Earth's Gravitational Field Research Articles

Chaotic libration and control of a space tether-sail system in Earth polar orbits with J2 perturbation

The recently proposed space tether-sail system could enable various interesting and important potential space missions thanks to its thin and long connecting tether and solar radiation pressure (SRP) force without consuming propellants. This paper focuses on nonlinear libration and its control of a tether-sail system in Earth polar orbits. Firstly, nonlinear coupled in-plane and out-of-plane dynamics of the system with a rigid mass-distributed tether and two point masses (a chief satellite and sail respectively) is established using the Lagrangian equation method. Secondly, the predicted occurrence of chaotic in- and out-of-plane librational motions is verified utilizing numerical tools such as presenting the time history of libration, the phase plane, the Poincaré section and power spectral density(PSD). Specifically, the paper investigates the sensitivity of nonlinear dynamical responses to initial values, focuses on the chaotic motion caused by the coupling between the in- and out-of-plane librations, the J2 perturbation of the Earth gravitational field and the small eccentricity of the orbits, also studies the nonlinear librational characteristics influenced by the initial mechanical energy (the Hamiltonian). Thirdly, chaotic librational motions will be controlled merely using modulatable SRP force by the sail propellantlessly. A sliding mode controller based on exponential approaching law is developed. To mitigate the effects of control torque saturation, an input compensator based on Radial Basis Function (RBF) neural network is designed. In addition, to address the cumbersome and inefficient manual tuning of control parameters for the sliding mode controller, a parameter tuning algorithm based on Learning Automata is designed. This algorithm is capable of tuning a high-quality set of controller parameters within 100 iterations. The effectiveness of the propellantless actuators for chaotic libration motion control and developed control algorithm is supported by numerical simulations.

Modeling the Recovery of the Earth's Gravitational Field from Satellite Measurements Using Parallel Computations

Modeling the Recovery of the Earth's Gravitational Field from Satellite Measurements Using Parallel Computations

GRACE and GRACE Follow‐On Gravity Observations of Intermediate‐Depth Earthquakes Contrasted With Those of Shallow Events

AbstractEarthquakes involve mass redistribution within the solid Earth and the ocean, and as a result, perturb the Earth's gravitational field. For most of the shallow (<60 km) earthquakes with Mw > 8.0, the GRACE satellite gravity measurements suggest considerable volumetric disturbance of rocks. At a spatial scale of hundreds of km, the effect of volumetric change exceeds gravity change by vertical deformation; for example, negative gravity anomalies associated with volumetric expansion are characteristic patterns after shallow thrust events. In this study, however, we report contrasting observations of gravity change from two intermediate‐depth (100–150 km) earthquakes of 2016 & 2017 Mw 8.0 (two combined) Papua New Guinea thrust faulting events and 2019 Mw 8.0 Peru normal faulting and highlight the importance of compressibility in earthquake deformation. The combined 2016/17 thrust events resulted in a positive gravity anomaly of 5–6 microGal around the epicenter, while the 2019 normal faulting produced a negative gravity anomaly of 3–4 microGal. Our modeling found that these gravity changes are manifestation of vertical deformation with limited volumetric change, distinct from gravity changes after the shallow earthquakes. The stronger resistance of rocks to volume change at intermediate‐depth results in largely incompressible deformation and thus in a gravity change dominated by vertical deformation. In addition, malleable rocks under high pressure and temperature at depth facilitated substantial afterslip and/or fast viscoelastic relaxation causing additional vertical deformation and gravity change equivalent to the coseismic change. For the Papua New Guinea events, this means that postseismic relaxation enhanced coseismic uplift and relative sea level decrease.

Advancements in geodesy techniques for Arctic region monitoring

The Arctic region is undergoing unprecedented environmental changes due to global climate change, necessitating robust monitoring and research efforts. Geodesy, the science of accurately measuring Earth's shape, orientation, and gravitational field, plays a critical role in understanding these changes. This article explores the applications, challenges, and future directions of geodesy in the Arctic. Satellite-based techniques such as GNSS, SAR, and satellite altimetry are utilized to monitor ice mass loss, sea level rise, and land deformation with high precision. Challenges in Arctic geodesy include harsh environmental conditions, data accuracy, and the integration of multi-source data. Despite these challenges, ongoing advancements in satellite technology, data processing algorithms, and collaboration initiatives hold promise for addressing these issues and improving our understanding of Arctic environmental dynamics. By leveraging geodesy techniques and emerging technologies, researchers can contribute to the sustainable management of the Arctic environment and its broader implications for global climate change mitigation and adaptation.

