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The study of higher plant growth in space started in the 1950s both on the Russian and the American sides. The first experiments were intended to assess whether plants could grow outside Earth and to determine what differences there were between spaceflight-grown and Earth-grown plants. As plant-growth hardware started to adapt to spaceflight, more opportunities for plant experiments in space became available. Direct microgravity effects started being differentiated from confinement effects and Earth orbit started to become a laboratory where plants could be grown without the influence of Earth gravity. Experiments have shown that, with adapted ventilation, plant growth in space is similar to plant growth on Earth in 1 g, except for some morphological traits. However, only small-scale experiments on plant growth were performed in Earth orbit, which provided insufficient data on crop yield for reduced gravity environments. Challenges remain to grow plants in space, in terms of nutrient delivery, li...

Subject of Research.The paper presents research results and the simulation of errors caused by determining the Earth gravity field parameters for regions with high segmentation of gravity field. The Kalman filtering estimation of determining errors is shown. Method. Simulation model for the realization of inertial geodetic method for determining the Earth gravity field parameters is proposed. The model is based on high-precision inertial navigation system (INS) at the free gyro and high-accuracy satellite system. The possibility of finding the conformity between the determined and stochastic approaches in gravity potential modeling is shown with the example of a point-mass model. Main Results. Computer simulation shows that for determining the Earth gravity field parameters gyro error model can be reduced to two significant indexes, one for each gyro. It is also shown that for regions with high segmentation of gravity field point-mass model can be used. This model is a superposition of attractive and repulsive masses - the so-called gravitational dipole. Practical Relevance. The reduction of gyro error model can reduce the dimension of the Kalman filter used in the integrated system, which decreases the computation time and increases the visibility of the state vector. Finding the conformity between the determined and stochastic approaches allows the application of determined and statistical terminology. Also it helps to create a simulation model for regions with high segmentation of gravity field.

This article belongs to a series of papers covering a complex study regarding the impact of a 6.2kg cylindrical body on a 2000x1000x4mm plate using the software based on finite element theory. This study is considering the plate to be fixed on all 4 sides and a cylindrical body hits it with impact speeds from 1 to 20m/s. Also, the standard earth gravity is considered to be active. The studies were carried out in ANSYS 12.1. Both, plate and body are considered to be made from structural steel. At the impact, the geometry is presented in below figure

We estimate the signature of the climate-induced mass transfers in repeated absolute gravity measurements based on satellite gravimetric measurements from the Gravity Recovery and Climate Experiment (GRACE) mission. We show results at the globe scale and compare them with repeated absolute gravity (AG) time behavior in three zones where AG surveys have been published: Northwestern Europe, Canada, and Tibet. For 10 yearly campaigns, the uncertainties affecting the determination of a linear gravity rate of change range 3–4 nm/s^2/a in most cases, in the absence of instrumental artifacts. The results are consistent with what is observed for long-term repeated campaigns. We also discuss the possible artifact that can result from using short AG survey to determine the tectonic effects in a zone of high hydrological variability. We call into question the tectonic interpretation of several gravity changes reported from stations in Tibet, in particular the variation observed prior to the 2015 Gorkha earthquake.

Long-duration bed rest is widely employed to simulate the effects of microgravity on various physiological systems, especially for studies of bone, muscle, and the cardiovascular system. This microgravity analog is also extensively used to develop and test countermeasures to microgravity-altered adaptations to Earth gravity. Initial investigations of bone loss used horizontal bed rest with the view that this model represented the closest approximation to inactivity and minimization of hydrostatic effects, but all Earth-based analogs must contend with the constant force of gravity by adjustment of the G vector. Later concerns about the lack of similarity between headward fluid shifts in space and those with horizontal bed rest encouraged the use of 6 degree head-down tilt (HDT) bed rest as pioneered by Russian investigators. Headward fluid shifts in space may redistribute bone from the legs to the head. At present, HDT bed rest with normal volunteers is the most common analog for microgravity simulation and to test countermeasures for bone loss, muscle and cardiac atrophy, orthostatic intolerance, and reduced muscle strength/exercise capacity. Also, current physiologic countermeasures are focused on long-duration missions such as Mars, so in this review we emphasize HDT bed rest studies with durations of 30 days and longer. However, recent results suggest that the HDT bed rest analog is less representative as an analog for other important physiological problems of long-duration space flight such as fluid shifts, spinal dysfunction and radiation hazards.

For a stationary system, coarse alignment is used to initially determine the orientation of the INS by utilizing the Earth gravity and rotation vectors. Yet, a gyro-free INS has only accelerometers and hence cannot measure the Earth rotation vector and thus cannot deduce its yaw angle. In this paper, we formulate the coarse-alignment procedure and derive error characteristics for a gyro-free system. In addition, a comparison between different configurations of accelerometers is being conducted.

The paper investigates the elastic, thermal, and electrical coupling effects on the dynamics and libration stability of flexible bare electrodynamic tethers in the end-of-mission satellite deorbit. A high-fidelity model is developed by considering transverse and longitudinal dynamics and libration dynamics of the tether and environmental effects with the latest models for atmospheric and plasma density, as well as Earth gravity and magnetic fields. The long-term orbital and libration dynamics of the tether are analyzed by a nodal position finite element method and symplectic time integration. Orbital motion limited theory is used to model the electron collection by bare electrodynamic tethers, whereas a Fowler–Nordheim equation is used for a Spindt array cathode. The thermal effect and its coupling with the dynamics of electrodynamic tethers are investigated parametrically. It is found that the thermal effect significantly affects the stability of electrodynamic tethers, which must be considered in the st...

