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Discussing the problem of the external gravitational potential of the rotating Earth, we have to consider the fundamental postulate of the finite speed of the propagation of gravitation. This can be done using the expressions for the gravitational aberration compared to the Liénard–Wiechert solution of the retarded potentials. The term gravitational counter-aberration or co-aberration is introduced to describe the pattern of the propagation of the gravitational signal emitted by the rotating Earth. It is proved that in the first approximation, the classic theory of the aberration of light can be applied to calculate this effect. Some effects of the gravitational aberration on the external gravity field of the rotating Earth may influence the orbit determination of the Earth artificial satellites.

To address the accuracy requirements of initial alignment of high-precision inertial navigation systems (INSs), gravity disturbance compensation for INSs based on a spherical harmonic model is investigated herein. First, the horizontal component of gravity disturbance at an alignment point is calculated using the high-resolution Earth Gravity Model EIGEN-6C4 and then compensated to the initial alignment. Subsequently, the self-alignment algorithm of solidified coordinate frame is used to derive the misalignment angle equation of gravity disturbance affecting the initial alignment. Meanwhile, the coupling relationship between the measurement error of an inertial unit and the gravity disturbance is simulated and analyzed. Finally, a laser strapdown inertial navigation system experiment is performed. The simulation result shows that the pitch angle, roll angle, and heading angle errors reduced by $27.41^{\prime \prime }$ , $- 0.37^{\prime \prime }$ , and $6.72^{\prime \prime }$ , respectively, after the gravity disturbance compensation. Experiment result shows that the alignment performance after compensation has been improved and the heading angle error is reduced by $6.76^{\prime \prime }$ . The simulations and experiments results validate the theoretical analysis.

Accepted: 2019-10-05, 資料番号: SA1190180000

The Gravity Recovery and Climate Experiment Follow-On (GRACE-FO), launched May 22, 2018 and collecting science data since June 2018, is extending the 15-year data record of Earth mass change established by its predecessor GRACE mission (2002-2017). The GRACE-FO satellites carry onboard a novel technology demonstration instrument for intersatellite ranging, the Laser Ranging Interferometer (LRI), in addition to the microwave interferometer (MWI) carried on GRACE. The LRI has out-performed its in-orbit performance requirements both in terms of accuracy as well as the duration of tracking. Here, we compare and validate LRI-based gravity solutions for January 2019 to September 2020 against the MWI solutions. The comparison between the two sets of gravity solutions shows great similarities in general and nearly perfect consistency at a large hydrologic basin spatial scale (100,000 km

7 p.-1 fig., Plants are a necessary component of any system of bioregenerative life-support for human space exploration. For this purpose, plants must be capable of surviving and adapting to gravity levels different from the Earth gravity, namely microgravity, as it exists on board of spacecrafts orbiting the Earth, and partial-g, as it exists on the surface of the Moon or Mars. Gravity is a fundamental environmental factor for driving plant growth and development through gravitropism. Exposure to real or simulated microgravity produces a stress response in plants, which show cellular alterations and gene expression reprogramming. Partial-g studies have been performed in the ISS using centrifuges and in ground based facilities, by implementing adaptations in them. Seedlings and cell cultures were used in these studies. The Mars gravity level is capable of stimulating the gravitropic response of the roots and preserving the auxin polar transport. Furthermore, whereas Moon gravity produces alterations comparable, or even stronger than microgravity, the intensity of the alterations found at Mars gravity was milder. An adaptive response has been found in these experiments, showing upregulation of WRKY transcription factors involved in acclimation. This knowledge must be improved by incorporating plants to the coming projects of Moon exploration., Work performed in the authors’ laboratory was supported by different grants of the Spanish National Agency for Research of the Spanish Government, e.g., Grants #ESP2015-64323-R and #RTI2018-099309-B-I00 (co-funded by EU-ERDF).

We present a construction of the optical whispering gallery mode (WGM) resonator gravimeter. The sensitive element of the device is a resonator, placed on a cantilever, which moves with the change of gravity, variating the distance with coupling element. The gravity acceleration is measured by the change of the resonator eigenmode parameters.

