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The current practice for experimentally evaluating the performance of extraterrestrial rovers/rover wheels is to conduct tests on earth on a soil simulant, appropriate to the regolith on the extraterrestrial body of interest. In the tests, the normal load (force) applied by the rover/rover wheel to the soil simulant is set identical to that expected on the extraterrestrial surface, taking into account its acceleration due to gravity. It should be pointed out, however, that the soil simulant used in the tests is subject to earth gravity, while the regolith on the extraterrestrial surface is subject to a different gravity. Thus, it is uncertain whether the performance of the rover/rover wheel obtained from tests on earth represents that on the extraterrestrial surface. This issue has been explored previously. A method has been proposed for conducting tests of the rover/rover wheel on earth with identical mass to that on the extraterrestrial surface, instead of with identical normal load used in the current practice [1]. This paper provides further evidence to substantiate the merits of the proposed method, based on a detailed analysis of the test data obtained under various gravity conditions, produced in an aircraft undergoing parabolic flight manoeuvres [8]. In the study, the effect of slip on wheel sinkage has been evaluated. It is found that gravity has little effect on the slip and sinkage relationship of the rover wheel under self-propelled conditions.

The Chapter briefly illustrates the historical development of the concept of Figure of the Earth. The purpose is to arrive at a sharp definition of this concept to be used in the framework of the modern approach to the determination of the Earth gravity field via the solution of a Boundary Value Problem. The main formulation of the geodetic Boundary Value Problem (GBVP), known as Molodensky Problem, is also introduced in two versions, non-linear and linear.

International audience; Many if not most small asteroids are rubble piles covered by regolith, and small perturbations may be enough to disturb their surfaces in complex ways due to microgravity. Experiments to study low-gravity regolith dynamics are challenging, and properly validated numerical simulations can provide valuable insights. In this paper, we investigate numerically size segregation among regolith grains, which is likely to occur after repeated shaking events. In particular, we are interested in the so-called Brazil-nut effect (BNE), i.e. the migration of a large intruder towards the top of a vertically shaken granular system. We go a step forward in simulating this effect by implementing horizontal periodic boundary conditions (PBC) in the N-body code pkdgrav, with the aim of making the simulations more representative of the expected asteroid environment. We study the influence of PBC on the BNE in Earth gravity and compare them with a walled case. We also investigate the influence of static and rolling friction on the BNE. With walls, we observe the well-known convection mechanism driving the BNE. However, we find that a different mechanism, consisting of void filling, is responsible for the BNE with PBC, and we discuss its relevance in light of previous studies. By running simulations in 10−4g, we show that this void-filling mechanism remains relevant in a low-gravity environment. However, we find that depending on the gravity level, the void-filling mechanism is differently influenced by the friction properties of particles. We speculate that this is likely due to a change in the granular flow time-scales.

Ballistic trajectories are computed which would enable a sample return mission to Europa without capturing, descending, or landing. The low-cost mission concept utilizes a free return trajectory that also involves a close flyby of Europa. Near Europa, a small impactor would kinetically impact the icy moon and generate a plume, subsequently sampled by the spacecraft. A broad search algorithm is developed to construct feasible itineraries, which considers Venus and Earth gravity assist sequences. High-quality solutions are then differentially corrected to be continuous using high-fidelity dynamics. The complete methodology is applicable to other outer-planet moons, notably Enceladus. The outbound VEEGA option is found to signifcantly reduce launch C3 compared to alternate options. The characteristics and quality of the solutions exhibit substantial variation over the 12-year period of Jupiter. Nevertheless, a variety of optimized results are computed with C3 as low as 16.0 sq.km/sq.sec, re-entry speed well below that of the Stardust capsule, and flight times of 9 to 15 years.

Multichannel singular spectrum analysis (MSSA) is applied to the globally gridded oceanic angular momentum (OAM) data from ECCO (KF080) model, Atmospheric Angular Momentum from ECMWF model, and Earth gravity field from GRACE satellites. Principal components of the oceanic, atmospheric, and hydrological changes and their influence on the rotation of the Earth (polar motion PM and length of day LOD) are extracted. The regions where mass and motion terms make the largest input into PM excitation and LOD changes are identified. The trends, annual, and other global-scale modes are separated. Multichannel singular spectrum analysis is found to be a promising method for signal filtering and modes decomposition. Possible connections between climate change and Earth rotation are discussed.

Lack of understanding of flow boiling behavior in reduced gravity poses a major challenge to the development of future space vehicles utilizing two-phase thermal control systems (TCSs). A cost effective method to investigating the influence of reduced gravity on flow boiling is to perform ground experiments at different orientations relative to Earth gravity. This paper is the first part of a two-part study aimed at exploring flow boiling mechanisms of FC-72 in a rectangular channel heated along one wall or two opposite walls. Experiments are performed in vertical upflow, vertical downflow and horizontal flow, subject to large variations in mass velocity, inlet quality and wall heat flux. Detailed measurements are used to investigate the influences of orientation, and therefore gravity, on boiling curve, local and average heat transfer coefficients, and pressure drop, and their relationship with interfacial behavior is captured with high-speed video. For horizontal flow, the effects of gravity are reflected in appreciable stratification across the channel at low mass velocities, with gravity aiding vapor removal from, and liquid return to the bottom heated wall, while accumulating vapor along the top heated wall. For vertical upflow and vertical downflow, with both single-sided and double-sided heating, there is far better symmetry in vapor formation along the channel. The heat transfer coefficient shows significant variations among the different orientations and heating configurations at low mass velocities, but becomes insensitive to orientation above 800 kg/m2 s, proving inertia around this mass velocity is effective at negating any gravity effects. For low mass velocities, pressure drops are fairly equal for vertical upflow and vertical downflow, but greater than for horizontal flows. However, fairly equal pressure drops are achieved at high mass velocities for all orientations. Overall, this study proves that gravity effects on two-phase pressure drop and two-phase heat transfer are dictated mostly by mass velocity and, to a lesser extent, by inlet quality.