By combining a Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) Earth Gravity Model (EGM) and in situ gravity data obtained from the Japanese Antarctic Research Expedition (JARE) surveys, we estimated the regional gravity field in the area of Syowa Station, a Japanese research station located in Lutzow-Holm Bay, East Antarctica. In situ data sets that were used consisted of land gravity data collected since 1967, shipborne data collected since 1985 and airborne gravity data collected in 2006. The GOCE direct (DIR) solution release 5 (R5) model was used as the long-wavelength reference of the gravity field. Using these data sets, we calculated gravity anomalies and geoid heights at 1-by-1′ grid by means of least-squares collocation. The resulting geoid height at Syowa Station was compared with a local height based on GPS, spirit leveling and tide gauge data. The result suggests that the sea surface height at Syowa Station is −1.57 m, which is consistent with a dynamic ocean topography model. During this investigation, we also evaluated GOCE EGMs and other recent EGMs by comparing them with the airborne gravity data. The results indicate that the GOCE DIR R5 produced the smallest RMS (Root Mean Square) differences and that the newer models performed nearly as well. These comparisons demonstrate the importance of using reliable in situ data when evaluating satellite-only EGMs.

Steady-state global chemistry calculations for 15 different flames in both normal earth gravity and micro-gravity conditions are implemented using an axi-symmetric CFD code. 9 different normal laminar diffusion flames of methane-air in normal earth gravity condition with varying CO2 mole fraction have been implemented using 5.5 mm diameter burner. Out of these 9 different flames, 4 flames are different mole fraction of CO2 dilution in fuel (20%, 30%, 40%, 50% CO2 and rest are CH4), 4 flames are different mole fraction of CO2 in air inlet (50%, 60%, 70%, 79% CO2 and rest are O2) and 1 flame is methane-air (21% O2 and 79% N2). The effect of CO2 enhancement in fuel and air inlet on flame shape, size and maximum temperature has been described in this paper. Additionally, 6 different inverse laminar diffusion flames of ethane-air with varying O2 mole fraction (21%, 30%, 50% O2 and rest are N2) with both normal earth gravity and micro-gravity have been implemented using 5.5 mm diameter burner and the maximum temperature results are compared with the available literature. For methane-air normal laminar diffusion flames, effect of CO2 enhancement in both air and fuel inlet cause a decrease in flame temperature. For ethane-air inverse laminar diffusion flames, effect of O2 enrichment in air inlet cause an increase in flame temperature.

The transition from single-phase to two-phase thermal systems in future space vehicles demands a thorough understanding of flow boiling critical heat flux (CHF) in reduced gravity, including microgravity. This study is a comprehensive, consolidated investigation of the complex trends of flow boiling CHF in a rectangular channel in both microgravity and for different orientations in Earth gravity. It is shown that the Interfacial Lift-off Model provides good predictions of CHF data for both gravitational environments and both single-sided and double-sided heating. CHF mechanism in Earth gravity is shown to be highly sensitive to flow orientation at very low velocities, but is consistent with the wavy vapor layer depiction of the Interfacial Lift-off Model at high velocities. The model predicts a stable vapor-liquid interface for downflow with a downward-facing heated wall at lower velocities, and wavy interface with a critical wavelength that decreases with increasing velocity at higher velocities. Predicted CHF values for microgravity fall about midway between the maxima and minima for Earth gravity. Overall, predicted values of CHF and key interfacial parameters for all orientations in Earth gravity and for microgravity converge above ∼1.5 m/s, which points to a velocity threshold above which inertia begins to effectively negate gravity effects.

Predicting critical heat flux is a crucial task when designing a heat flux controlled flow boiling thermal management system. In this study, a mechanistic CHF model based on parallel-to-flow and perpendicular-to-wall hydrodynamic instabilities is implemented to flow boiling in rectangular channels. This study is a comprehensive, consolidated investigation of the flow boiling CHF in single-sided and double-sided heated rectangular channels with subcooled and saturated inlet conditions and different orientations in Earth gravity and in microgravity. The model predictions are compared to highly subcooled, slightly subcooled, and saturated two-phase inlet CHF experimental data and show good agreement, evidenced by an MAE of 11.07%. The CHF model captures in all configurations with good accuracy, low-velocity gravity-dominated flows as well as high-velocity inertia-dominated flows. The hydrodynamic instabilities based CHF model offers an entirely theoretical approach to predicting CHF in such rectangular channels with superior performance capability.

We observe propelling accelerations of a half-kilogram size matter mass, during low energy electric discharges, into a patented “Space Electric Thruster” named “Emitter”. This device is made of a Graphite-based, partially superconducting material, at laboratory temperature, and metallic conductors. That emitter propels from theoretically predicted interaction, and emission, of Gravitational Quanta, bearing a momentum, so without ejecting matter particles in Space. From accelerations values measured, with different electric energies, two discharge directions, and three propelling directions, versus the Earth Gravity acceleration direction, we measure the amplitude of several previously unknown phenomena. (i) Quantum nature of Earth Gravity. (ii) Propagation direction of Earth Gravity Quanta. (iii) Expansion of atomic lattice in emitter materials, pushed by Gravitational Quanta. (iiii) Push of free electrons, from the electric powering currents, by Gravitational Quanta. These phenomena confirm predictions from the Inertia and Gravitation model we proposed, and we used to develop our emitters. Same model predicts the observed constant orbital velocity of stars into galaxies, without any Dark Matter mass. And it predicts physical phenomena, observed in our laboratory and published, with another kind of emitter, at cryogenic temperature, during electric discharges.