Search for Spin-Dependent Gravitational Interactions at Earth Range.

Among the four fundamental forces, only gravity does not couple to particle spins according to the general theory of relativity. We test this principle by searching for an anomalous scalar coupling between the neutron spin and the Earth's gravity on the ground. We develop an atomic gas comagnetometer to measure the ratio of nuclear spin-precession frequencies between ^{129}Xe and ^{131}Xe, and search for a change of this ratio to the precision of 10^{-9} as the sensor is flipped in Earth's gravitational field. The null results of this search set an upper limit on the coupling energy between the neutron spin and the gravity on the ground at 5.3×10^{-22} eV (95% confidence level), resulting in a 17-fold improvement over the previous limit. The results can also be used to constrain several other anomalous interactions. In particular, the limit on the coupling strength of axion-mediated monopole-dipole interactions at the range of Earth's radius is improved by a factor of 17.

Spherical harmonics representation of the gravitational phase shift

We investigate the general relativistic phase of an electromagnetic wave as it propagates in the gravitational field of the Earth, which is modeled as an isolated, weakly aspherical gravitating body. We introduce coordinate systems to describe light propagation in the Earth's vicinity along with the relevant coordinate transformations, and discuss the transformations between proper and coordinate times. We represent the Earth's gravitational field using Cartesian symmetric trace-free (STF) mass multipole moments. The light propagation equation is solvable along the trajectory of a light ray to all STF orders $\ensuremath{\ell}$. Although we focus primarily on the quadrupole ($\ensuremath{\ell}=2$), octupole ($\ensuremath{\ell}=3$), and hexadecapole ($\ensuremath{\ell}=4$) cases, our approach is valid to all orders. We express the STF moments via spherical harmonic coefficients of various degree and order, ${C}_{\ensuremath{\ell}k},{S}_{\ensuremath{\ell}k}$. The result is the gravitational phase shift expressed in terms of the spherical harmonics. These results are new. We also consider contributions due to tides and the Earth's rotation. We estimate the characteristic magnitudes of each term of the resulting overall gravitational phase shift. The terms assessed are either large enough to impact current-generation clocks or will become significant as future-generation clocks offer greater sensitivity. Our formulation is useful for many practical and scientific applications, including space-based time and frequency transfers, relativistic geodesy and navigation, as well as quantum communication links and space-based tests of fundamental physics.

Building a model of the Earth's gravitational field within the Caribbean Sea based on satellite altimetry data

Methods for processing measurement information collected over the past 30 years by altimetry spacecraft with various measurement technologies and orbit characteristics are systematized and described. The description and classification of measurement information files is given. Based on the removal-recovery method, a software package for determining the characteristics of the gravitational field and the figure of the Earth by satellite altimetry has been developed. On the example of a geologically complex and seismically active region (the Caribbean Sea), a model of the gravity field (gravity anomalies) was constructed and its accuracy characteristics were evaluated. The calculated standard deviation of gravity anomalies from the data of the EGM2008 global model does not exceed 4 mGal in the open sea and 14 mGal in the coastal zone, which corresponds to the international level. At the moment, a digital interactive gravity model of the Global Ocean is used to solve applied problems of geophysics and geology, in particular, to forecast oil and gas fields.

Исследование точности глобальных моделей геопотенциала EGM2008, EIGEN-6C4, GECO, SGG-UGM-1, SGG-UGM-2, XGM2019 на территории Российской Федерации

The improvement of the gravimetric knowledge of the Russian Federation and the creation of new models of the Earth's gravitational field (EGF) in the form of spherical harmonics of the geopotential set the task of choosing the most suitable model based on the characteristics of the gravitational field on the territory of Russia. The satellite gravity missions CHAMP, GRACE and GOCE provide a homoge-neous and almost complete global coverage of information about the Earth's gravitational field. The paper presents the results of a study of the accuracy of modern high-degree global geopotential models for determining various characteristics of the Earth's gravitational field on the territory of the Russian Federation. The models EGM2008, EIGEN-6C4, GECO, SGG-UGM-1, SGG-UGM-2 and XGM2019 were used as the tested geopotential models. The results of the study are presented in the form of statistical parameters and histograms of the distribution of differences g between the gravity values obtained from ground-based gravimetric measurements and calculated from model data. The high-degree model EIGEN-6C4 has a smaller standard deviation ( = 5,24 mGal) compared to other geopotential models. Based on the distribution of differences, we can conclude that the EIGEN 6C4 model is the most suitable for the territory of the Russian Federation.

