scholarly journals Satellite Gravimetry: A Review of Its Realization

2021 ◽  
Author(s):  
Frank Flechtner ◽  
Christoph Reigber ◽  
Reiner Rummel ◽  
Georges Balmino
Keyword(s):  
Gravitational Field ◽  
Gravity Field ◽  
Water Cycle ◽  
Temporal Changes ◽  
Sensor Technology ◽  
Satellite Gravimetry ◽  
The Earth ◽  
Earth’S Gravitational Field ◽  
Gravity Field Determination ◽  
Space Age

AbstractSince Kepler, Newton and Huygens in the seventeenth century, geodesy has been concerned with determining the figure, orientation and gravitational field of the Earth. With the beginning of the space age in 1957, a new branch of geodesy was created, satellite geodesy. Only with satellites did geodesy become truly global. Oceans were no longer obstacles and the Earth as a whole could be observed and measured in consistent series of measurements. Of particular interest is the determination of the spatial structures and finally the temporal changes of the Earth's gravitational field. The knowledge of the gravitational field represents the natural bridge to the study of the physics of the Earth's interior, the circulation of our oceans and, more recently, the climate. Today, key findings on climate change are derived from the temporal changes in the gravitational field: on ice mass loss in Greenland and Antarctica, sea level rise and generally on changes in the global water cycle. This has only become possible with dedicated gravity satellite missions opening a method known as satellite gravimetry. In the first forty years of space age, satellite gravimetry was based on the analysis of the orbital motion of satellites. Due to the uneven distribution of observatories over the globe, the initially inaccurate measuring methods and the inadequacies of the evaluation models, the reconstruction of global models of the Earth's gravitational field was a great challenge. The transition from passive satellites for gravity field determination to satellites equipped with special sensor technology, which was initiated in the last decade of the twentieth century, brought decisive progress. In the chronological sequence of the launch of such new satellites, the history, mission objectives and measuring principles of the missions CHAMP, GRACE and GOCE flown since 2000 are outlined and essential scientific results of the individual missions are highlighted. The special features of the GRACE Follow-On Mission, which was launched in 2018, and the plans for a next generation of gravity field missions are also discussed.

scholarly journals Accurate Time Calculations of Falling Bodies in the Earth's Gravitational Field and Comparisons with Newton's Laws of Vertical Motion

2021 ◽  
pp. 44-53
Author(s):  
A. Ebaid ◽  
Shorouq M. S. Al-Qahtani ◽  
Afaf A. A. Al-Jaber ◽  
Wejdan S. S. Alatwai ◽  
Wafaa T. M. Alharbi
Keyword(s):  
Gravitational Field ◽  
Real Life ◽  
Vertical Motion ◽  
Exact Form ◽  
Potential Danger ◽  
Accurate Calculation ◽  
The Earth ◽  
Earth’S Gravitational Field ◽  
Celestial Bodies ◽  
Newton’S Laws

The Earth is exposed annually to the fall of some meteorites and probably other celestial bodies which cause a potential danger to vital areas in several countries. Consequently, the accurate calculation of the falling time of such bodies is useful in order to take the necessary procedures for protecting these areas. In this paper, Newton’s law of general gravitation is applied to analyze the vertical motion in the Earth’s gravitational field. The falling time is obtained in exact form. The results are applied on several objects in real life.

The research unit NEROGRAV: first results on stochastic modeling for gravity field determination with real GRACE and GRACE-FO data

2020 ◽  
Author(s):  
Natalia Panafidina ◽  
Michael Murböck ◽  
Christoph Dahle ◽  
Karl Hans Neumayer ◽  
Frank Flechtner ◽  
...  
Keyword(s):  
Data Processing ◽  
Gravity Field ◽  
Stochastic Modeling ◽  
Real Data ◽  
Research Unit ◽  
Model Errors ◽  
Satellite Gravimetry ◽  
Gravity Field Determination ◽  
Stochastic Properties ◽  
Background Models