We support the very recent discovery of two impact craters under the ice of northwest Greenland (Hiawatha Glacier and Paterson). These discoveries are based mainly on geology and bedrock topography. We added an analysis of gravity field aspects (descriptors) in addition to the traditional gravity and magnetic anomalies. The gravity aspects (the Marussi tensor of the second derivatives, the gravity invariants and their special ratio, strike angles and virtual deformations) provide more complex and comprehensive information about the underground density variations due to a causative body than ordinary gravity anomalies. They show signals typical for the individual geological features like a mountain/volcano, fault, (river)valley, (paleo)lake, (ground)water, hydrocarbon/mineral deposits, etc., as well as for the targets known as impact craters. Our method has been tested on various geological features on the Earth and the Moon. The gravity aspects are, in our case, derived from the recent global static combined Earth gravity field model EIGEN 6C4 with a ground resolution ~9 km and a precision ~10 mGal. A further data come from the digital magnetic field database EMAG 2 with resolution ~5 km. Our method is novel and independent of anything which led to discoveries of these craters in Greenland.

To maximize the science return of asteroid exploration, multi-target asteroid missions are preferred. In this paper, the accessibility of asteroids in a mission, including both near-Earth asteroid (NEA) sample return and main-belt asteroid (MBA) rendezvous using gravity assists (GAs) is investigated. 1081 NEAs and 37 MBAs are chosen as candidates with given constraints. A Tisserand graph with modified tick marks is applied to give a straightforward and quick reference of the possible gravity-assist sequences. The patched conic method is adopted to compute the total velocity increments for six types of gravity-assist trajectories. The particle swarm optimization (PSO) algorithm is employed to minimize the total delta-V. To reduce the computational complexity of the optimization problem, only 50 optimal asteroid groups attained under the mission path of Earth-NEA-EGA1(the first Earth gravity assist)-MBA (ENEM) are reserved to be further optimized for the remaining other five trajectory paths. Feasible trajectory design results with launch dates between 2022 and 2028 are presented.

The selection of an appropriate global gravity field model and refinement method can effectively improve the accuracy of the refined regional geoid model in a certain research area. We analyzed the accuracy of Experimental Geopotential Model (XGM2016) based on the GPS-leveling data and the modification parameters of the global mean square errors in the KTH geoid refinement in Jilin Province, China. The regional geoid was refined based on Earth Gravitational Model (EGM2008) and XGM2016 using both the Helmert condensation method with an RCR procedure and the KTH method. A comparison of the original two gravity field models to the GPS-leveling benchmarks showed that the accuracies of XGM2016 and EGM2008 in the plain area of Jilin Province are similar with a standard deviation (STD) of 5.8 cm, whereas the accuracy of EGM2008 in the high mountainous area is 1.4 cm better than that of XGM2016, which may be attributed to its low resolution. The modification parameters between the two gravity field models showed that the coefficient error of XGM2016 model was lower than that of EGM2008 for the same degree of expansion. The different modification limits and integral radii may produce a centimeter level difference in global mean square error, while the influence of the truncation error caused by the integral was at the millimeter level. The terrestrial gravity data error accounted for the majority of the global mean square error. The optimal least squares modification obtained the minimum global mean square error, and the global mean square error calculated based on XGM2016 model was reduced by about 1~3 cm compared with EGM2008. The refined geoid based on the two gravity field models indicated that both KTH and RCR method can effectively improve the STD of the geoid model from about six to three centimeters. The refined accuracy of EGM2008 model using RCR and KTH methods is slightly better than that of XGM2016 model in the plain and high mountain areas after seven-parameter fitting. EGM2008 based on the KTH method was the most precise at ± 2.0 cm in the plain area and ± 2.4 cm in the mountainous area. Generally, for the refined geoid based on the two Earth gravity models, KTH produced results similar to RCR in the plain area, and had relatively better performance for the mountainous area where terrestrial gravity data is sparse and unevenly distributed.

An analysis of current static and time-variable gravity field models is presented focusing on the medium to high frequencies of the geopotential as expressed by the spherical harmonic coefficients. A validation scheme of the gravity field models is implemented based on dynamic orbit determination that is applied in a degree-wise cumulative sense of the individual spherical harmonics. The approach is applied to real data of the Gravity Field and Steady-State Ocean Circulation (GOCE) and Gravity Recovery and Climate Experiment (GRACE) satellite missions, as well as to GRACE inter-satellite K-band ranging (KBR) data. Since the proposed scheme aims at capturing gravitational discrepancies, we consider a few deterministic empirical parameters in order to avoid absorbing part of the gravity signal that may be included in the monitored orbit residuals. The present contribution aims at a band-limited analysis for identifying characteristic degree ranges and thresholds of the various GRACE- and GOCE-based gravity field models. The degree range 100–180 is investigated based on the degree-wise cumulative approach. The identified degree thresholds have values of 130 and 160 based on the GRACE KBR data and the GOCE orbit analysis, respectively.

Aiming at the existence of gyro drift error in low-cost MEMS sensors, a quaternion attitude matrix updating compensation algorithm is designed and implemented. The algorithm uses the body attitude measured by the gyroscope to rotate the known earth gravity vector to the body coordinate system, and then with the accelerometer observed gravity vector make vector cross product. The results as a measure of the gyro drift error metrics, and by the use of adaptive PID algorithm to track. In this paper, the quadrotor is used as the platform to realize the algorithm, and the attitude of the body is measured using a low-cost MEMS sensor with integrated gyroscope and accelerometer. The drift calibration output is superimposed on the gyroscope observation data to compensate. Through attitude control experiments, the algorithm can accurately track drift error and achieve high-precision quadrotor attitude, which can achieve good attitude control effects.