This is an experimental study on highly subcooled flow boiling of water for assessing the effect of gravitational acceleration on flow boiling heat transfer. The experiments are conducted in a macro-channel 3 mm high, 40 mm wide and 120 mm long at water mass fluxes of 330, 630 and 830 kg/m2 s and heat fluxes in the range 200–900 kW/m2. Increased gravitational accelerations, from 1.8 to 9 times the Earth-gravity are achieved with the use of a ∼3 m radius centrifuge (Large Diameter Centrifuge, ESTEC/European Space Agency). Two distinct channel inclinations are examined; horizontal, where the gravitational acceleration is normal to the boiling surface, and vertical, where the gravitational acceleration is parallel to the boiling surface and opposite to flow direction. Experiments at hyper-gravity conditions show that for the horizontal channel inclination, flow boiling heat transfer coefficient increases, whereas for the vertical channel inclination it decreases. The observed deviations lie approximately between +15% and −40% from the Earth-g value. An interpretation of the present results is attempted based on the effect of liquid-phase natural and forced convection combined with the effect of buoyancy at vapor bubbles. The tendency of the heat transfer coefficient experimental data with respect to changes in gravitational acceleration allows the development of a gravity-modified version of the well-known two phase model of Liu-Winterton, by incorporating a linearly dependent gravity multiplier.

Global monitoring of time-variable Earth gravity field from space – at first, observation of secular changes in the Earth flattening by SLR satellites and in recent years especially the regional hydrology variations revealed by the GRACE mission – has revolutionized the exploration of the Earth in many fields. To be able to obtain this rather weak part of the measured signal, it is necessary to measure/model and to subtract all other gravitational and nongravitational forces whose magnitude is not negligible compared to that of the time-variable gravity. In our paper, we analyze the influence of the perturbations arising from the general theory of relativity. Using the modelled data over one year of three example satellites at altitudes 250 km (GOCE), 450 km (Swarm A) and 5900 km (LAGEOS-1), we characterized the magnitude and frequency of occurrence of the three main general relativistic perturbing terms and compared their action to other relevant accelerations. Namely, for GOCE and Swarm A the accelerations due to time-varying gravity reach 10−9 − 10−8 m s−2, for LAGEOS-1 10−11 − 10−10 m s−2; relative to the preceding, the dominant relativistic term is greater by one order of magnitude in the radial direction, the relativistic precession terms happen to be comparable in the cross-track direction. Therefore, for a proper extraction of the time-varying part of the gravity signal, all three relativistic terms have to be taken into account. This conclusion is validated by the real monthly gravity fields obtained through the inversion of GPS orbits of the Swarm A satellite.

In the ongoing MOCAST+ study (funded by the Italian Space Agency), the use of an enhanced cold atom interferometer is proposed for a satellite gravity mission. The instrument consists of an interferometric gravitational gradiometer with Strontium atoms, on which an optical frequency measurement is implemented by means of an ultra-stable laser, in order to also provide time measurements. The study is investigating whether this combination can give the possibility of improving the estimation of gravity models even at low harmonic degrees with inherent advantages in the modeling of mass transport and its global variations: this would represent fundamental information, e.g. in the study of variations in the hydrological cycle and relative mass exchange between atmosphere, oceans, cryosphere and solid Earth.The main lines of the MOCAST+ proposal are: two satellites on a polar orbit (reference altitude 342 km) at a distance of about 100 km with atomic samples on board interrogated by the same clock laser (noise of the local oscillator in common). The atom interferometer should allow to collect observations of differences of the gravitational potential (which will contribute to the estimate of the low frequencies of the Earth gravity field model) and of second derivatives of the gravitational potential along one or more orthogonal directions, which will be not necessarily the same for the two satellitesIn this presentation, the mathematical model for the application of the space-wise approach to the simulated data will be described, consisting in a filter - gridding - harmonic analysis scheme that is to be repeated for several Monte Carlo samples extracted for the same simulated scenario, in order to produce a sample estimate of the error covariance matrix of the harmonic coefficients.The data analysis based on the formulated mathematical model will be applied to both static and time-variable gravity field, performing simulations over a limited time span and extending the resulting accuracy to a longer period by covariance propagation, assuming to have other independent solutions with the same accuracy. In particular, the time-variable analysis will be mainly dedicated to assessing the accuracy in estimating the rate of change in geodynamic processes for which a linear variation in time can be reasonably assumed.