<p><span lang="en-US">The central hypothesis of the Research Unit (RU) NEROGRAV reads: only by concurrently improving and better understanding of sensor data, background models, and processing strategies of satellite gravimetry, the resolution, accuracy, and long-term consistency of mass transport series from satellite gravimetry can be significantly increased; and only in that case the potential of future technological sensor developments can be fully exploited. Two of the individual projects (IPs) within the RU work on stochastic modeling for GRACE and GRACE-FO gravity field determination. TU München and TU Berlin are responsible for IP4 (OSTPAG: optimized space-time parameterization for GRACE and GRACE-FO data analysis), where besides optimal parameterization the focus is on the stochastic modeling of the key observations, i.e. GRACE and GRACE-FO inter-satellite ranging and accelerometer observations, in a simulation (TU München) and real data (TU Berlin) environment. IP5 (ISTORE: improved stochastic modeling in GRACE/GRACE-FO real data processing), which GFZ is responsible for, works on the optimal utilization of the stochastic properties of the main GRACE and GRACE-FO observation types and the main background models. </span></p> <p><span lang="en-US">This presentation gives first insights into the TU Berlin and GFZ results of these two IPs which are both related on stochastic modeling for real data processing based on GFZ GRACE and GRACE-FO RL06 processing. We present analysis of ranging observations and corresponding residuals of three test years of GRACE and GRACE-FO real data in the time and frequency domain. Based on the residual analysis we show results of the effects of different filter matrices, which take into account the stochastic properties of the ranging observations in order to decorrelate them. The stochastic modeling of the background models in IP5 starts with Monte-Carlo simulations on background model errors of atmospheric and oceanic mass variations. Different representations of variance-covariance matrices of this model information are tested as input for real GRACE data processing and their effect on gravity field determination are analyzed.</span></p>

Gravitational acceleration of a weakly relativistic electron in a conducting drift tube

2018 ◽  
Vol 33 (33) ◽  
pp. 1850192 ◽  
Author(s):  
V. I. Denisov ◽  
I. P. Denisova ◽  
M. G. Gapochka ◽  
A. F. Korolev ◽  
N. N. Koshelev
Keyword(s):  
Gravitational Field ◽  
Relativistic Electron ◽  
Horizontal Plane ◽  
Drift Tube ◽  
Gravitational Force ◽  
Vertical Direction ◽  
Gravitational Acceleration ◽  
The Earth ◽  
Earth’S Gravitational Field

We propose the idea of method for observing the effect of the Earth’s gravitational field on the motion of an electron. Earlier attempts to measure such an effect proved unsuccessful due to the fact that under the conductive sheath, the gravitational force acting on the non-relativistic electron is completely compensated by Barnhill–Schiff force. Therefore, experiments of this kind were unable to measure the effect of the Earth’s gravitational field on the motion of electrons. In this paper, we propose to use electrons moving with relativistic speeds in the horizontal plane, and with non-relativistic speeds in the vertical direction, in which case the gravitational force on these electrons is not fully compensated by the Barnhill–Schiff force. Calculations showed that in this case, it is possible to measure the force exerted on an electron by the gravitational field of the Earth.

scholarly journals Constants related to the Earth and Moon

1965 ◽  
Vol 21 ◽  
pp. 67-79
Author(s):  
Harold Jeffreys
Keyword(s):  
Gravitational Field ◽  
The Moon ◽  
The Earth ◽  
Earth’S Gravitational Field ◽  
Tesseral Harmonics

The author discusses various determinations of zonal and tesseral harmonics of the Earth's gravitational field, the values of the solar parallax, and the constants related to the figure of the Moon and its motion.