Water droplet mobility on a hydrophobic surface cannot be guaranteed even when the droplet exhibits a high contact angle (CA) with the surface. In fact, droplet mobility on a surface, especially a fibrous surface, has remained an unsolved empirical problem. This paper is a combined experimental-computational study focused on droplet mobility on a fibrous surface. Electrospun polystyrene (PS) coatings were used in this work for their ability to exhibit high CAs simultaneously with low droplet mobility. To simplify this otherwise complicated problem and better isolate droplet-fiber interactions, the orientation of the fibers in the coatings was limited to the x and y directions. As the earth gravity was not strong enough to mobilize small droplets on PS coatings, experiments were conducted using ferrofluid droplets, and a magnet was used to make them move on the surface. Experimentally validated numerical simulations were used to enhance our understanding of the forces acting on a droplet before moving on the surface. Effects of Young-Laplace CA and fiber-fiber spacing on droplet mobility were investigated. In particular, it was found that droplet mobility depends strongly on the balance of forces exerted on the droplet by the fibers on the receding and advancing sides.

In high-precision GNSS/INS integrated navigation systems, the effect of gravity disturbance to the position, velocity and attitude estimation should be considered. The velocity and position errors induced by gravity disturbance can be corrected directly by GNSS position and velocity through Kalman filtering. The horizontal components of gravity disturbance defined as DOV can affect the roll and pitch estimation and should be compensated by gravity map products, such as EGM2008 or other earth gravity models. While the effect of gravity anomaly to the attitude estimation is usually ignored, since it is much smaller than normal gravity and can be absorbed by the vertical accelerometer’s bias. However, in some special cases, such as IMU rotating around one certain horizontal axis, the gravity anomaly can transfer to horizontal accelerometers, and introduce attitude estimation error. In this paper, we analyze the effect of gravity anomaly on attitude estimation in GNSS/INS integrated navigation systems under overturning cases. A theoretical analysis in the case that IMU rotate around east-axis and north-axis to the attitude estimation is derived based on IMU error propagation functions. It is indicated that the rotation around east-axis (north-axis) can introduce pitch (roll) estimation error proportional to gravity anomaly, the yaw estimation is also be affected due to the intercoupling characteristic of attitude errors, and which more sensitive to the rotation around east-axis while not north-axis. Then, the simulation is conducted and agrees well with the theoretical results. Finally, an RLG (Ring Laser Gyroscope) IMU, which has similar quality to Honeywell HG9900, is fixed on a dual-axis turntable to access the effect of gravity anomaly. The experimental result shows that the yaw error induced by gravity anomaly with magnitude 100mGal can reach 15 arcsecs when IMU rotation around a certain horizontal axis at an angle rate of 1.5°/s°.

Many countries around the world have accelerated the paces of space exploration in recent years. The small gravity field on the surface of the Lunar, Mars and other stars has shown its great influence on the mechanical properties of subsurface soils. A type of magnetic cohesionless soil, made from the cement and Fe3O4 magnetic powder, was prepared and adopted to carry out a series of triaxial compression tests under a confining stress condition within the range of 5-30 kPa. The tests were conduct under four different gravity fields (i.e. 0 g, 1/3 g, 2/3 g and 1 g; g indicates the earth gravity acceleration), by using the geotechnical magneto-gravity model testing equipment developed by China University of Mining and Technology. The experimental results show that the mechanical properties of cohesionless soil, including tangential modulus, failure strength, cohesion and friction angle, tend to increase with the gravity field during the shearing process, when a constant confining pressure is applied. In addition, relationships between the mechanical properties and gravity field were proposed. This research provides some insights into the mechanics under various gravity-induced stress gradients, and therefore contribute to the further development of surface excavation, base construction and resource exploitation on the Lunar, Mars and other planets.

In the construction of super-tall buildings, it is rather important to control the verticality. In general, a laser plummet is used to transmit coordinates of reference points from the ground layer-by-layer, which can effectively control the verticality of super-tall buildings. However, the errors in transmission will accumulate with increasing height and motion of the buildings in construction. This paper presents a global navigation satellite system (GNSS)-based method to check the results of laser plumbing. The method consists of four steps: (1) Computing the coordinate time series of monitoring points by adjusting the GNSS monitoring network observations at each epoch, (2) Analyzing the horizontal motion of super-tall buildings and its effect on vertical reference transmission, (3) Calculating the deflections of the vertical at the monitoring point using an Earth gravity field model and a geoid model. With deflections of the vertical, the static GNSS-measured coordinates are aligned to the same datum as used by the laser plummet, and (4) Finally, validating/checking the result of laser plumbing by comparing it with static GNSS results corrected by deflections of the vertical. A case study of a 438-m high building is tested in Guangzhou, China. The result demonstrates that the gross errors of baseline vectors can be eliminated effectively by GNSS network adjustment of the first step. The two-dimensional displacements can be measured at millimeter-level accuracy, the difference between the coordinates of the static GNSS measurement and laser plumbing is less than &plusmn, 2.0 cm after correction with the deflections of the vertical, which meets the design requirement of &plusmn, 3.0 cm according to the Technical Specification for Concrete Structures of Tall Buildings in China.