Global geopotential models (GGMs) provide important information about the Earth gravity field in terms of precise gravity anomaly, gravity disturbance, and geoid height on global and regional scales. The GGMs based on the Gravity Recovery and steady-state Ocean Circulation Explorer (GOCE) satellite gravity mission provided by the International Center for Global Earth Models (ICGEM) differ in their accuracy and spatial resolution. In this paper, we evaluate the free-air gravity anomalies and geoid heights determined from several recent GOCE-based GGMs using the corresponding gravity functions (i.e., gravity anomalies and geoid heights) obtained from the Earth Gravitational Model 2008 (EGM2008) over the Kingdom of Saudi Arabia (KSA). Moreover, free-air gravity anomalies determined from GOCE-based GGMs have also been compared with the corresponding ones obtained from ground-based “terrestrial” gravity measurements over the study area. The latter comparison, using the available 3500 terrestrial gravity observations, applies the spectral enhanced method (SEM). We use the SEM to compensate the missed high-frequency component of geoid heights in GOCE-based GGMs using EGM2008 and a high-resolution digital terrain model based on the Shuttle Radar Topography Mission (SRTM). The statistical comparisons of the computed results in terms of free-air gravity anomalies and geoid heights obtained from GOCE-based GGMs are in general agreement. The estimated standard deviations of differences are 5 mGal (20 cm), 6–7 mGal (22–24 cm), and 8 mGal (25.9 cm) at spherical harmonic (SH) degree/order (d/o) 200, 240, and 280, respectively. Free-air gravity anomalies computed from available terrestrial gravity data, using the SEM, have been compared with the corresponding ones estimated from GOCE-based GGMs, and the results indicate an improvement over EGM2008 in the medium wavelengths. Investigation of various releases of GOCE-based GGM, up to d/o 200, reveals that the fourth and fifth releases of GOCE-based GGMs developed with the use of time-wise solution strategies (TIM_R4 and TIM_R5) approximate the gravity field well over the KSA region, since they provide the least standard deviation differences at SH. Thus, the TIM_R5 and TIM_R4 are suggested as reference models for recovering the long wavelength up to SH d/o 200 and 240, respectively, when modeling the gravimetric quasi-geoid over the KSA area.

EIGEN-6c4 data is validated against ground survey data, allowing the generation of a new Bouguer anomalies map for Venezuela using formulas which take into account the Earth curvature. The improvement of the latest combined global gravity field model EIGEN-6c4 in Venezuela is compared with the 2008 Earth Gravity Model (EGM2008) using statistical analysis. The geological analysis has been focused on the Guiana shield, where the principal discrepancies of magnitude and trend between both models were noticed. The trend of the anomalies on Amazonas and Bolivar states reveals the orientation of the principal structures and provinces which match with geological formations of Guapore shield towards the south. The new improvements calculating this global model and new data from GOCE satellite mission, besides of five years of new ground and marine surveys data available that EGM2008 couldn’t take into account, make this actualized Bouguer anomalies map necessary for geosciences in Venezuela. The improved resolution of 1 km shall allow representing smaller geological bodies and doing approximations more suited to geological settings.

Gravity surveying is challenging in Antarctica because of its hostile environment and inaccessibility. Nevertheless, many ground-based, airborne, and shipborne gravity campaigns have been completed by the geophysical and geodetic communities since the 1980s. We present the first modern Antarctic-wide gravity data compilation derived from 13 million data points covering an area of 10 million km2, which corresponds to 73% coverage of the continent. The remove-compute-restore technique was applied for gridding, which facilitated leveling of the different gravity data sets with respect to an Earth gravity model derived from satellite data alone. The resulting free-air and Bouguer gravity anomaly grids of 10 km resolution are publicly available. These grids will enable new high-resolution combined Earth gravity models to be derived and represent a major step forward toward solving the geodetic polar data gap problem. They provide a new tool to investigate continental-scale lithospheric structure and geological evolution of Antarctica.

Empirical Mode Decomposition (EMD) is a decomposition algorithm which is used to analyze nonlinear and time-varying. Different from the traditional signal analysis method, the decomposition is data-driven and self-adaptive. EMD has been widely used in blind source separation and received attention because of its potential application in signal processing. EMD algorithm and its application in earth gravity tide signal are introduced. EMD is a potential method in the earth gravity tide signal. So we can extract useful information from it to understand earthquake precursors.

Since 2006 the gravity change at 17 points in Sweden has been observed with Lantmateriet’s absolute gravimeter FG5-233. The main purpose of the observations is to study the postglacial rebound in Fennoscandia. In 2010, a suspected jump of a few μGal can be seen in the gravity time series that significantly affects the estimated gravity rate of changes. It is shown that if the jump is not considered, then the absolute value of the gravity rate of change is systematically underestimated compared to the land uplift model NKG2014LU_test. In this paper two different ways to estimate and apply corrections of the jump are demonstrated. The first is to estimate the jump from the observations themselves within a least squares adjustment, while the second is to assume the instrument bias obtained in international comparisons of absolute gravimeters. The best agreement between land uplift model and estimated rates of change of gravity is achieved by correcting the data with the official biases reported from the international comparisons.

This paper describes implementation of an electronic compass and calibration method. Firstly describes used hardware and then focus on the method of sensor calibration parameters. The eCompass uses a three-axis accelerometer and three-axis magnetometer. The compass heading is a function of all three accelerometer readings and all three magnetometer readings. The accelerometer measures the components of the earth gravity and provide pitch and roll angle information which is used to correct the magnetometer data. The magnetometer measures the components of earth’s magnetic field (called geomagnetic field) to determine the heading angle to the magnetic north.

K-band ranging (KBR) system and GNSS receiver are the key payloads of the gravity exploration satellite which employs LEO satellite tracking LEO satellite technology. Ultra-stable crystal oscillator, providing precise inter-satellite distance measurement with clock frequency reference, is the key component of the KBR-GNSS system. Therefore, real-time and dynamic monitoring on-orbit ultra-stable oscillator (USO)’s frequency stability are very necessary. First of all, the analysis formula of DOWR with time-tag corrected is deduced based on the study of the KBR-GNSS measuring principle. Second, the coupling relationship between Allan variance formula and inter-satellite time difference is analyzed deeply. Two methods of inversing USO Allan variance are proposed, of which one is using inter-satellite time difference measurement and the other one is employing inter-satellite distance measurement. Finally, referring to GRACE satellite payload scheme, a set of KBR-GNSS system is developed, by using which, the effectiveness of the two algorithms is validated and their advantages and disadvantages are compared meanwhile. The research results of this paper have some references to the design of inter-satellite ranging system of Chinese first generation earth gravity exploration satellite.

