOCE data has made a unique contribution and provides insights that would not have been possible without GOCE

International audience; Data from the first year of ESA's Swarm constellation mission are used to derive the Swarm Initial Field Model (SIFM), a new model of the Earth's magnetic field and its time variation. In addition to the conventional magnetic field observations provided by each of the three Swarm satellites, explicit advantage is taken of the constellation aspect by including east-west magnetic intensity gradient information from the lower satellite pair. Along-track differences in magnetic intensity provide further information concerning the north-south gradient. The SIFM static field shows excellent agreement (up to at least degree 60) with recent field models derived from CHAMP data, providing an initial validation of the quality of the Swarm magnetic measurements. Use of gradient data improves the determination of both the static field and its secular variation, with the mean misfit for east-west intensity differences between the lower satellite pair being only 0.12 nT.

The European Space Agency (ESA) Swarm spacecraft mission is the first multisatellite ionospheric mission with two low-orbiting spacecraft that are flying in parallel at a distance of ~100–140 km, thus allowing derivation of spatial gradients of ionospheric parameters not only along the orbits but also in the direction perpendicular to them. A third satellite with a higher orbit regularly crosses the paths of the lower spacecraft. Using the Swarm magnetic and electric field instruments, we present a novel technique that allows derivation of two-dimensional (2-D) maps of ionospheric conductances, currents, and electric field in the area between the trajectories of the two lower spacecraft, and even to some extent outside of it. This technique is based on Spherical Elementary Current Systems. We present test cases of modeled situations from which we calculate virtual Swarm data and show that the technique is able to reconstruct the model electric field, horizontal currents, and conductances with a very good accuracy. Larger errors arise for the reconstruction of the 2-D field-aligned currents (FAC), especially in the area outside of the spacecraft orbits. However, even in this case the general pattern of FAC is recovered, and the magnitudes are valid in an integrated sense. Finally, using an MHD model run, we show how our technique allows estimation of the ionosphere-magnetosphere coupling parameter K, if conjugate observations of the magnetospheric magnetic and electric field are available. In the case of a magnetospheric multisatellite mission (e.g., the ESA Cluster mission) several K estimates at nearby points can be generated.

ESA’s Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) was operated in an extremely low Earth orbit down to 229 km altitude to map the Earth’s gravity field. As anticipated, on 21 Oct 2013 drag-free control stopped owing to the depletion of fuel for GOCE’s ion propulsion system. To get the most out of what was still a fully functional spacecraft designed to fly in a drag environment, ESA kept operating the mission as long as possible in the ensuing orbital decay phase. Exceeding all expectations, the S/C remained functional and contact could be maintained down to extreme altitudes of little over 100 km, less than 1.5 hours before re-entry. This allowed collecting a set of most valuable data prior to GOCE’s demise on 11 Nov 2013 close to the Falkland Islands. The paper presents the preparation and execution of this unique operations campaign.

A force model for the lunar albedo effect on low lunar orbiters is developed on the basis of Clementine imagery and absolute albedo measurements. The model, named the Delft Lunar Albedo Model 1 (DLAM-1), is a 15 × 15 spherical harmonics expansion, and is intended for improved force modeling for low satellite orbits as well as to minimise aliasing of non-gravitational force model defects in future lunar gravity solutions. The development of the model from the available lunar albedo data sources is described, followed by a discussion on its calibration using absolute albedo measurements and its correlation with main selenological features. DLAM-1 is next applied in low lunar orbit determination, and results for orbits typical of lunar mapping missions are presented. Finally, the effect of lunar albedo on future gravity solutions is analysed with particular emphasis on gravity mapping from global data sets, i.e. satellite-to-satellite tracking, which is expected to be a core experiment of coming lunar missions. It is shown that albedo-induced orbit perturbations have a magnitude and frequency signature which are non-negligible for precise orbit and gravity modeling. Radial orbit errors for low orbits are in the order of 1–2 m for one week arcs.