Evidence suggests that humans rely on an earth gravity prior for sensory-motor tasks like catching or reaching. Even under earth-discrepant conditions, this prior biases perception and action towards assuming a gravitational downwards acceleration of 9.81 m/s2. This can be particularly detrimental in interactions with virtual environments employing earth-discrepant gravity conditions for their visual presentation. The present study thus investigates how well humans discriminate visually presented gravities and which cues they use to extract gravity from the visual scene. To this end, we employed a Two-Interval Forced-Choice Design. In Experiment 1, participants had to judge which of two presented parabolas had the higher underlying gravity. We used two initial vertical velocities, two horizontal velocities and a constant target size. Experiment 2 added a manipulation of the reliability of the target size. Experiment 1 shows that participants have generally high discrimination thresholds for visually presented gravities, with weber fractions of 13 to beyond 30 %. We identified the rate of change of the elevation angle (ẏ) and the visual angle (θ) as major cues. Experiment 2 suggests furthermore that size variability has a small influence on discrimination thresholds, while at the same time larger size variability increases reliance on ẏ and decreases reliance on θ. All in all, even though we use all available information, humans display low precision when extracting the governing gravity from a visual scene, which might further impact our capabilities of adapting to earth-discrepant gravity conditions with visual information alone.

In order to apply the positioning results of BDS receiver into engineering practice, geodetic height obtained from positioning calculation of receiver should be converted into normal height, therefore it is needed to calculate height anomaly. Also in order to meet the meter level height conversion demand, reduce the memory space consumption by height conversion program and accelerate the program running speed, this paper shows one fast height conversion computation method with the reduced order spherical harmonic coefficients of the gravity model, namely that the height anomaly computed respectively with spherical harmonic coefficients of EGM96 gravity model extending to degree 360 and order 360 and EGM08 earth gravity field extending to degree 2190 and order 2159 is deemed as benchmark, and summarizes the time consumption and relative accuracy of the fast height conversion method. According to the test and comparative analysis of height anomaly computed between world-wide grid points and Asia-Pacific region grid points, test results indicate that this height anomaly computation method with reduced-order spherical harmonic coefficients of EGM96 gravity model can meet the height conversion accuracy and speed demand for positioning results of BDS receivers all over the world or in Asia-Pacific region.

Gravity is a permanent environmental signal guiding plant growth and development. Gravity sensing in plants starts with the displacement of starch-filled plastids called statoliths, ultimately leading to auxin redistribution and organ curvature. While the involvement in gravity sensing of several actors such as calcium is known, the effect of statolith displacement on calcium changes remains enigmatic. Microgravity is a unique environmental condition offering the opportunity to decipher this link. In this study, roots of Brassica napus were grown aboard the International Space Station (ISS) either in microgravity or in a centrifuge simulating Earth gravity. The impact of short simulated gravity onset and removal was measured on statolith positioning and intracellular free calcium was assessed using pyroantimonate precipitates as cytosolic calcium markers. Our findings show that a ten-minute onset or removal of gravity induces very low statolith displacement, but which is, nevertheless, associated with an increase of the number of pyroantimonate precipitates. These results highlight that a change in the cytosolic calcium distribution is triggered in absence of a significant statolith displacement.

In 2016, we published "A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth gravity model. Measurement of Earth's dragging of inertial frames [1]", a measurement of frame-dragging, a fundamental prediction of Einstein's theory of General Relativity, using the laser-ranged satellites LARES, LAGEOS and LAGEOS 2. The formal error, or precision, of our test was about 0.2% of frame-dragging, whereas the systematic error was estimated to be about 5%. In the 2017 paper "A comment on "A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth gravity model by I. Ciufolini et al." "by L. Iorio [2] (called I2017 in the following), it was incorrectly claimed that, when comparing different Earth gravity field models, the systematic error in our test due to the Earth's even zonal harmonics of degree 6, 8, 10 could be aslarge as 15%, 6% and 36%, respectively. Furthermore, I2017 contains other, also incorrect, claims about the number of necessary significant decimal digits of the coefficients used in our test (claimed to be nine), in order to eliminate the largest uncertainties in the even zonals of degree 2 and 4, and about the non-repeatability of our test. Here we analyze and rebut those claims in I2017., Comment: Published on The European Physical Journal C 78, no. 11 (2018): 880

This chapter reviews the status of space missions employing high resolution laser interferometry, a technology which just recently entered space operation. Two application areas i) space-based gravitational wave detection and ii) earth gravity field measurement are discussed and the mission concepts and technology development for space are described, with the focus on distance metrology relying on heterodyne interferometry.

Water is matter for life on Earth and influences every aspect of our living planet. Water is crucial in forming the Earth’s unique ecosystem environment that supports the survival of human beings and other lives. Under the forcing of solar radiation, earth gravity, and other energy interaction, water cycle is the cyclical processes of transformation of water, including the transmission and phase transitions of water in the land, ocean, and atmosphere ( Trenberth et al., 2007 ; Trenberth et al., 2011 ; Oki and Kanae, 2006 ). The presence of water makes the earth unique from other planets.

A variety of future space missions rely on the availability of high-performance optical frequency references with applications in fundamental physics, geoscience, Earth observation and global satellite navigation systems (GNSS). Examples are the gravitational wave detector LISA (Laser Interferometer Space Antenna), the Earth gravity mission NGGM (Next Generation Gravity Mission) and missions, dedicated to tests of Special Relativity, e.g. by performing a Kennedy-Thorndike experiment testing the boost dependence of the speed of light. In this context, we developed optical frequency references based on Doppler-free spectroscopy of molecular iodine where compactness and mechanical and thermal stability are main design criteria. We demonstrated a frequency instability of 6•10-15 at 1 s integration time and 3•10-15 for integration times between 100 s and 1.000 s. Furthermore, a very compact spectroscopy setup was realized for the sounding rocket mission JOKARUS which was successfully flown in May 2018. In a current activity, an integrated high-performance iodine-based frequency reference is developed which serves as a demonstrator for future GNSS using optical technologies.