The GRACE mission that was launched in 2002 has impressively proven the feasibility of low-orbit satellite-to-satellite tracking for Earth gravity observations. Especially mass transport related to Earth's hydrological system could be well resolved both spatially and temporally. This allows to study processes such as polar ice sheet decline and ground water depletion in great detail. Owing to GRACE's success, NASA and GFZ will launch the successor mission GRACE Follow-On in 2017. In addition to the microwave ranging system, GRACE Follow-On will be the first mission to use a Laser Ranging Interferometer as technology demonstrator to track intersatellite distance changes with unprecedented precision. This new ranging device inherits some of the technologies which have been developed for the future spaceborne gravitational wave detector LISA. I will present the architecture of the Laser Ranging Interferometer, point out similarities and differences to LISA, and conclude with the current status of the flight hardware production. DFG/QUEST BMBF/03F0654B

One of the challenges of field testing planetary rovers on Earth is the difference in gravity between the test and the intended operating conditions. This not only changes the weight exerted by the robot on the surface but also affects the behaviour of the granular surface itself, and unfortunatly no field test can fully address this shortcoming. This research introduces novel experimentation that for the first time subjects planetary excavator robots to gravity offload (a cable pulls up on the robot with 5/6 its weight, to simulate lunar gravity) while they dig. Excavating with gravity offload underestimates the detrimental effects of gravity on traction, but overestimates the detrimental effects on excavation resistance; though not ideal, this is a more balanced test than excavating in Earth gravity, which underestimates detrimental effects on both traction and resistance. Experiments demonstrate that continuous excavation (e.g. bucket-wheel) fares better than discrete excavation (e.g. front-loader) when subjected to gravity offload, and is better suited for planetary excavation. This key result is incorporated into the development of a novel planetary excavator prototype. Lessons learned from the prototype development also address ways to mitigate suspension lift-off for lightweight skid-steer robots, a problem encountered during mobility field testing.

Experimental studies have been carried out using the in-house developed propellant samples at the atmospheric conditions to examine the influence of propellant surface orientation / attitude on burn rate. A series of burning tests are conducted with different grain orientations, viz., vertical, inverted and horizontal. We have observed 5 % burn rate augmentation on end-burning grains when the burning surface evolution was against the earth gravity compared to the normal vertical candle burning condition. We conjectured that the coupled effects of the instantaneous variations of the propellant burning surface attitude and the flight acceleration during the mission could alter the flame structure due to the local gravitational influence, which in turn alter the burn rate. This paper throws light for developing a suitable gravitational force dependant burn rate model for improving the performance prediction of solid rocket motors for aerospace applications.

This paper deals with the geopotential approach to investigate the present Brazilian Height System (BHS). Geopotential numbers are derived from Global Positioning System (GPS) satellite surveying and disturbing potential on selected benchmarks. A model for the disturbing potential can be obtained by an existing set of spherical harmonic coefficients such as the Earth Gravity Model 2008 (EGM08). The approach provides absolute evaluation of local normal geopotential numbers (aka spheropotential numbers) related to a so-called World Height System (WHS). To test the validity of the proposed methodology, a numerical experiment was carried out related to a test region in Southern Brazil. The accuracy of the derived geopotential numbers was tested versus local normal geopotential numbers based on 262 GPS/leveling points. The root mean square error (RMSE) value for metric offset of BHS derived from geopotential numbers and the disturbing potential modeling in the test area was estimated to be near 0.224 meters in the absolute view. Therefore, since these spheropotential numbers are referred to a local datum, these results of comparisons may be an indicator of the mean bias of local network due to the effect of local Sea Surface Topography (SSTop) and possible offset between the unknown reference for the BHS and the quasigeoid model in the region. Este trabalho apresenta uma investigação realizada a respeito da Rede Altimétrica Fundamental do Brasil (RAFB) com base em posicionamento GPS (Global Positioning System) e determinação do distúrbio do potencial sobre referências de nível. Um modelo para o distúrbio do potencial pode ser obtido com base nos coeficientes do desenvolvimento em séries de funções harmônicas esféricas do potencial gravitacional como os do Earth Gravity Model 2008 (EGM08) por exemplo. A abordagem provê a base para avaliação absoluta de números geopotenciais normais (ou números esferopotencias) locais relativamente a um Sistema Global de Altitudes (SGA). Para verificar a validade desta metodologia proposta um experimento numérico foi desenvolvido em relação a uma área teste no sul do Brasil. As acurácias dos números geopotenciais obtidos foram testadas em relação a números geopotenciais normais com base em 262 pontos GPS sobre a rede de nivelamento. O valor do erro médio quadrático (EMQ) em termos de um desvio métrico absoluto do Sistema Altimétrico Brasileiro (SAB) obtido a partir dos números geopotenciais e do distúrbio do potencial na área teste foi estimado em cerca de 0,224 metros. Uma vez que os números esferopotenciais são referidos ao datum local, os resultados das comparações efetivadas podem ser um indicador do desvio da rede local em vista da topografia do nível médio do mar (TNMM) e a possível inconsistência entre a origem do SAB e o modelo do quase-geóide para a região.

The low-altitude effects of LARES are examined to determined how they can impact the outcome of the hoped 1% frame-dragging measurement in the LARES–LAGEOS experiment. This analysis, based on a different approach than other studies recently appearing in the literature, shows that the spherical harmonics of the Earth gravity field with degree ℓ > 60 may represent a threat because their errors map significantly into LARES orbital disturbances compared to frame-dragging. The GIF48 model was used. It is questionable whether future Earth gravity models by GRACE and GOCE will be of sufficient accuracy.

Analysis is given of a relatively new method for studying the distribution and dynamics of land water resources, which is based on measuring the anomalies of Earth gravity field with the use of GRACE satellite system. The international satellite experiment on determining the gravity and climate changes has been carried out since 2002 with the aim of making high-frequency (within the frequency range of 10900–36000 GHz) measurements of time variations in Earth’s gravity field. The measurement method and the procedure of data processing and evaluating the hydrological-geohydrological characteristics of large river basins and regions based on GRACE data.

Formulas are given for calculating corrections to the acceleration of gravity which eliminate the effect of variations in the parameters of the earth’s surface layer.

The aim of this study was to evaluate the uplift capacity of buried pipes to propose a new anchoring system using geogrids as an alternative and to improve the uplift resistance and inhibit the upward movement of pipes, which can compromise pipeline operation. The simulation was performed in a general scale model of 1/10 using the geotechnical centrifuge of the State University of Norte Fluminense (UENF) at 10 times earth gravity acceleration to keep the similitude between the prototype and the model. The tests were carried out for two different sand densities, two geogrid widths, and three burial depths. The geogrid was manufactured in a laboratory to mimic the behavior of a real-scale geogrid when subjected to upward displacements. Therefore, an amount of 24 pullout tests were conducted in small-scale models at 10 g. A pipe of outer diameter D was anchored to a geogrid with a width of 2D in six tests and to a geogrid with a width of 3D in six other tests. No anchoring system was used in 12 tests...