In a 2-alternative forced-choice protocol, observers judged the duration of ball motions shown on an immersive virtual-reality display as approaching in the sagittal plane along parabolic trajectories compatible with Earth gravity effects. In different trials, the ball shifted along the parabolas with one of three different laws of motion: constant tangential velocity, constant vertical velocity, or gravitational acceleration. Only the latter motion was fully consistent with Newton’s laws in the Earth gravitational field, whereas the motions with constant velocity profiles obeyed the spatio-temporal constraint of parabolic paths dictated by gravity but violated the kinematic constraints. We found that the discrimination of duration was accurate and precise for all types of motions, but the discrimination for the trajectories at constant tangential velocity was slightly but significantly more precise than that for the trajectories at gravitational acceleration or constant vertical velocity. The results are compatible with a heuristic internal representation of gravity effects that can be engaged when viewing projectiles shifting along parabolic paths compatible with Earth gravity, irrespective of the specific kinematics. Opportunistic use of a moving frame attached to the target may favour visual tracking of targets with constant tangential velocity, accounting for the slightly superior duration discrimination.

We are just beginning to understand how spaceflight may impact brain function. As NASA proceeds with plans to send astronauts to the Moon and commercial space travel interest increases, it is critical to understand how the human brain and peripheral nervous system respond to zero gravity. Here, we developed and refined head-worn transcranial magnetic stimulation (TMS) systems capable of reliably and quickly determining the amount of electromagnetism each individual needs to detect electromyographic (EMG) threshold levels in the thumb (called the resting motor threshold (rMT)). We then collected rMTs in 10 healthy adult participants in the laboratory at baseline, and subsequently at three time points onboard an airplane: (T1) pre-flight at Earth gravity, (T2) during zero gravity periods induced by parabolic flight and (T3) post-flight at Earth gravity. Overall, the subjects required 12.6% less electromagnetism applied to the brain to cause thumb muscle activation during weightlessness compared to Earth gravity, suggesting neurophysiological changes occur during brief periods of zero gravity. We discuss several candidate explanations for this finding, including upward shift of the brain within the skull, acute increases in cortical excitability, changes in intracranial pressure, and diffuse spinal or neuromuscular system effects. All of these possible explanations warrant further study. In summary, we documented neurophysiological changes during brief episodes of zero gravity and thus highlighting the need for further studies of human brain function in altered gravity conditions to optimally prepare for prolonged microgravity exposure during spaceflight.

Objective: The creation of artificial gravity on board a space station is one of the promising methods for preventing health problems during space missions; a short-radius centrifuge (SRC) is the model of such a method on Earth. Our goal was to evaluate the sensitivity of bioimpedance polysegmental measurements for monitoring of the body regions' blood-filling redistribution and to analyze the dynamics of blood-filling redistribution during rotation in three SRC rotation modes. Approach: Nine healthy male volunteers have been observed under three SRC rotation modes with a maximum acceleration of 2.05 standard Earth gravity (g), 2.47 g, 2.98 g along the body vertical axis towards the legs with a rotation radius of 235 cm. The 5 kHz electrical resistance was evaluated using a bioimpedance analyzer in a polysegmental mode. Main results: Twenty-five correct records were made, of which four records were incomplete since the tests had to be stopped because the subjects were not feeling well. There was a blood-filling decrease in the head region; resistance increased to +15.4% ± 4.1% in the first SRC rotation mode. The electrical resistance of the leg regions decreased to −16.5% ± 2.3%. Slowdown of the SRC led to the reverse changes in resistance. The blood redistribution in the head and leg regions was independent of the mode of SRC rotation during the first 30 min, and varied on average by +10% and −15% respectively. Significance: Bioimpedance monitoring is promising for detection and prediction of blood circulation changes during rotation on the SRC.

Humans expect downwards moving objects to accelerate and upwards moving objects to decelerate. These results have been interpreted as humans maintaining an internal model of gravity. We have previously suggested an interpretation of these results within a Bayesian framework of perception: earth gravity could be represented as a Strong Prior that overrules noisy sensory information (Likelihood) and therefore attracts the final percept (Posterior) very strongly. Based on this framework, we use published data from a timing task involving gravitational motion to determine the mean and the standard deviation of the Strong Earth Gravity Prior. To get its mean, we refine a model of mean timing errors we proposed in a previous paper (Björn Jörges & López-Moliner, 2019), while expands the range of conditions under which it yields adequate predictions of performance. This underscores our previous conclusion that the gravity prior is likely to be very close to 9.81 m/s². To obtain the standard deviation, we identify different sources of sensory and motor variability reflected in timing errors. We then model timing responses based on quantitative assumptions about these sensory and motor errors for a range of standard deviations of the earth gravity prior, and find that a standard deviation of around 2 m/s² makes for the best fit. This value is likely to represent an upper bound, as there are strong theoretical reasons along with support empirical evidence for the standard deviation of the earth gravity being lower than this value.