Dust and sand motion are a common sight on Mars. Understanding the interaction of atmosphere and Martian soil is fundamental to describe the planet’s weather, climate and surface morphology. We set up a wind tunnel to study the lift of a mixture between very fine sand and dust in a Mars simulant soil. The experiments were carried out under Martian gravity in a parabolic flight. The reduced gravity was provided by a centrifuge under external microgravity. The onset of saltation was measured for a fluid threshold shear velocity of 0.82 ± 0.04 m/s. This is considerably lower than found under Earth gravity. In addition to a reduction in weight, this low threshold can be attributed to gravity dependent cohesive forces within the sand bed, which drop by 2/3 under Martian gravity. The new threshold for saltation leads to a simulation of the annual dust cycle with a Mars GCM that is in agreement with observations.

The paper focuses on the problem of gravity anomaly determination by airborne gravimetry data. To solve the problem, nonlocal information on the Earth gravity field is needed, usually provided by one of the Earth’s global gravity field models. The possibility of using spherical wavelet expansion for combining airborne gravimetry and global data is studied. Combination algorithms based on optimal estimation methods are developed and tested using Arctic airborne gravity survey data and EGM2008 global model.

Earth`s gravity field recovery was improved after the pre-processing upgrade of the Gravity Recovery And Climate Experiments (GRACE) satellite`s star trackers. The star tracker measurements were filtered with a tighter low-pass filtering of 0.025Hz cutoff frequency, instead of a nominal filtering of 0.1Hz cutoff frequency. In addition, a jump removal algorithm was applied to remove discontinuities, due to direct Sun and/or Moon interventions, in the star tracker measurements. During the K-Band Ranging (KBR) calibration maneuvers, large attitude variations could be detected concurrently by both of the star trackers and the accelerometer. The misalignment angles of star trackers between the true frame and the normal frame could be determined by comparing measurements from these sensors. In this paper, new Earth` gravity field maps were obtained using above improvement. Based on comparisons to nominal Earth`s gravity field maps, the new Earth`s gravity field maps were found better than the nominal ones. Among the applied methods, the misalignment calibration of the star trackers had a major impact on the improvement of the new Earth`s gravity field maps.

Moving-base gravity gradiometry has proven to be a convenient method to determine the Earth’s gravity field. The ESA mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) has enabled to map the Earth gravity field and its gradients with a resolution of 80 km, leading to significant advances in physical oceanography and solid Earth physics. At smaller scales, airborne gravity gradiometry has been increasingly used during the past decade in mineral and hydrocarbon exploration. In both cases the sensitivity of gradiometers to the short wavelengths of the gravity field is of crucial interest. Here, we quantify and characterize the error on the gravity gradients estimated from measurements performed with a new instrument concept, called GREMLIT, for typical airborne conditions. GREMLIT is an ultra-sensitive planar gravitational gradiometer which consists in a planar acceleration gradiometer together with 3 gyroscopes. To conduct this error analysis, a simulation of a realistic airborne survey with GREMLIT is carried out. We first simulate realistic GREMLIT synthetic data, taking into account the acceleration gradiometer and gyroscope noises and biases and the variation of orientation of the measurement reference frame. Then, we estimate the gravity gradients from these data. Special attention is paid to the processing of the gyroscopes measurements whose accuracy is not commensurate with the ultra-sensitive gradiometer. We propose a method to calibrate the gyroscopes biases with a precision of the order $$10^{-8}$$ rad/s. In order to transform the tensor from the measurement frame to the local geodetic frame, we estimate the error induced when replacing the non-measured elements of the gravity gradient tensor by an a priori model. With the appropriate smoothing, we show that it is possible to achieve a precision better than 2E for an along-track spatial resolution of 2 km.

Firstly, the Earth's gravitational field from the past Challenging Minisatellite Payload (CHAMP) mission is determined using the energy conservation principle, the combined error model of the cumulative geoid height influenced by three instrument errors from the current Gravity Recovery and Climate Experiment (GRACE) and future GRACE Follow-On missions is established based on the semi-analytical method, and the Earth's gravitational field from the executed Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission is recovered by the space-time-wise approach. Secondly, the cumulative geoid height errors are 1.727 × 10 −1 m, 1.839 × 10 −1 m and 9.025 × 10 −2 m at degrees 70,120 and 250 from the implemented three-stage satellite gravity missions consisting of CHAMP, GRACE and GOCE, which preferably accord with those from the existing earth gravity field models involving EIGEN-CHAMP03S, EIGEN-GRACE02S and GO_CONS_GCF_2_DIR_R1. The cumulative geoid height error is 6.847 × 10 −2 m at degree 250 from the future GRACE Follow-On mission. Finally, the complementarity among the four-stage satellite gravity missions including CHAMP, GRACE, GOCE and GRACE Follow-On is demonstrated contrastively.

Spectral characteristics of modern models of the Earth’s gravity field obtained from the CHAMP, GRACE and GOCE space gravity missions are considered. The resolution is estimated for a specified accuracy.