The Inner Formation Flying System (IFFS) consisting of an outer satellite and an inner satellite which is a sphere proof mass freely flying in the shield cavity can construct a pure gravity orbit to precisely detect the earth gravity field. The residual gas in the cavity is a significant disturbance source due to the temperature in-homogeneity and relative motion of the inner satellite. The expressions of the disturbance forces were derived based on the property of rarefied gas, including the radiometer effect and the damping force. According to the current design of IFFS, heat transfer analysis of the cavity and the inner satellite was carried out, and the surface temperature distribution of the cavity and the inner satellite was given. The relative motion of the inner satellite was obtained from the formation control simulation of IFFS. Then the residual gas disturbance was calculated. The disturbance acceleration acting on the inner satellite due to the radiometer effect was on the order of 10−11 m s−2 and the damping acceleration was on the order of 10−15 m s−2.

For almost 10 years, the Gravity Recovery and Climate Experiment (GRACE) has provided information about the Earth gravity field with unprecedented accuracy. Efforts are ongoing to approach the GRACE baseline accuracy as there still remains an order of magnitude between the present error level of the gravity field solutions and the GRACE baseline. At the current level of accuracy, thorough investigation of sensor related effects is necessary as they are one of the potential contributors to the error budget. In the science mode operations, the twin satellites are kept precisely pointed with their KBR antennas towards each other. It is the task of the onboard attitude and orbit control system (AOCS) to keep the satellites in the required formation. We analyzed long time series of the inter-satellite pointing variations as they reflect the AOCS performance and characteristics. We present significant systematic effects in the inter-satellite pointing and discuss their possible sources. Prominent features are especially related to the magnetic torquer characteristics, star cameras’ performance and KBR antenna calibration parameters. The relation between the magnetic torquer attitude control and the Earth magnetic field, impact of the different performance of the two star camera heads on the attitude control and the features due to uncertainties in the calibration parameters relating the star camera frame to K-frame are discussed in detail. Proper understanding of these effects will help to reduce their impact on the science data and subsequently increase the accuracy of the gravity field solutions. Moreover, understanding the complexity of the onboard system is essential not only for increasing the accuracy of the GRACE data but also for the development of the future gravity field satellite missions.

SUMMARY Gravity rate of change is an important quantity in the investigation of glacial isostatic adjustment (GIA). However, measurements with absolute and relative gravimeters are laborious and time-consuming, especially in the vast GIA-affected regions of high latitudes with insufficient infrastructure. Results of the Gravity Recovery And Climate Experiment (GRACE) satellite mission have thus provided tremendous new insight as they fully cover those areas. To better constrain the GIA model (i.e. improve the glaciation history and Earth parameters) with new gravity data, we analyse the currently determined errors in gravity rate of change from absolute gravity (AG) and GRACE measurements in North America and Fennoscandia to test their sensitivity for different ice models, lithospheric thickness, background viscosity and lateral mantle viscosity variations. We provide detailed sensitivity maps for these four parameters and highlight areas that need more AG measurements to further improve our understanding of GIA. The best detectable parameter with both methods in both regions is the sensitivity to ice model changes, which covers large areas in the sensitivity maps. Also, most of these areas are isolated from sensitive areas of the other three parameters. The latter mainly overlap with ice model sensitivity and each other. Regarding existing AG stations, more stations are strongly needed in northwestern and Arctic Canada. In contrast, a quite dense network of stations already exists in Fennoscandia. With an extension to a few sites in northwestern Russia, a complete station network is provided to study the GIA parameters. The data of dense networks would yield a comprehensive picture of gravity change, which can be further used for studies of the Earth’s interior and geodynamic processes.

SUMMARY Global gravity field models, derived from satellite measurements integrated with terrestrial observations, provide a model of the Earth's gravity field with high spatial resolution and accuracy. The Earth Gravity Model EGM08, a spherical harmonic expansion of the geopotential up to degree and order 2159, has been used to calculate two functionals of the geopotential: the gravity anomaly and the vertical gravity gradient applied to the South Central Andes area. The satellite-only field of the highest resolution has been developed with the observations of satellite GOCE, up to degree and order 250. The topographic effect, a fundamental quantity for the downward continuation and validation of satellite gravity gradiometry data, was calculated from a digital elevation model which was converted into a set of tesseroids. This data is used to calculate the anomalous potential and vertical gravity gradient. In the Southern Central Andes region the geological structures are very complex, but not well resolved. The processing and interpreting of the gravity anomaly and vertical gradients allow the comparison with geological maps and known tectonic structures. Using this as a basis, a few features can be clearly depicted as the contact between Pacific oceanic crust and the Andean fold and thrust belt, the seamount chains over the Oceanic Nazca Plate, and the Famatinian and Pampean Ranges. Moreover the contact between the Rio de la Plata craton and the Pampia Terrain is of great interest, since it represents a boundary that has not been clearly defined until now. Another great lineament, the Valle Fertil-Desaguadero mega-lineament, an expression of the contact between Cuyania and Pampia terranes, can also be clearly depicted. The authors attempt to demonstrate that the new gravity fields can be used for identifying geological features, and therefore serve as useful innovative tools in geophysical exploration.

Inner-Formation Gravity Measurement Satellite System (IFGMSS) is used to explore the Earth gravity using two satellites in an inner-formation flying mode. To fulfill the mission, relative position of the two satellites is required to be zeroed and attitude of the outer satellite should be stabilized in real-time. This paper proposed an integrated control scheme for the IFGMSS, and the main idea is to use only thrusters to control the relative position and attitude. The integrated control loop contains a control law's module and a control allocation law's module. The control law based on the feedback linearization method makes nonlinear dynamics counteracted and uses PD control law to reformulate the dynamics into a linear form. The integrated control allocation law is designed to assign the commanded control force and moment to each thruster dynamically. We transfer the control allocation problem into a linear programming (LP) problem and use the Optimal Theory to calculate the corresponding thrust of each thruster. Finally, an IFGMSS mission is simulated, where the two satellites fly in a circle orbit with a 300 km's altitude. Results using the integrated control scheme and the traditional separated control scheme are compared and analyzed. It has been found that the integrated control scheme is superior to the separated control scheme in output ability, level of redundancy and fuel cost.