The idea of using space laser interferometer to measure the relative displacement change between two satellites has been considered for space gravitational waves detection and Earth gravity filed mapping in recent years. Some investigations on the key issues of laser interferometer in our working team have been presented in this paper. An on-ground laser interferometer prototype used for the demonstration of satellite-to-satellite ranging has been constructed, which is equipped with phasemeter, laser pointing modulation and laser phase-locking control. The experimental results show that path-length measurement sensitivity of the laser interferometer reaches 200 pm/√ Hz, and phase measurement precision achieves 2π × 10− 5 rad/√ Hz, and laser pointing modulation precision is better than 80 nrad/√ Hz, and laser phase-locking control precision attains 2π × 10− 4 rad/√ Hz within the frequency regime of 1 mHz–1 Hz. All of these demonstrate that the proposed laser interferometer has very promising feasibility to meet the requirement of the Taiji, TianQin and Space Advanced Gravity Measurement (SAGM) missions which are put forward by Chinese scientists.

A fire during manned space exploration can cause serious casualties and disrupt the mission if the initial response is delayed. Therefore, measurement technology that can detect fire in the early stage of ignition is important. There have been a number of works that investigate the smoke behaviors in microgravity as the foundation for a reliable method for sensing a fire during spaceflight. For space missions to the outer planets, however, a strategy of detecting smoke as an indicator of fire should be adjusted to cover the fire scenario that can be greatly affected by changes in gravity (microgravity, lunar, Mars, and Earth gravity). Therefore, as a preliminary study on fire detectors of the manned pressurized module, the present study examined the smoke particle behavior and detection characteristics with respect to changes in gravity using numerical analysis. In particular, the effects of the combination of buoyancy and ventilation flow on the smoke particle movement pattern was investigated to further improve the understanding of the fire detection characteristics of the smoke detector, assuming that a fire occurred in different gravity environments inside the pressurized module. To this end, we modeled the internal shape of Destiny and performed a series of numerical analysis using the Fire Dynamics Simulator (FDS). The findings of this study can provide basic data for the design of a fire detection system for manned space exploration modules.

Foucault long pendulums, with spherical suspended mass, show Earth rotation by the constant velocity drift of their oscillation plane. Maurice Allais used a short, 84 centimeters pendulum, with a suspended bronze disc mass. He recorded its oscillation plane drift velocity, during solar eclipses, in 1954 and 1959. Both times, he noticed an anomalous drift of the oscillation plane. Several authors confirmed the effect, during next solar eclipses, with other types of pendulums. Then a group of Geophysicists, from the Science Academy of China, used an accurate digital gravimeter to measure Earth Gravity acceleration during March 09, 1997 solar eclipse. Their gravimeter recorded two drops of Earth Gravity acceleration (respectively 5.02 and 7.7 µ Gals) before and during first and last contacts of the Moon disc. However there was no acceleration drop during eclipse totality. Same phenomena were confirmed later, during next solar eclipses, with the same gravimeter. No classical causes for these facts were found, since modern gravimeters take care of temperature and atmospheric pressure variations. We analyse the effect of Moon rotation, and of solar Corona mass, in the frame of our Quantum model of Inertia and of Gravitation. The model predicts that Moon / Earth Gravity acceleration changes, when the Moon direction is close to the Sun one, as observed from the gravimeter place. That phenomenon should be tied to Quantum fluctuations dispersion by matter. Recorded measurements confirm that interpretation.