Since the Gravity Recovery and Climate Experiment (GRACE) collinear formation has some fatal drawbacks including north-south striping error, etc., this study carries out the feasibility demonstrations on the next-generation Along-Cross-Radial(ACR)-Cartwheel twin-satellite formation for improving the spatial resolution of the Earth's gravitational field by the intersatellite range-rate interpolation method. Firstly, the Earth's gravitational field from ACR-Cartwheel-A/B complete up to degree and order 120 is precisely recovered using the satellite orbital parameters and the measurement precision of key payloads from the twin GRACE satellites. The research results show that the accuracy of the Earth's gravitational field determination from the next-generation ACR-Cartwheel twin-satellite formation is averagely improved by 2.6 times than that from the EIGEN-GRACE02S model released by the German GeoForschungsZentrum (GFZ) in Potsdam, which sufficiently verifies that the next-generation ACR-Cartwheel twin-satellite formation is obviously better than the current GRACE collinear formation. Secondly, the Earth's gravitational field complete up to degree and order 120 is accurately measured based on the satellite orbital parameters (e.g. orbital altitude of 350 km, intersatellite range of 100 km, orbital inclination of 89° and orbital eccentricity of 0.0046), the measurement precision of key payloads (e.g. 10−7 m·s−1 in intersatellite range-rate, 10−3 m in orbital position, 10−6 m·s−1 in orbital velocity and 10−11 m·s−2 in non-conservative force), an observation time of 30 days and a sampling interval of 10 s by the Longitudinal-Along-Radial (Lo-AR)-Cartwheel-A/B, Latitudinal-Along-Radial (La-AR)-Cartwheel-A/B and ACR-Cartwheel-A/B twin-satellite formations using the intersatellite range-rate interpolation method, and the cumulative geoid height errors are 5.115×10−4 m, 4.923×10−4 m and 3.488×10−4 m, respectively. The results of this study are as follows. (1) Since the orbital stability of the La-AR-Cartwheel-A/B formation is superior to the Lo-AR-Cartwheel-A/B formation, the accuracy of satellite gravity recovery from the La-AR-Cartwheel-A/B formation is higher than that from the Lo-AR-Cartwheel-A/B formation. (2) Because the ACR-Cartwheel-A/B twin-satellite formation can synchronously obtain gravity information in the along-track, cross-track and radial-track directions, satellite observation data are provided with some strong points consisting of homogeneity, isotropy, and so on. In a word, the next-generation ACR-Cartwheel twin-satellite formation will prospectively play a significant role in producing the Earth gravity field model with higher accuracy and resolution.

In Geodesy, the heights of points are normally orthometric heights measured above the geoid (an equipotential surface created by the earth masses and rotation which approximately coincides with the mean sea level) or the normal heights. It is necessary to transform the GNSS/GPS measured ellipsoidal heights (h) to classical physical heights (orthometric H/Normal H). The total gravity potential of the earth (W) is the summation of two components; gravitational potential (V) by earth masses and the centrifugal potential (Ω). The centrifugal potential is directly calculated, while the gravitational potential (V) needs to be modeled globally or locally using given measurements. The global models of the earth gravitational potential/gravity models (or so-called geoid models) are mostly given using spherical harmonics (SH). A modified approach of SH was defined to fit the use of SH for regional gravity/potential modeling called spherical cap harmonics (SCH). Due to the numerical difficulties of SCH, a simplified approach of SCH is selected to be used for a combined modeling of the earth potential using a variety of observations. This approach is called the Adjusted Spherical Cap harmonics.

Quarks move within the nucleon at relativistic speeds. This causes intertia. This inertia results in gravitational mass-effect. For short distances this is the strong force, for distant objects it is gravity. This is due to an increase in the gravitational constant related to the velocity of objects moving at speeds close to the speed of light. This relation is calculable with a formula presented in the text.

The rate of change of surface gravity, dg/dt, and vertical deformation rate of the solid surface, du/dt, are two observables of glacial isostatic adjustment (GIA). They contribute with different information on the same phenomenon. Their relation contains information of the underlying physics and a trustworthy relation allows to combine these observations to strengthen the overall observational accuracy of the phenomenon. In this paper we investigate the predicted relation between dg/dt and du/dt in previously glaciated areas. We use the normal mode approach for one dimensional earth models and solutions of the sea level equation with time-dependent coastline geometry. Numerical predictions of dg/dt and du/dt are computed for Laurentia, Fennoscandia and the British Isles respectively, using six different earth models. Within each region a linear trend is then fitted using the relation dg/dt = C du/dt + dg_0/dt. The estimated C and dg_0/dt differ more between the regions than between different earth models within each region. For Fennoscandia C ≈ −0.163 μGal/mm and for Laurentia C ≈ −0.152 μGal/mm. Maximum residuals between the linear trend and spatially varying model predictions of dg/dt are 0.04 μGal/yr in Fennoscandia and 0.17 μGal/yr in Laurentia. For the British Isles the results are harder to interpret, mainly since this region is located on the zero uplift isoline of Fennoscandia. In addition, we show temporal variation of the relation since the last glacial maximum till present-day. The temporal and spatial variation of the relation between dg/dt and du/dt can be explained by (i) the elastic respectively viscous proportion of the total signal and (ii) the spectral composition of the regional signal. Additional local effects, such as the Newtonian attraction and elastic deformation from local sea level changes, are examined in a case study for six stations in the Nordic absolute gravity network. The influence of these local effects on the relation between View the dg/dt and du/dt is negligible except for extreme locations close to the sea.

Our visual system takes into account the effects of Earth gravity to interpret biological motion (BM), but the neural substrates of this process remain unclear. Here we measured functional magnetic resonance (fMRI) signals while participants viewed intact or scrambled stick-figure animations of walking, running, hopping, and skipping recorded at normal or reduced gravity. We found that regions sensitive to BM configuration in the occipito-temporal cortex (OTC) were more active for reduced than normal gravity but with intact stimuli only. Effective connectivity analysis suggests that predictive coding of gravity effects underlies BM interpretation. This process might be implemented by a family of snapshot neurons involved in action monitoring.