The direct earth horizon and starlight observation with earth sensor and star sensor is often used in the satellite autonomous orbit determination, which is a stable autonomous navigation method but with some defects that need to be improved. On the one hand, both the orbit state equation and measure equation are nonlinear, in which only the 2nd zonal harmonic of the non-spherical earth gravity is introduced while the other perturbation terms are regarded as white noise, which in fact all these terms have certain models themselves that are usually non-Gaussian distribution. In this case, Unscented Particle Filter (UPF) is present to be used for the satellite autonomous orbit determination; On the other hand, the error of earth sensor is a vital problem for the precision of satellite-earth center distance determination, which will damage the observation of orbit information. In this paper, the UPF uses the Unscented Kalman Filter (UKF) to generate sophisticated proposal distributions. It can not only avoid the limitation of the UKF which only apply to Gaussian distributions but also avoid the limitation of the standard PF which can not include the new measurements. The other improvement to the autonomous orbit determination method is embedding a earth correction based on star sensor measurement into the UPF observation step, which enhances the final orbit determination precision a lot. The simulation results show that the presented method has higher accuracy and more stable characteristic than the standard PF and UKF, especially when the earth correction is absent.

Inner-Formation Gravity Measurement Satellite System (IFGMSS) is used to map the gravity field of Earth. The IFGMSS consists of two satellites in which one is called “inner satellite” and the other one is named as “outer satellite”. To measure the pure Earth gravity, the inner satellite is located in the cavity of the outer satellite. Because of the shield effect of the cavity, the inner satellite is affected only by the gravitational force, so it can sense Earth gravity precisely. To avoid the collision between the inner satellite and the outer satellite, it is best to perform a real-time control on the outer satellite. In orbit, the mass of the outer satellite decreases with the consumption of its propellant. The orbit angular rate of the inner satellite varies with time due to various disturbing forces. These two parameters’ uncertainties make the C–W function be not so accurate to describe the formation behavior of these two satellites. Furthermore, the thrusters also have some uncertainties due to the unmodelled dynamics. To cancel the effects caused by the above uncertainties, we have studied the robust control method based on the μ -synthesis. This μ -synthesis eliminates the conservativeness and improves the control efficiency comparing with the H ∞ method. Finally, to test the control method, we simulate an IFGMSS mission in which the satellite runs in a sun synchronous circular orbit with an altitude of 300 km. The simulation results show the effectiveness of the robust control method. The performances of the closed-loop system with the μ -controller are tested by the μ -analysis. It has found that the nominal performance, the robust stability and the robust performance are all achieved. The transient simulation results further prove the control response is fast and the accuracy of the relative position meets the demand of the gravity measurement.

The first results are presented of ESA MAXUS 8 sounding rocket benchmark experiment on γ-TiAl (Nb,B) intermetallics solidification, that was a part of the IMPRESS EU FP6 project. Having the aim to investigate the columnar and equiaxed primary microstructures formation at diffusion controlled melt growth, an experiment was designed applying the power-down directional solidification technique with fixing quench in automatic spaceborne furnace module TEM03-5M. Two related alloys were tested: one inoculated with boron grain refiner Ti-44Al-7.5Nb-2.7B (at.%); and the other Ti-45.5Al-8Nb (at.%) without grain refinement. The series of terrestrial reference processes has been performed accordingly in counter-gravity solidification direction. The numerical studies of heat-mass transfer, melt hydrodynamics and temporal solidification dynamics of these alloys have been implemented under the earth-and zero-gravity approximations using the GIGAN software package (IPPE). The comparison is performed of numerical model findings with the real microstructure and composition of samples, whose analyses were carried out by backscattered scanning electron microscopy (SEM) and X-ray microprobe (EDX) techniques. The convection-induced peritectic macrosegregation effect appearance and development in ground-based reference ingots is analytically observed and numerically studied. The achieved microstructure formation in space benchmarks is discussed.

The Earth’s gravity field is related to the topographic potential in medium and higher degrees, which is isostatically compensated. Hence, the topographic-isostatic (TI) data are indispensable for extending an available Earth Gravitational Model (EGM) to higher degrees. Here we use TI harmonic coefficients to construct a Synthetic Earth Gravitational Model (SEGM) to extend the EGMs to higher degrees. To achieve a high-quality SEGM, a global geopotential model (EGM96) is used to describe the low degrees, whereas the medium and high degrees are obtained from the TI or topographic potential. This study differes from others in that it uses a new gravimetric-isostatic model for determining the TI potential. We test different alternatives based on TI or only topographic data to determine the SEGM. Although the topography is isostatically compensated only to about degree 40–60, our study shows that using a compensation model improves the SEGM in comparison with using only topographic data for higher degree harmonics. This is because the TI data better adjust the applied Butterworth filter, which bridges the known EGM and the new high-degree potential field than the topographic data alone.

The HY-2 satellite carrying a satellite-borne GPS receiver is the first Chinese radar altimeter satellite, whose radial orbit determination precision must reach the centimeter level. Now HY-2 is in the test phase so that the observations are not openly released. In order to study the precise orbit determination precision and procedure for HY-2 based on the satellite-borne GPS technique, the satellite-borne GPS data are simulated in this paper. The HY-2 satellite-borne GPS antenna can receive at least seven GPS satellites each epoch, which can validate the GPS receiver and antenna design. What’s more, the precise orbit determination processing flow is given and precise orbit determination experiments are conducted using the HY-2-borne GPS data with both the reduced-dynamic method and the kinematic geometry method. With the 1 and 3 mm phase data random errors, the radial orbit determination precision can achieve the centimeter level using these two methods and the kinematic orbit accuracy is slightly lower than that of the reduced-dynamic orbit. The earth gravity field model is an important factor which seriously affects the precise orbit determination of altimeter satellites. The reduced-dynamic orbit determination experiments are made with different earth gravity field models, such as EIGEN2, EGM96, TEG4, and GEMT3. Using a large number of high precision satellite-borne GPS data, the HY-2 precise orbit determination can reach the centimeter level with commonly used earth gravity field models up to above 50 degrees and orders.