A Next Generation Gravity Mission (NGGM) concept for measuring the Earth's variable gravity field has been recently proposed by ESA. The mission objective consists in measuring the temporal variations of the Earth gravity field over a long-time span, with very high spatial and temporal resolutions. This paper focuses on the guidance, navigation and control (GNC) design for the science phase of the NGGM mission. NGGM will consist of a two-satellite long-distance formation like GRACE, where each satellite will be controlled to be drag-free like GOCE. Satellite-to-satellite distance variations, encoding gravity anomalies, will be measured by laser interferometry. The formation satellites, distant up to 200 km, will fly in a quasi-polar orbit at an Earth altitude between 300 and 450 km. Orbit and formation control counteract bias and drift of the residual drag-free accelerations, in order to reach orbit/formation long-term stability. Drag-free control allows the formation to fly counteracting the atmospheric drag, ideally subject only to gravity. Orbit and formation control, designed through the innovative Integrated Formation Control (IFC), have been integrated into a unique control system, aiming at stabilizing the formation triangle consisting of satellites and Earth Center of Masses. In addition, both spacecraft must align their control axis to the satellite-to-satellite line (SSL) with micro-radian accuracy. This is made possible by specific optical sensors and the inter-satellite laser interferometer, capable of materializing the SSL. Such sensors allow each satellite to pursue an autonomous alignment after a suitable acquisition procedure. Pointing control is severely constrained by the angular drag-free control, which must ideally zero the angular acceleration vector, in the science frequency band. The control unit has been designed according to the Embedded Model Control methodology and is organized in a hierarchical way, where the drag-free control plays the role of a wide-band inner loop, and orbit/formation and attitude/pointing controls are the narrow band outer loops. The relevant state equations were converted to discrete time providing the embedded model, a fundamental part of the control unit. The state predictor, control law and reference generator were built on and interfaced to the embedded model. Simulated results, via a high-fidelity simulator, prove the concept validity and show that the control performances are in agreement with the defined mission requirements. Indeed, the presented control strategy is shown to be capable of keeping the attitude and formation variables stable within the required boundaries, all over the 10-year mission, through a low-thrust authority in the order of a few milli-Newton.

We present the results of photometric observations of the TOPEX/Poseidon satellite performed during 2008–2016. The satellite become space debris after a failure in January, 2006, in a low Earth orbit. In the Laboratory of Space Research of Uzhhorod National University 73 light curves of the spacecraft were obtained. Standardization of photometric light curves is briefly explained. We have calculated the color indices of reflecting surfaces and the spin rate change. The general tendency of the latter is described by an exponential decay function. The satellite spin periods based on 126 light curves (including 53 light curves from the MMT-9 project operating since 2014) were taken into account. In 2016 the period of its own rotation reached its minimum of 10.6 s. A method to derive the direction of the spin axis of an artificial satellite and the angles of the light scattered by its surface has been developed in the Laboratory of Space Research of Uzhhorod National University. We briefly describe the “Orientation” program used for these purposes. The orientation of the TOPEX/Poseidon satellite in mid-2016 is given. The angle of precession β = 45°–50° and period of precession P pr = 141.5 s have been defined. The reasons for the identified nature of the satellite’s own rotation have been found. They amount to the perturbation caused by a deviation of the Earth gravity field from a central-symmetric shape and the presence of moving parts on the satellite.

The recent discovery that the Earth is retarding each year by a fraction of a second its revolution around the Sun led to investigations and speculations about the cause of such a defect in what was thought to be a perfect clock. The emission of thermal radiation by the Sun cannot justify this discrepancy even if a fraction of unknown dark matter is added to increase the Sun mass loss. The increase of distance of Earth/Moon center of mass from the Sun is estimated of the order of one centimeter per year. However experimental measurements suggest values of the order from 5 to 15 centimeters, hard to be measured for the distances involved. To solve this problem, sophisticated orbital analysis has been proposed, changes in the gravitational constant G have been suggested and more precise mass/distance measurements in the solar system, asteroids included, have been requested. The present paper shows how the use of an elementary model for the Earth/Moon orbit together with a new theory for the gravitational constant G, coherent with Newton law, can solve this problem. The comprehension of gravity, the ultimate unexplained force of the universe, is the key to solve this and the many remaining question marks in the books of physics.

Basing on the energy conservation, an analysis method on the gravity of antimatter is proposed by investigating the change of potential energy during high energy photon transfers to electron and positron in earth gravity field. Potential energy equations are deducted and proved that the force between matter and antimatter is attractive, and then the force between antimatter and antimatter is proved to be attractive too. So the gravity is attractive without considering matter or antimatter.

The Earth-viewed images acquired by the space probe OSIRIS-REx during its Earth gravity assist flyby maneuver on 22 September 2017 provided an opportunity to radiometrically calibrate the onboard NavCam imagers. Spatially-, temporally-, and angularly-matched radiances from the Earth viewing GOES-15 and DSCOVR-EPIC imagers were used as references for deriving the calibration gain of the NavCam sensors. An optimized all-sky tropical ocean ray-matching (ATO-RM) calibration approach that accounts for the spectral band differences, navigation errors, and angular geometry differences between NavCam and the reference imagers is formulated in this paper. Prior to ray-matching, the GOES-15 and EPIC pixel level radiances were mapped into the NavCam field of view. The NavCam 1 ATO-RM gain is found to be 9.874 &times, 10&minus, 2 Wm&minus, 2sr&minus, 1&micro, m&minus, 1DN&minus, 1 with an uncertainty of 3.7%. The ATO-RM approach predicted an offset of 164, which is close to the true space DN of 170. The pre-launch NavCam 1 and 2 gains were compared with the ATO-RM gain and were found to be within 2.1% and 2.8%, respectively, suggesting that sensor performance is stable in space. The ATO-RM calibration was found to be consistent within 3.9% over a factor of &plusmn, 2 NavCam 2 exposure times. This approach can easily be adapted to inter-calibrate other space probe cameras given the current constellation of geostationary imagers.