Groundwater storage change estimation using GRACE data and Google Earth Engine: A basin scale study

Groundwater is the main source of drinking and irrigation water available in the majority of the Ghaghara River basin (GRB), which is a trans-boundary river basin and characterized by a sub-humid climate that possesses a lot of uncertainty due to non-precise measurement of water and energy flux. The basin is classified as an upper mountainous basin, geographical coverage of the GRB covers countries like China, Nepal, and India. The study is intended to estimate variation in groundwater storage based on satellite observations of the time-varying Earth's gravitational field from the Gravity Recovery and Climate Experiments (GRACE). In this study, soil moisture has been estimated from the TerraClimate data and rainfall from the Climate Hazards Group InfraRed Precipitation with Station (CHIRPS) using Google Earth Engine (GEE). The long-term trends and spatio-temporal variation of groundwater have been analyzed from April 2002 to January 2017. The groundwater trend has shown a drastic decline in storage level. On an average 2.28 cm of decline in groundwater storage per year and a total of 36.61 cm of decline in groundwater storage from 2002 to 2017 has been observed. The GRACE data showed that the southwest region of the GRB has a high storage level. The present research findings outline that implementation of suitable and a feasible water conservation scheme is necessary for improved management of water resources in the entire GRB.

Control system for ion Penning traps at the AEgIS experiment at CERN

The AEgIS experiment located at the Antiproton Decelerator at CERN aims to measure the gravitational fall of a cold antihydrogen pulsed beam. The precise observation of the antiatoms in the Earth gravitational field requires a controlled production and manipulation of antihydrogen. The neutral antimatter is obtained via a charge exchange reaction between a cold plasma of antiprotons from ELENA decelerator and a pulse of Rydberg positronium atoms. The current custom electronics designed to operate the 5 and 1 T Penning traps are going to be replaced by a control system based on the ARTIQ & Sinara open hardware and software ecosystem. This solution is present in many atomic, molecular and optical physics experiments and devices such as quantum computers. We report the status of the implementation as well as the main features of the new control system.

Оптимізація перельотів між низькими орбітами з суттєвою різницею довгот висхідних вузлів

At present, satellite systems, each comprising hundreds of satellites, are, and are to be, deployed in low orbits. In addition, existing satellite systems are replenished. There has appeared a trend towards the development of modular satellites, which will lead to the development of easy-to-maintain spacecraft consisting of many small structural modules with standardized interface mechanisms. To extend the life of all these systems and reduce their maintenance cost, it is advisable to develop a system for their maintenance. Despite the relatively large number of works on the rendezvous problem, this problem is considered in a somewhat simplified formulation, which is not sufficient for spacecraft servicing in low orbits. As a rule, the consideration is limited to coplanar rendezvous problems in an impulse formulation. In real conditions, rendezvous maneuvers in low orbits are nontrivial. As is known, the orbital parameters of low-orbit spacecraft may differ significantly: the difference in the longitude of ascending nodes (LAN) may reach tens and even hundreds of degrees. Because of this, the energy consumption for an orbital plane change becomes unacceptably high for modern service spacecraft. This energy consumption can be reduced by using the precession of the line of nodes due to the non-centrality of the Earth's gravitational field. A waiting maneuver of a service spacecraft in a well-chosen orbit makes it possible to eliminate the mismatch between the LANs of the service spacecraft’s parking and destination orbits, thus significantly reducing the orbital transfer energy consumption. However, the long wait time of the service spacecraft in its parking orbit significantly increases the total orbital transfer time. The aim of this article is to develop a mathematical model of bicriteria optimization of a transfer of a service spacecraft with a low constant thrust engine between low near-circular orbits with significantly different LANs. This problem is solved by averaging the service spacecraft’s dynamics equations over a fast parameter and using a genetic algorithm of global Pareto optimization. The novelty of the results obtained lies in a formulation of a bicriteria optimization problem and the development of a mathematical model for choosing an optimal service spacecraft parking orbit. The mathematical model developed may be used in planning service spacecraft transfers between low near-circular orbits with significantly different LANs.