With a growing number of nations interested in planetary exploration, research and development of extraterrestrial rovers have been intensified. The usual practice is to test the performances of rovers on soil simulants on earth, prior to their deployment to extraterrestrial bodies. It is noted that in the tests the soil simulant is subject to the earth gravity, while the terrain on the extraterrestrial surface is subject to a different gravity. Therefore, it is uncertain whether the rover/rover wheel would exhibit the same performance on the extraterrestrial surface as that obtained from tests conducted on earth. This paper describes a practical methodology that can be employed to predict the performances of rover wheels on extraterrestrial surfaces, based on test results obtained on earth. As rigid wheels are used in many extraterrestrial rovers, this study focuses on examining the effects of gravity on the sinkage and compaction resistance of rigid rover wheels. Predictions obtained using the methodology are shown to correlate reasonably well with test data

On the basis of Space-Wise Least Square method, three numerical methods including Cholesky decomposition, pre-conditioned conjugate gradient and Open Multi-Processing parallel algorithm are applied into the determination of gravity field with satellite gravity gradiometry data. The results show that, Cholesky decomposition method has been unable to meet the requirements of computation efficiency when the computer hardware is limited. Pre-conditioned conjugate gradient method can improve the computation efficiency of huge matrix inversion, but it also brings a certain loss of precision. The application of Open Multi-Processing parallel algorithm could achieve a good compromise between accuracy and computation efficiency. Key words: satellite gravity gradiometry; Cholesky decomposition; pre-conditioned conjugate gradient; open multi-processing parallel algorithm; data processing

Downward continuation is one of the vital steps in pre-processing of satellite gravity gradient (SGG) data when recovering the earth gravity field by space-wise method. Mathematic downward continuation model of the SGG data based on Poisson integral iteration method was constructed, of which the downward continuation effects based on ‘Direct’ and ‘Remove-Restore’ schemes were analyzed and discussed with simulated SGG data. Results show that the precision of ‘Remove- Restore’ scheme is better than that of the ‘Direct’ scheme at the height of both 5 kilometers and 250 kilometers, i.e., the ‘Remove- Restore’ technique could improve the precision of downward continuation results based on Poisson integral iteration method in a certain degree.

New studies on the influence of inter-satellite range on the accuracy of the Earth's gravitational field recovery were carried out based on the Inter-satellite Range Interpolation Method (IRIM). Firstly, the IRIM observation equation by introducing the precise inter-satellite range into the Line-Of-Sight (LOS) component of the relative orbital position vector was established for the first time using the original satellite observations including the orbital position of the spaceborne Global Positioning System (GPS) receiver, the inter-satellite range of the K-Band Ranging (KBR) system and the non-conservative force of the accelerometer (ACC). Secondly, the nine-point IRIM formula is shown by a comparison of multipoint IRIM formulas to be preferable for effectively improving the accuracy of the Earth's gravitational field recovery. Thirdly, the WHIGG-GEGM01S (GRACE Earth Gravity Model developed by Wuhan Institute of Geodesy and Geophysics) global gravity field model, complete up to degree and order 120, is produced using the GRACE Level-1B data products, acquired during 2008-01-01 to 2008-12-31 and released by the American Jet Propulsion Laboratory (JPL). Cumulative geoid height and gravity anomaly errors are 1.098 × 10−1 m and 1.741 × 10−6 m/s2 at degree 120, respectively. Finally, the availability of the WHIGG-GEGM01S model is validated by the GPS/Levelling observations in the U.S., Europe and Australia.

Several previous Synthetic Earth Gravity Model (SEGM) simulations are based on existing information about the Earth’s internal mass distribution. However, currently available information is insufficient to model the Earth’s anomalous gravity field on a global scale. The low-frequency information is missing when modelling only topography, bathymetry and crust (including the Mohorovicic discontinuity), but the inclusion of information on the mantle and core does not seem to significantly improve this situation. This paper presents a method to determine a more realistic SEGM by considering simulated 3D mass distributions within the upper mantle as a proxy for all unmodelled masses within the Earth. The aim is to improve an initial SEGM based on forward gravity modelling of the topography, bathymetry and crust such that the missing low-frequency information is now included. The simulated 3D mass distribution has been derived through an interactive and iterative mass model optimisation algorithm, which minimises geoid height differences with respect to a degree-360 spherical harmonic expansion of the EGM2008 global external gravity field model. We present the developed optimisation algorithm by applying it to the development of a global SEGM that gives a reasonably close fit to EGM2008, and certainly closer than a SEGM based only on the topography, bathymetry and crust.

Gravity data are sensitive to local vertical offsets across high-angle faults, where rocks with different densities are juxtaposed. Yet high densities in some Mesozoic sedimentary rocks just above the basement may smear out the subtle gravity signatures of basement faults. At this study the gravity data processing tends to avoid ill-described “black-box” techniques. The study area is situated in the Palomas site, Cuatrocienegas region, Coahuila, NE Mexico. The San Marcos Fault is at least 300 km long and has WNW-ESE trend from the central part of Nuevo Leon State through Coahuila, and finally to the eastern part of Chihuahua State. Gravimetric data shows that the lowest values of free air and Bouguer anomalies are in the southern part of the area, and the highest values are in the western and central part of the area. Between these parts exists a zone of high horizontal gravity gradient. Configuration of linear elements of gravity field (gradient zones) delimited the San Marcos Fault in the San Marcos valley below thickness of recent sedimentary cover. Two density models were carried out, which showed that the Cretaceous rocks are in discordant contact with the Paleo- zoic rocks that can be related to the San Marcos Fault. The density was determinate using to Nettleton’s method, which results highlight the presence of the San Marcos Fault. Density models showed that the Quaternary sediments are in direct contact with the San Marcos Fault.

The aim of the present paper is to describe the results of flow boiling heat transfer at low gravity and compare them with those obtained at earth gravity, evaluating possible differences. The experimental campaigns at low gravity have been performed with parabolic flights. The paper will show the analysis of differences between the heat transfer coefficients at normal and at zero gravity, and the study of the effects of mass flux, heat flux, and tube diameter on boiling phenomena at microgravity. Three tube diameters are tested: 6.0, 4.0, and 2.0 mm. With respect to terrestrial gravity, both heat transfer rate enhancement (up to 15–20%) and deterioration (up to 35%) have been observed. Heat transfer differences for the two gravity conditions may be related to the different bubble size in each of them. The size of a bubble in flow boiling is generally affected by the gravity level, being larger at low gravity, unless inertial forces are largely predominant over buoyancy and other forces acting on the bubble itself when detaching from a heating wall. Heat transfer enhancements at low gravity, are observed in those conditions where the flow pattern is bubbly flow at normal gravity and intermittent flow at low gravity. The results are presented in a flow boiling gravity influence map, which can be considered a useful tool for designing boiling systems for space applications.