This paper describes the sensitivity of both the orbital frame domain selection and the gravity model on the performance of on-board real-time orbit determination. Practical error sources, which affect the navigation solution of spaceborne global positioning system (GPS) receivers, are analyzed first. Then, a reasonable orbital frame (radial, in-track, cross-track (RIC)) is proposed to clearly represent the characteristics of the error in order to improve the performance of the orbit determination (OD) logic. In addition, the sensitivity of the gravity model affecting the orbit determination logic is analyzed by comparison with the precise orbit ephemeris (POE) of the Challenging Minisatellite Payload (CHAMP) satellite, and it is confirmed that the Gravity Recovery And Climate Experiment (GRACE) Gravity Model 03 (GGM03) outperforms the Earth Gravity Model 1996 (EGM96). The effects of both proposed orbit frames and the gravity model on the orbit determination logic are verified using a GPS simulator and observation data from the CHAMP satellite. Moreover, the practical performance of on-board real-time orbit determination logic is verified by updating the software of the spaceborne GPS receiver, GPS-12, on DubaiSat-2 operating at low Earth orbit (LEO). The results show that the position accuracy of on-board real-time orbit determination logic in GPS-12 is improved by 59%, from 12.6 m (1 &sigma, ) to 5.1 m (1 &sigma, ), after applying the proposed methods. The velocity accuracy is also improved by 57%, from 13.7 mm/s (1 &sigma, ) to 5.9 mm/s (1 &sigma, ).

Fluctuations of the earth's gravity field are a major noise source for ground-based experiments investigating general relativity phenomena such as Gravitational Waves (GWs). Mass density variations caused by local seismic or atmospheric perturbations determine spurious differential displacements of the free falling test masses, what is called Gravity Gradient Noise (GGN); it mimics GW effects. This GGN is expected to become dominant in the infrasound domain and must be tackled for the future realization of observatories exploring GWs at low frequency. GGN will be studied with the MIGA experiment, a demonstrator for low frequency GW detection based on atom interferometry - now in construction at the low noise underground laboratory LSBB in France. MIGA will provide precise measurements of local gravity, probed by a network of three free-falling atom test masses separated up to 150~m. We model the effect of GGN for MIGA and use seismic and atmospheric data recorded at LSBB to characterize their impact on the future measurements. We show that the antenna will be able to characterize GGN using dedicated data analysis methods., Comment: 10 pages, 13 figures

For studies of the European Space Agency ESA, Fraunhofer ILT develops and builds narrowband, power-stabilized fundamental mode fiber amplifiers especially for future space-based gravitational-wave detectors, e.g. LISA, and for Earth gravity field missions. In this paper, we present the status of our ongoing work, based on a highly stable fiber amplifier designed for a Next Generation Gravity field Mission (NGGM) pre-study, towards power scaling as well as enhancement of the Technology Readiness Level (TRL). Our amplifier has already demonstrated to meet the requirements for future gravity field missions. It features a design that is free of stimulated Brillouin scattering (SBS) and a feedback loop for power stabilization.

In this chapter we try to outline the main concepts used to estimate and describe the gravity field. The aim is to show the interplay between the geometry of the field, represented in terms of equipotential surfaces and plumb lines, and the mathematical relations that connect observable gravity values to the gravity potential. This is especially done in a linearized form, after a normal potential is defined, based on the ellipsoidal geometry, and used as reference function in the subsequent linearization.