Till the present day the recovery of the lunar gravity field from satellite tracking data depends in a crucial way on the level and method of regularisation. With Earth-based tracking only, the spatial data coverage is limited to only slightly more than 50% and the inverse problem remains severely ill-posed. The development of global gravity models suitable for precise orbit modeling as well as geophysical studies therefore requires a significant level of regularisation, limiting the solution power over the far-side where no gravity information is available. Unconstrained solutions, within the framework of global harmonic base functions, are only possible for very low degrees (

After a descent phase of about half a year, the Gravity field and steady-state Ocean Circulation Explorer (GOCE) reached the final orbital altitude of the first measurement and operational phase (MOP-1) in September 2009. Due to this very low orbital altitude and the inactive drag compensation during descent, the generation of reliable predictions of the GOCE trajectory turned out to be a major challenge even for short prediction intervals. As predictions of good quality are a prerequisite for frequent ranging from the tracking network of the International Laser Ranging Service (ILRS), Satellite Laser Ranging (SLR) data of GOCE was very sparse at mission start and made it difficult to independently calibrate and optimize the orbit determination based on data of the Global Positioning System (GPS). In addition to the GOCE orbit predictions provided by the European Space Agency (ESA), the Astronomical Institute of the University of Bern (AIUB) started providing predictions on July 22, 2009, as part of the Level 1b to Level 2 data processing performed at AIUB. The predictions based on the 12-h ultra-rapid products of the International GNSS Service (IGS) were originally intended to primarily serve the daylight passes in the early evening hours over Europe. The corresponding along-track prediction errors were often kept below 50 m during the descent phase and allowed for the first successful SLR tracking of GOCE over Europe on July 29, 2009, by the Zimmerwald observatory. Additional predictions based on the IGS 18-h ultra-rapid products are provided by AIUB since September 20, 2009, to further optimize the GOCE SLR tracking. In this article, the development of the GOCE prediction service at AIUB is presented, and the quality of the orbit predictions is assessed for periods with and without active drag compensation. The prediction quality is discussed as a function of the prediction interval, the quality of the input products for the GPS satellite orbits and clocks, and the availability of the GOCE GPS data. From the methodological point of view, different approaches for the treatment of the non-gravitational accelerations acting on the GOCE satellite are discussed and their impact on the prediction quality is assessed, in particular during the descent phase. Eventually, an outlook is given on the significance of GOCE SLR tracking to identify systematic errors in the GPS-based orbit determination, e.g., cross-track errors induced by mismodeled GOCE GPS phase center variations (PCVs).

GOCE, ESA’s first Earth gravity mission, is currently to be launched early in 2009 into a sun-synchronous orbit. Using the full-scale numerical propagator, we investigated the satellite’s free fall from the initial injection altitude of 280 km down to the first measurement phase altitude (at 264 km). During this decay phase the satellite will pass below the 16:1 resonance (268.4 km). The effect of this resonance, together with the uncertainty in the solar activity prediction, has a distinct impact on the evolution of the orbital elements. Then, to maintain a near-constant and extremely low altitude for the measurement operational phases, the satellite will use an ion thruster to compensate for the atmospheric drag. In order to obtain the groundtrack grid dense enough for a proper sampling of the gravitational field, ESA set constraints for a minimum groundtrack repeat period. We studied suitable repeat cycles (resonant orbits) in the vicinity of 16:1 resonance; we found that they differ greatly in stability towards small perturbations of the satellite’s mean altitude and in temporal evolution of the groundtrack coverage. The results obtained from the usual analytical treatment of orbital resonances were refined by more realistic numerical simulations. Finally, we formulated suggestions that might be useful in GOCE orbit planning.

“What's up?” is a question that is answered by the gravity field. Gravity not only determines what is up and down but also reflects the Earth's mass distribution and its changes with time.

All present-day lunar gravity field models are — with the exception of a minor contribution from lunar laser ranging data to the second-degree harmonics — satellite-only models. Orbit analysis is therefore a fundamental tool for quality assessment, alongside arguments of compatibility imposed by selenophysics. A general problem in selenodesy and selenophysics is the lack of independent data to serve purposes of calibration and validation of basically any result. Model assessment techniques may therefore be quasi-circular and far from independent. Regarding the use of prior information from lunar physics, primarily the assumptions on coefficient amplitudes and the distribution of the selenopotential signal power over the degrees, the indicia of their correctness are for the larger part provided by the induced improvement in measurement fit of the satellite orbits. One prob-lem of satellite orbit and orbit error measures, on the other hand, is that they are “global” measures of the selenopotential quality, as opposed to a direct function of location on the lunar sphere, and that RMS-of-fit values over several-day satellite arcs actually contain very little spatial information on the intrinsic selenopotential model quality. Nevertheless, gravity field models capable of predicting reasonable mass anomaly structures and estimates of crustal thickness tend to be considered reliable. It should therefore be clear that it is only through continued iteration over the available data sets, along with improved modelling in several branches of selenoscience, that solid quality assessment and statistically significant quality improvement of lunar gravity field models may be achieved.