Considerable improvements in the measurement of the Earth gravity field from GOCE satellite mission have provided global gravity field models with homogeneous coverage, high precision and good spatial resolution. In particular, the vertical gravity gradient (Tzz), in comparison to the classic Bouguer anomaly, defines more accurately superficial mass heterogeneities. Moreover, the correction of these satellitederived data from the effect of Earth topographic masses by means of new techniques taking into account the Earth curvature, improves results in regional analyses. In a recent work we found a correlation between Tzz and slip distribution for the 2010 Maule Mw ¼ 8.8 earthquake. In the present work, we derive the vertical gravity gradient from the last GOCE only model, corrected by the topographic effect and also by the sediments on depocenters of the offshore region at the PerueChile margin, in order to study a spatial relationship between different lobes of the gravity derived signal and the seismic sources of large megathrust earthquakes. In particular, we analyze this relation for the slip models of the 1996 Mw ¼ 7.7 Nazca, 2001 Mw ¼ 8.4 Arequipa, 2007 Mw ¼ 8.0 Pisco events and for the slip models of the 2014 Mw ¼ 8.2 Pisagua and Mw ¼ 7.7 Iquique earthquakes from Schurr et al. (2014), including the previously analyzed 2010 Mw ¼ 8.8 Maule event. Then we find a good correlation between vertical gravity gradients and main rupture zones, correlation that becomes even stronger as the event magnitude increases. Besides this, a gravity fall in the gravity gradient was noticed over the area of the main slip patches at least for the two years before 2014 Mw ¼ 8.2 Pisagua and Mw ¼ 7.7 Iquique earthquakes. Additionally, we found temporal variations of the gravity field after 2010 Mw ¼ 8.8 Maule event, related to the main patches of the slip distribution, and coseismic deformation. Therefore, we analyzed vertical gravity gradient field variations as an indirect measure of the variable seismic coupling finding a potential relationship between Tzz and the seismic b-value. These relationships exemplify the strong potential of the satellite only derived models as a predictive tool to determine potential seismic energy released in a subduction segment, determining the potential size of a potential rupture zone, and in particular internal slip distribution that allows inferring coseismic displacement field at surface. Fil: Alvarez Pontoriero, Orlando. Universidad Nacional de San Juan. Facultad de Ciencias Exactas, Fisicas y Naturales. Instituto Geofisico Sismologico Volponi; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Nacif Suvire, Silvina Valeria. Universidad Nacional de San Juan. Facultad de Ciencias Exactas, Fisicas y Naturales. Instituto Geofisico Sismologico Volponi; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Spagnotto, Silvana Liz. Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Folguera Telichevsky, Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Estudios Andinos "Don Pablo Groeber". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Estudios Andinos ; Argentina Fil: Gimenez, Mario Ernesto. Universidad Nacional de San Juan. Facultad de Ciencias Exactas, Fisicas y Naturales. Instituto Geofisico Sismologico Volponi; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Chlieh, Mohamed. Observatoire de la Cote D'Azur; Francia Fil: Braitenberg, Carla. Universita Degli Studi Di Trieste; Italia

The estimation of the zero-height geopotential level of a local vertical datum (LVD) is a key task towards the connection of isolated physical height frames and their unification into a common vertical reference system. Such an estimate resolves, in principle, the ‘ambiguity’ of a traditional crust-fixed LVD by linking it with a particular equipotential surface of Earth’s gravity field under the presence of an external geopotential model. The aim of this paper is to study the estimation scheme that can be followed for solving the aforementioned problem based on the joint inversion of co-located GPS and leveling heights in conjunction with a fixed Earth gravity field model. Several case studies with real data are also presented that provide, for the first time, precise estimates of the LVD offsets for a number of Hellenic islands across the Aegean and Ionian Sea.

Continuous tracking of geodetic satellites using the Satellite Laser Ranging technique has provided unprecedented opportunity in long- to medium-wavelength gravity field modelling. Numerous gravity field models have been derived from such observations and have been made freely available to the science community for research purpose. The accuracy of most of the latest gravity field models in terms of precise orbit determination is currently at cm level. Improvement in the Earth gravity field modelling is anticipated as quantitative and qualitative data (in particular from low earth orbit satellites) become available in the future. Such expectations require that the accuracy and precision of existing gravity field models be assessed. The validation of gravity field models in terms of satellite orbit determination is often based on the difference between the observed and computed range. The resulting range residuals are considered an important index when determining the accuracy of the gravity models and hence the satellite orbits. In this contribution we investigate the general improvement in gravity field modelling over a period of 15 years. The orbit accuracy of twelve gravity field models (both satellite-only and combined models) were assessed by analysing seven months of data from LAGEOS 1 and 2 using HartRAO analysis software. Results show that the gravity field models developed over the years have improved by at least a factor of 2 since 1990, considering improvement in O-C residuals.

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.

SUMMARY In areas dominated by Glacial Isostatic Adjustment (GIA), the free-air gravity anomaly rate can be converted to uplift rate to good approximation by using a simple spectral relation. We provide quantitative comparisons between gravity rates derived from monthly gravity field solutions (GFZ Potsdam, CSR Texas, IGG Bonn) from the Gravity Recovery and Climate Experiment (GRACE) satellite mission with uplift rates measured by GPS in these areas. The band-limited gravity data from the GRACE satellite mission can be brought to very good agreement with the point data from GPS by using scaling factors derived from a GIA model (the root-mean-square of differences is 0.55 mm yr –1 for a maximum uplift rate signal of 10 mm yr –1 ). The root-mean-square of the differences between GRACE derived uplift rates and GPS derived uplift rates decreases with increasing GRACE time period to a level below the uncertainty that is expected from GRACE observations, GPS measurements and the conversion from gravity rate to uplift rate. With the current length of time-series (more than 8 yr) applying filters and a hydrology correction to the GRACE data does not reduce the root-mean-square of differences significantly. The smallest root-mean-square was obtained with the GFZ solution in Fennoscandia and with the CSR solution in North America. With radial gravity rates in excellent agreement with GPS uplift rates, more information on the GIA process can be extracted from GRACE gravity field solutions in the form of tangential gravity rates, which are equivalent to a rate of change in the deflection of the vertical scaled by the magnitude of gravity rate vector. Tangential gravity rates derived from GRACE point towards the centre of the previously glaciated area, and are largest in a location close to the centre of the former ice sheet. Forward modelling showed that present day tangential gravity rates have maximum sensitivity between the centre and edge of the former ice sheet, while radial gravity rates are most sensitive in the centre of the former ice sheet. As a result, tangential gravity rates offer constraints on a two-layer mantle viscosity profile that are different from radial gravity rates, which can be exploited in future GIA studies.