We report the improved test of frame-dragging, an intriguing phenomenon predicted by Einstein's General Relativity, obtained using 7 years of Satellite Laser Ranging (SLR) data of the satellite LARES (ASI, 2012) and 26 years of SLR data of LAGEOS (NASA, 1976) and LAGEOS 2 (ASI and NASA, 1992). We used the static part and temporal variations of the Earth gravity field obtained by the space geodesy mission GRACE (NASA and DLR) and in particular the static Earth's gravity field model GGM05S augmented by a model for the 7-day temporal variations of the lowest degree Earth spherical harmonics. We used the orbital estimator GEODYN (NASA). We measured frame-dragging to be equal to 0.9910 +/- 0.02, where 1 is the theoretical prediction of General Relativity normalized to its frame-dragging value and +/- 0.02 is the estimated systematic error due to modelling errors in the orbital perturbations, mainly due to the errors in the Earth's gravity field determination. Therefore, our measurement confirms the prediction of General Relativity for frame-dragging with a few percent uncertainty., Comment: Submitted on September 27, 2019; accepted for publication on October 8, 2019 and published on October 23, 2019 in The European Physical Journal C: Eur. Phys. J. C (2019) 79:872 https://doi.org/10.1140/epjc/s10052-019-7386-z

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.

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...

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.

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.

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°.

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

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.

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.

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.

Laser ranging satellites have proved their efficiency for high precision testing of the effect of frame-dragging, one of remarkable predictions of the General Relativity. The analysis of the randomness properties of the residuals of LAGEOS and LAGEOS 2 satellites reveals the role of the thermal thrust -- Yarkovsky effect -- on the satellite which was in the orbit for longer period (LAGEOS). We also compute Earth's tidal modes affecting the satellite LARES. The recently obtained 5\% accuracy limit reached for the frame dragging effect based on the 3.5 year data of LARES analysed together with those of LAGEOS satellites and using the Earth gravity model of GRACE satellite, is also represented., 7 pages 3 figures

Recently, Ciufolini et al. reported on a test of the general relativistic gravitomagnetic Lense-Thirring effect by analyzing about 3.5 years of laser ranging data to the LAGEOS, LAGEOS II, LARES geodetic satellites orbiting the Earth. By using the GRACE-based GGM05S Earth's global gravity model and a linear combination of the nodes $\Omega$ of the three satellites designed to remove the impact of errors in the first two even zonal harmonic coefficients $J_2,~J_4$ of the multipolar expansion of the Newtonian part of the Earth's gravitational potential, they claimed an overall accuracy of $5\%$ for the Lense-Thirring caused node motion. We show that the scatter in the nominal values of the uncancelled even zonals of degree $\ell = 6,~8,~10$ from some of the most recent global gravity models does not yet allow to reach unambiguously and univocally the expected $\approx 1\%$ level, being large up to $\lesssim 15\%~(\ell=6),~6\%~(\ell=8),~36\%~(\ell=10)$ for some pairs of models., Comment: LaTeX2e, 14 pages, 9 tables, no figures. The European Physical Journal C, at press

We will discuss the following question: is the present day normal gravity field calculation suitable from the aspect of the applied geophysics/gravimetry? Today, the normal field or theoretical gravity is on a regular basis strictly related to a model of rotational biaxial ellipsoid with one important property, namely the constant potential on its surface. This condition, however, would require a specific density distribution within the model. Another issue is the treating the Earth atmosphere and topography. These masses are simply moved into the interior of such ellipsoid and “dissolved” there. In short, this approach does not fit the geophysical reality very well. Instead, in our contribution, we attempt to calculate the normal field as the gravity effect of a layered rotational ellipsoid, namely the gravitational effect of a suitable set of homeoid shells bounded by two similar ellipsoids having a constant ratio of axes, plus the centrifugal component. We believe that this approach will fit the structure and density distribution within the Earth much better. We analyze and present the primary differences between the two approaches, and we also discuss the relation of the normal field to the free-air correction.

The paper analyzes the possibility of the use of a gravity-assist maneuver for flight to Jupiter. The advantage of the Earth gravity-assist maneuver in comparison with the direct transfer in terms of reduction of amount of energy required per transfer is considered. Quantitative and qualitative evaluations of two transfer profiles are given.

The main principle and mathematical model of GOCE kinematic orbit adjustment for Earth gravity field model (EGM) validation and accelerometer calibration are presented. Based on 60 days GOCE kinematic orbits with 1–2 cm accuracy and accelerometer data from 2009-11-02 to 2009-12-31, the RMS-of-fit (ROF) of them using EGM2008, EIGEN-5C, ITG-GRACE2010S and GOCO01S up to 120, 150 and 180 degree and order (d/o) are evaluated and compared. The scale factors and biases of GOCE accelerometer data are calibrated and the energy balance method (EBM) is performed to test the accuracy of accelerometer calibration. The results show that GOCE orbits are also sensitive to EGM from 120 to 150 d/o. The ROFs of EGMs with 150 and 180 d/o are obviously better than those of EGMs with 120 d/o. The ROFs of GOCO01S and ITG-GRACE2010S are almost the same up to 120 and 150 d/o, which are about 3.3 cm and 1.8 cm, respectively. They are far better than those of EGM2008 and EIGEN-5C with the same d/o. The ROF of GOCO01S with 180 d/o is about 1.6 cm, which is the best one among those EGMs. The accelerometer calibration accuracies (ACAs) of ITG-GRACE2010S and GOCO01S are obviously higher that those of EGM2008 and EIGEN-5C. The ACA of GOCO01S with 180 d/o is far higher than that of EGMs with 120 d/o, and a little higher than that of ITG-GRACE2010S with 150 d/o. It is suggested that the newest released EGM such as GOCO01S or GOCO02S till at least 150 d/o should be chosen in GOCE precise orbit determination (POD) and accelerometer calibration.