On the development of a global model of the Earth's gravitational field based on integral approach

On the development of a global model of the Earth's gravitational field based on integral approach

A study of the EGM2008 model of Earth's gravitational field

AbstractThe Earth Gravity Model 2008 (EGM2008) is now some years old, and yet information on how to use it to calculate Earth's gravity remains obscure outside the field of geodesy. We describe the mathematics necessary to implement EGM2008, and use this to discuss several points of the model: its sensitivity to the number of spherical harmonics being summed, nuances and a trap for physicists and mathematicians in the normalisation it uses, and a comparison with other work. We conclude that one must not overestimate the precision shown by a global-fit model such as EGM2008.

Application of the wavelet transformation theory in the algorithm for constructing a quasigeoid model

Purpose. To investigate the interaction of geodesic and normal altitude indicators according to quasigeoid data, the joint use of space measurements and those performed on the Earths surface in the implementation of geodetic tasks. In this article, the task is to create a calculation algorithm for further research on the quasigeoid model and the application of the model in solving geodetic problems. Methodology. Reliable determination of the height anomaly requires great accuracy, therefore, the theory of wavelet-transformation was used in the model of the variant of space technologies as an alternative to the laborious leveling of the Earths surface, which characterizes the actual fluctuations from the normal of the Earths gravitational field, when calculating the mean square deviations of the plumb line is an urgent task. Findings. A block diagram of the calculation algorithm has been compiled using a software package to solve the boundary problem of physical geodesy, in which the Earths surface is subject to modern space measurements. Originality. The use of wavelet analysis for processing information from satellite data in geodesy improves the results of image classification, and the coefficients of the wavelet transformation can be used as indicators for recognizing the coordinates of points with high accuracy. Practical value. Application of the theory of wavelet transformations as a powerful mathematical tool for solving problems of geodetic information, data compression and recovery, increasing computing performance, encoding information.

An experimental numerics approach to the terrestrial brachistochrone

We revisit the classical and solved problem of the terrestrial brachistochrone, the fastest path between two points in earth's gravitation field, by an approach we refer to as experimental numerics. By this term we mean arriving at a qualified guess by deliberately taking inspiration from numerical results that are easily available.Since in many cases verification is easier than derivation, this approach may have some educational merits.Current software tools such as Jupyter Notebooks blend coding with documentation and allow leveraging this approach to enable new ways in modern teaching.The intended audience are graduate students with prior knowledge of multivariate calculus, ordinary differential equations (ODEs), calculus of variations and classical physics, particularly mechanics.

A Review of GNSS/GPS in Hydrogeodesy: Hydrologic Loading Applications and Their Implications for Water Resource Research.

Hydrogeodesy, a relatively new field within the earth sciences, is the analysis of the distribution and movement of terrestrial water at Earth's surface using measurements of Earth's shape, orientation, and gravitational field. In this paper, we review the current state of hydrogeodesy with a specific focus on Global Navigation Satellite System (GNSS)/Global Positioning System measurements of hydrologic loading. As water cycles through the hydrosphere, GNSS stations anchored to Earth's crust measure the associated movement of the land surface under the weight of changing hydrologic loads. Recent advances in GNSS‐based hydrogeodesy have led to exciting applications of hydrologic loading and subsequent terrestrial water storage (TWS) estimates. We describe how GNSS position time series respond to climatic drivers, can be used to estimate TWS across temporal scales, and can improve drought characterization. We aim to facilitate hydrologists' use of GNSS‐observed surface deformation as an emerging tool for investigating and quantifying water resources, propose methods to further strengthen collaborative research and exchange between geodesists and hydrologists, and offer ideas about pressing questions in hydrology that GNSS may help to answer.

A novel nuclear emulsion detector for measurement of quantum states of ultracold neutrons in the Earth's gravitational field