The Earth’s gravity field modelling is an ill-posed problem having a sensitive solution to the error of data. Satellite gravity gradiometry (SGG) is a space technique to measure the second-order derivatives of geopotential for modelling this field, but the measurements should be validated prior to use. The existing terrestrial gravity anomalies and Earth gravity models can be used for this purpose. In this paper, the second-order vertical–horizontal (VH) and horizontal–horizontal (HH) derivatives of the extended Stokes formula in the local north-oriented frame are modified using biased, unbiased and optimum types of least-squares modification. These modified integral estimators are used to generate the VH and HH gradients at 250 km level for validation purpose of the SGG data. It is shown that, unlike the integral estimator for generating the second-order radial derivative of geopotential, the system of equations from which the modification parameters are obtained is unstable for all types of modification, with large cap size and high degree, and regularization is strongly required for solving the system. Numerical studies in Fennoscandia show that the SGG data can be estimated with an accuracy of 1 mE using an integral estimator modified by a biased type least-squares modification. In this case an integration cap size of 2.5° and a degree of modification of 100 for integrating 30′ × 30′ gravity anomalies are required.

Marine gravity aided INS navigation, in which Gravity anomaly and gravity gradient of earth gravity field from sensors sensitive to gravity have been supplementary information aided to correct positioning error accumulated with time to achieve precise navigation and graphic trace, has been a fervent and frontier issue in underwater passive navigation technology in application to Autonomous Underwater Vehicle (AUV). Core theoretical technology of gravity aided INS navigation was matching algorithm, in which Terrain Contour Matching (TERCOM), Sandia Inertial Terrain Aided Navigation (SITAN) and Iterative Closest Contour Point (ICCP) were three typical representatives based on gravity reference map. However, these algorithms more or less had some limitations in certain conditions such as a relatively larger INS positioning error. Aiming at the application limitation that positioning error from INS were commonly large when after a long voyage AUVs entered into the region in which gravity could be used to matching, above three algorithms were integrated to use on base of expounding their algorithm models, computation progress and advantages and disadvantages analysis, then integration theory, algorithm design and model foundation were presented to meet practice application demand better.

The formation control of a long-distance, drag-free, low-thrust, low-Earth orbit satellite is outlined, in view of future Earth-gravity monitoring missions employing long baseline interferometry (>10 km) and lasting at least six years. To this purpose, a formation consisting of two drag-free satellites, orbiting at a fixed distance in a sun-synchronous orbit, has been proposed. Formation fluctuations are bounded by a 500×50×50 m3 wide (along-track, cross-track and radial) box. Although at first not seemingly demanding, the formation control induces non-gravitational accelerations, that are obliged to respect tight drag-free requirements, and are constrained by millinewton thrust bounds so as to curtail electric thruster throttability. In addition, formation fluctuations due to tide forces should not be impaired as their measurement is the mission goal. Requirements are formulated as a set of four time and frequency-domain inequalities, which are suitably parameterized by control gains. By exploiting the properties and asymptotic approximations of close-loop Hill's equation, explicit design inequalities are obtained leading to a first-trial control design. Simulated runs through fine spacecraft and low-Earth-orbit simulation, which is dominated by a highly variable thermosphere drag, show that the first-trial design meets the tight control requirements, and demonstrates mission feasibility.

The adhesion and the compressibility of the soft soil will vary as the earth gravity changes. In this study, the pressure-sinkage characteristics in low gravity conditions were investigated by three-dimensional Discrete Element Method (DEM). The data of the DEM parameters were obtained by analyzing the pressure-sinkage relationship embedded in laboratory testing data. The pressure-sinkage experiments of the sample soil in different gravities were simulated by using the software PFC3D. Using the Bekker formula, the values of pressure-sinkage parameters were obtained. The results show that, when the earth gravity changes from one sixth of the standard earth gravity to the standard earth gravity, the sinkage exponent increases lineally. The cohesive module of deformation increases along the conic trend. The low gravities have a sensitive affect on the data of the frictional module of deformation, and the data distribute beside a line. The change laws of the pressure-sinkage parameters provide instructions for the optimization design of vehicles working in low gravity field planet.

Based on satellite dynamics, 1 year’s CHAMP geometric precise orbit data are used in this paper to fit the satellite orbits by Cowell II numerical integral and partitioned Bayesian least square parameter estimation. Time series of low degree geopotential coefficients and are respectively calculated, which reflects obviously seasonal variations of and . The results / month, /month indicate the geodynamical shape of the earth is getting rounder and rounder and at the same time its pear-shaped component adds gradually.

In this paper, the spatial gravity distribution over Tibetan Plateau and the gravity rate of change at Lhasa for different Gaussian filter radii are computed using GRACE data. Results show that the estimate of the gravity rate of change is spatialradius-dependent of the Gaussian filter. The GRACE-estimated gravity rate of change agrees well with the surface measured one. In other words, the GRACE-estimated gravity rate of change has a limited value as that obtained by surface measurement when the spatial filter radius reaches zero. Then numerical simulations are made for different spatial radii of the Gaussian filter to investigate its behaviors when applied to surface signals. Results show that the estimate of a physical signal is filter-radius dependent. If the computing area is equal to or less than the mass area, especially for a uniformly distributed mass, the estimate gives an almost correct result, no matter what filter radius is used. The estimate has large error because of the signal leakage caused by harmonic truncation if the computing area is much bigger than the mass distribution (or inverse for a small mass anomaly). If a mass anomaly is too small, it is difficult to recover it from space observation unless the filter radius is extremely small. If the computing point (or area) is outside the mass distribution, the estimated result is almost zero, particularly for small filter radii. These properties of the Gaussian filter are helpful in applying GRACE data in different geophysical problems with different spatial position and geometrical size. We further discuss physical sources causing the scalar gravity change at Lhasa. Discussions indicate that the gravity rate of change at Lhasa is not caused by the present-day ice melting (PDIM) (or Little Ice Age, LIA) effect because no ice melting occurs in Lhasa city and nearby. The gravity rate of change is attributable mainly to tectonic deformation associated with the Indian Plate collision. Simultaneous surface displacement, surface denudation, and GIA effects are not negligible.

Precise terrain elevation information is required in various remote sensing and Engineering projects. There are many technologies to derive the terrain elevation information like GPS, ground surveys, LiDAR, Photogrammetry. GPS is the most widely used technology to obtain information due to its ease of operation. However the usage of ellipsoidal heights, i.e. with respect to WGS84 has limited usage in hydrological applications. GPS heights must be converted into orthometric heights for use in hydrological applications, and this requires geoid undulation information. These geoid undulations can be deduced from earth gravity models. There are various earth gravity models available for ready usage like EGM96, EGM2008, GFZ96 in the public domain. This paper discusses the improvements observed in deriving orthometric heights using EGM2008 over its predecessor model EGM96. The utilization of the new model in topographical mapping projects are also presented.