In the paper a theory of motion of low velocity penetrator (LVP) is presented and confronted with the results of tests of a mole-like penetrator performed in material similar to lunar regolith. This theory is based on the fact that the considered LVP comprises, in principle, of at least three moveable mechanical parts: the penetrator casing, the hammer and the support mass, and are surrounded by the regolith. For the first time equations of motion of such system in the mechanically resistive medium are derived and numerically solved. The model is focused on the interactions between LVP subsystems and and influence of these interactions on LVP general behavior. The interactions with surrounding regolith were simplified and equations describing these interactions contain two parameters which were determined during experimental campaigns of mole KRET (LVP penetrator developed at the Space Research Centre PAS). Two major results were achieved: (i) LVP stability map as a function of the LVP parameters responsible for energy distribution in the system and (ii) duration of the particular phases of the LVP movement. The stability of the LVP forward motion was analyzed with respect to mass parameters p 1 and p 2 and stiffness of the springs k d and k r , and let to define the region where LVP is able to move forward in both Earth gravity and near zero gravity environment. The duration of particular phases of the LVP motion allows better understanding of cross dependencies between LVP subsystems and future ways to improve the design.

This article extends the results of the experiments at the earth gravity described in Part I to the case of the parabolic flight experiments conducted in Bordeaux, France, in June 2013 on a Novespace plane during a parabolic flight campaign that was supported by NASA and ESA. This second part details the droplet generator, heating system and the experimental rig developed for the flight experiments at zero gravity (0g) and supergravity (1.8g). Even though the setup used in the flights was an offshoot of the setup developed in the ground experiments of Part I, it had a number of modifications dictated by safety and space restrictions. After the experimental Section 1, the results of the heat flux measurements during the parabolic flights are described and discussed in Section 2, followed by conclusions.

The ITER poloidal field (PF) feeder busbar which carries 52 kA current will be subjected to high Lorentz force due to the background magnetic field aroused by the coils and the self-field between a pair of PF busbars. Peak magnetic force requires dense supports. But to minimize the heat load to the busbars as well as the cryo-pipes, fewer and thinner supports design is proposed, so a balance between mechanical strength and thermal insulation performance should be achieved. This paper presents the analysis on support system design for ITER 4th PF feeder including the S-bend box, the cryostat feed-through, the in-cryostat-feeder. An electric–magnetic coupled analysis aims to get real magnetic force load under the worst scenario, then the Lorentz force result is imported into the mechanical analysis, applied on the busbars, meanwhile the busbar supports, the containment duct, the gimbals, the separator plate and the cryo-pipes, the cold mass supports are contained in the finite element model to check the full system performance under Lorentz forces, earth gravity and thermal contract at 4.5 K. Based on the analytical results, the quantity and the spaces between busbar supports in the 4th PF feeder have been studied and the detail design optimized.

This paper shows the effect of self-shadowing on the coupled attitude–orbit dynamics of objects with high area-to-mass ratios (HAMR) in simulating standard multi layer insulation materials (MLI) as tilted single rigid sheets. Efficient and computationally fast self-shadowing methods have been developed. This includes an approximate self-shadowing method and a rapid exact self-shadowing method. Accuracy considerations are made and the effect of a chosen tessellation is shown. The coupled orbit–attitude perturbations of solar radiation pressure and Earth gravity field are taken into account. The results are compared to the attitude–orbit dynamics, when neglecting self-shadowing effects. An averaged physical shadow-map model is developed and compared to the full self-shadowing simulation. The combined effect of solar radiation pressure and self-shadowing leads to a rapid spin-up of the objects, even though they have uniform reflection properties. As a result, the observed brightness of these objects is subject to rapid changes.