Hypothetical short-range interactions could be detected by measuring the wavefunctions of gravitationally bound ultracold neutrons (UCNs) on a mirror in the Earth's gravitational field.Searches for them with higher sensitivity require detectors with higher spatial resolution.We developed and have been improving an UCN detector with a high spatial resolution, which consists of a Si substrate, a thin converter layer including ^10B_4C, and a layer of fine-grained nuclear emulsion.Its resolution was estimated to be less than 100 nm by fitting tracks of either ^7Li nuclei or α-particles, which were created when neutrons interacted with the ^10B_4C layer.For actual measurements of the spatial distributions, the following two improvements were made.The first improvement was to establish a method to align microscopic images with high accuracy within a wide region of 65 mm × 0.2 mm.We created reference marks of 1 μm and 5 μm diameter with an interval of 50 μm and 500 μm, respectively, on the Si substrate by electron beam lithography and realized a position accuracy of less than 30 nm.The second improvement was to build a holder for the detector that could maintain the atmospheric pressure around the nuclear emulsion to utilize it under a vacuum during exposure to UCNs.The intrinsic resolution of the improved detector was estimated to be better than0.56(8) μm by evaluating the blur of a transmission image of a gadolinium grating taken by cold neutrons.The evaluation included the precision of the gadolinium grating.A test exposure was conducted to obtain the spatial distribution of UCNs in the quantized states on a mirror in the Earth's gravitational field.The distribution was obtained, fitted with the theoretical curve, and turned out to be reasonable for UCNs in quantized states when we considered a blurring of 6.9 μm.The blurring was well explained as a result of neutron refraction due to the large surface roughness on the upstream side of the Si substrate.By using a double-side-polished Si substrate, a resolution of less than 0.56 μm is expected to be achieved for UCNs.

Sliding mode control for attitude maneuvers of Helianthus solar sail

The recent successes of demonstration missions based on solar sail technology have paved the way for designing new mission scenarios with propellantless propulsion systems. In this context, the Italian Space Agency has been supporting a preliminary study of Helianthus, an innovative concept of deep-space mission, which is designed to use a solar sail to generate an artificial equilibrium point in the Sun–Earth gravitational field. Exploiting such a vantage point, located along the Sun–Earth line, Helianthus will be able to perform scientific observations of the solar corona and send to Earth an early warning information in case of solar flares. The attitude control system required to maintain the spacecraft at the unstable artificial equilibrium point is actuated by electrochromic devices, which change their optical properties in response to an electric input, thus generating suitable control torques. The aim of this work is to illustrate a possible control strategy that guarantees the spacecraft station keeping with feasible attitude maneuvers. A nonlinear sliding mode controller is used for the robustness properties it guarantees, and its performance is illustrated in some test maneuvers.

The estimation of frequency shift when solving the problem of chronometric leveling by using satellite navigation technologies

The paper deals with the problem of frequency shift effect of quantum standards caused by moving them in the gravitational field of Earth. The study of this effect is highly topical for solving the problem of chronometric leveling when designing the systems of orthometric altitudes estimation on the geoid.

Tracking the source direction of surface mass loads using vertical and horizontal displacements from satellite geodesy: A case study of the inter-annual fluctuations in the water level in the Great Lakes

Climate oscillations with seasonal and longer periods drive surface water cycles and quasi-cycles at regional and global scales. Changes in terrestrial water storage produce responses in the Earth's gravitational field and crustal deformation. Here, we use techniques from the Global Positioning System (GPS) and the Gravity Recovery and Climate Experiment (GRACE) to reveal a normal pattern of inter-annual fluctuations in the water level in the North American Great Lakes (GL). The GRACE-estimated time series was in good agreement with in situ water level measurements from 2002 to 2018, especially in terms of phases. The amplitude of 3–4 inter-annual signals in water thickness was 4–6 cm, which is equivalent to a 50–75 km3 oscillation in surface water volume within the entire GL. The slightly larger annual and inter-annual fluctuation amplitudes estimated using GRACE data indicate that the aquifer system of the GL and its surroundings also contributes to seasonal mass changes. After 2013, water levels in the GL region rose abruptly, and the water mass increased by nearly 270 km3 until the end of 2018. We also used GPS- and GRACE-derived three-component displacements (vertical, northward, and eastward) to identify load patterns. GPS- and GRACE-estimated maximum probability source directions based on multi-channel singular spectrum analysis showed that most of the selected GPS sites point to the GL region, although the direction deviations of GPS results at a few sites are mainly caused by the combined effect of the local load and superposition of the distant GL. Our findings indicate that inter-annual displacement changes at different frequencies (1- to 8-year cycle) are primarily due to water volume fluctuations in the GL. The amplitudes estimated by GPS are greater than the GRACE-based and GL-modeled results at most stations, which reflects sensitivity differences between these geodetic solutions to the surface load, as hydrological processes in the local area around a station are difficult to identify using GRACE data with a resolution of ~300 km.