The Earth’s gravity field tends to change due to various reasons. These are diverse processes occurring inside the Earth or changes initiated by human activity. The increasing accuracy of measurements has enabled to take into consideration fluctuations in the gravity field. The article presents research study on the effect of gravity potential describing variations in the gravity field affecting gravity field elements related to the performed measurements. Due to the effect of the disturbing potential, a change in gravity and the deviation of vertical and equipotential surface deformation have been determined. The paper has analyzed the disturbing effect of the material point or homogeneous sphere and has specified the possibilities of assessing the disturbing effect of any form of the homogeneous body. Based on the tidal potential induced by the celestial body, the disturbing effect of the Moon and Sun onto the Earth’s gravity field has been assessed. The carried out research indicates that the range of deformation changes in the equipotential surface of the Earth’s gravity field induced by the effect of the Moon is equal to 0.4824 m, whereas that of the Sun makes 0.1861 m. The conducted studies prove that, due to the effect of the Moon, the direction of the vertical, in terms of the Earth’s surface, tends to change up to 0.0541", and as a result of the Sun’s effect it could reach 0.0204". Having assessed the Lunisolar effect in the first order vertical network measurements in Lithuania, in a polygon with the perimeter of 451 km, it has been determined that the closing error of normal height difference has decreased by the factor of 1.3.

Space agencies worldwide are actively exploring the implementation of two-phase thermal management systems to support astronaut life onboard future space vehicles and planetary bases. Key motivations for these efforts are to increase the efficiency of power utilization and reduce overall weight and volume. These advantages are realized by orders of magnitude enhancement in heat transfer coefficient achieved with flow boiling and condensation compared to single-phase systems. This study will review published literature concerning two-phase flow and heat transfer in reduced gravity. Discussed are the different methods and platforms dedicated to exploring the influence of reduced gravity, including ground flow boiling experiments performed at different orientations relative to Earth gravity, as well as reduced gravity adiabatic two-phase flow, pool boiling, flow boiling and CHF experiments. Despite the extensive data and flow visualization results available in the literature, it is shown that there is a severe shortage of useful correlations, mechanistic models and computational models, which compromises readiness to adopt flow boiling in future space systems. Key recommendations are provided concerning platform, heater design, and operating conditions for future studies to expedite the deployment of two-phase thermal management in future space missions.

ESA’s Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission and the American-German Gravity Recovery and Climate Experiment (GRACE) mission map the Earth’s gravity field and deliver valuable data for climate research.

In this work we present a new robotic system, Salto-1P, for exploring extreme jumping locomotion. Salto-1P weighs 0.098 kg, and has an active leg length of 14.4 cm. The robot is able to perform a standing vertical leap of 1.25 m, continuously hop to heights over 1 m, and jump over 2 m horizontally. Salto-1P uses aerodynamic thrusters and an inertial tail to control its attitude in the air. A linearized Raibert step controller was sufficient to enable unconstrained in-place hopping and forwards-backwards locomotion with external position feedback. We present studies of extreme jumping locomotion in which the robot spends just 7.7% of its time on the ground, experiencing accelerations of 14 times earth gravity in its stance phase. An experimentally collected dataset of 772 observed jumps was used to establish the range of achievable horizontal and vertical impulses for Salto-1P.

High-precision electrostatic accelerometers have achieved remarkable success in satellite Earth gravity field recovery missions. Ultralow-noise inertial sensors play important roles in space gravitational wave detection missions such as the Laser Interferometer Space Antenna (LISA) mission, and key technologies have been verified in the LISA Pathfinder mission. Meanwhile, at Huazhong University of Science and Technology (HUST, China), a space accelerometer and inertial sensor based on capacitive sensors and the electrostatic control technique have also been studied and developed independently for more than 16 years. In this paper, we review the operational principle, application, and requirements of the electrostatic accelerometer and inertial sensor in different space missions. The development and progress of a space electrostatic accelerometer at HUST, including ground investigation and space verification are presented.

Terrestrial laser scanning is an efficient technique in providing highly accurate point clouds for various geoscience applications. The point clouds have to be transformed to a well-defined reference frame, such as the global Geodetic Reference System 1980. The transformation to the geocentric coordinate frame is based on estimating seven Helmert parameters using several GNSS (Global Navigation Satellite System) referencing points. This paper proposes a method for direct point cloud georeferencing that provides coordinates in the geocentric frame. The proposed method employs the vertical deflection from an external global Earth gravity model and thus demands a minimum number of GNSS measurements. The proposed method can be helpful when the number of georeferencing GNSS points is limited, for instance in city corridors. It needs only two georeferencing points. The validation of the method in a field test reveals that the differences between the classical georefencing and the proposed method amount at maximum to 7 mm with the standard deviation of 8 mm for all of three coordinate components. The proposed method may serve as an alternative for the laser scanning data georeferencing, especially when the number of GNSS points is insufficient for classical methods.

The national/regional unified height datum is of great importance for the establishment of geospatial information infrastructure and the corresponding surveying applications. The geopotential-difference method is proposed for long-distance height-datum connection across seas based on global positioning system (GPS)/leveling, global geopotential model (GGM), and satellite altimetry data sets. For a case study, the Chinese height datum 1985 (CNHD85) in the mainland was connected to the local vertical datum (LVD) in Hainan across Qiongzhou Strait up to a distance over 30 km. The results show that this method is independent of the selection of virtual leveling lines. Furthermore, evaluation with an indirect approach shows that the choice of GGM affects the quality of the normal height connection, where the relative accuracies of the solutions based on the Earth Gravity Model 2008 (EGM2008), European Improved Gravity Model of the Earth by New Techniques 6C (EIGEN-6C), EIGEN-6C3STAT, and EIGEN-6C4 model...