The research unit NEROGRAV: first results on stochastic modeling for gravity field determination with real GRACE and GRACE-FO data

2020 ◽  
Author(s):  
Michael Murböck ◽  
Panafidina Natalia ◽  
Dahle Christoph ◽  
Neumayer Karl-Hans ◽  
Flechtner Frank ◽  
...  
Keyword(s):  
Data Processing ◽  
Gravity Field ◽  
Stochastic Modeling ◽  
Real Data ◽  
Research Unit ◽  
Model Errors ◽  
Satellite Gravimetry ◽  
Gravity Field Determination ◽  
Stochastic Properties ◽  
Background Models

<p>The central hypothesis of the Research Unit (RU) NEROGRAV (New Refined Observations of Climate Change from Spaceborne Gravity Missions), funded for three years by the German Research Foundation DFG, reads: only by concurrently improving and better understanding of sensor data, background models, and processing strategies of satellite gravimetry, the resolution, accuracy, and long-term consistency of mass transport series from satellite gravimetry can be significantly increased; and only in that case the potential of future technological sensor developments can be fully exploited. Two of the individual projects (IPs) within the RU work on stochastic modeling for GRACE and GRACE-FO gravity field determination. TU München and TU Berlin are responsible for IP4 (OSTPAG: optimized space-time parameterization for GRACE and GRACE-FO data analysis), where besides optimal parameterization the focus is on the stochastic modeling of the key observations, i.e. GRACE and GRACE-FO inter-satellite ranging and accelerometer observations, in a simulation (TU München) and real data (TU Berlin) environment. IP5 (ISTORE: improved stochastic modeling in GRACE/GRACE-FO real data processing), which GFZ is responsible for, works on the optimal utilization of the stochastic properties of the main GRACE and GRACE-FO observation types and the main background models.</p><p>This presentation gives first insights into the TU Berlin and GFZ results of these two IPs which are both related on stochastic modeling for real data processing based on GFZ GRACE and GRACE-FO RL06 processing. We present the analyses of K-band inter-satellite range observations and corresponding residuals of three test years of GRACE and GRACE-FO real data in the time and frequency domain. Based on the residual analysis we show results of the effects of different filter matrices, which take into account the stochastic properties of the range observations in order to decorrelate them. The stochastic modeling of the background models starts with Monte-Carlo simulations on background model errors of atmospheric and oceanic mass variations. Different representations of variance-covariance matrices of this model information are tested as input for real GRACE data processing and their effect on gravity field determination are analyzed.</p>

scholarly journals Regularization of the Gravity Field Inversion Process with High-Dimensional Vector Autoregressive Models

2021 ◽  
Vol 3 (1) ◽  
pp. 7
Author(s):  
Andreas Kvas ◽  
Torsten Mayer-Gürr
Keyword(s):  
Gravitational Field ◽  
Gravity Field ◽  
Var Model ◽  
High Dimensional ◽  
Model Output ◽  
Inversion Process ◽  
Vector Autoregressive ◽  
Gravity Field Recovery ◽  
Earth’S Gravitational Field ◽  
Continental Hydrology

Earth’s gravitational field provides invaluable insights into the changing nature of our planet. It reflects mass change caused by geophysical processes like continental hydrology, changes in the cryosphere or mass flux in the ocean. Satellite missions such as the NASA/DLR operated Gravity Recovery and Climate Experiment (GRACE), and its successor GRACE Follow-On (GRACE-FO) continuously monitor these temporal variations of the gravitational attraction. In contrast to other satellite remote sensing datasets, gravity field recovery is based on geophysical inversion which requires a global, homogeneous data coverage. GRACE and GRACE-FO typically reach this global coverage after about 30 days, so short-lived events such as floods, which occur on time frames from hours to weeks, require additional information to be properly resolved. In this contribution we treat Earth’s gravitational field as a stationary random process and model its spatio-temporal correlations in the form of a vector autoregressive (VAR) model. The satellite measurements are combined with this prior information in a Kalman smoother framework to regularize the inversion process, which allows us to estimate daily, global gravity field snapshots. To derive the prior, we analyze geophysical model output which reflects the expected signal content and temporal evolution of the estimated gravity field solutions. The main challenges here are the high dimensionality of the process, with a state vector size in the order of 103 to 104, and the limited amount of model output from which to estimate such a high-dimensional VAR model. We introduce geophysically motivated constraints in the VAR model estimation process to ensure a positive-definite covariance function.

The effect of atmospheric rotation on the orbital plane of a near-earth satellite

1960 ◽  
Vol 258 (1295) ◽  
pp. 516-528 ◽  
Keyword(s):  
Gravitational Field ◽  
Orbital Plane ◽  
Earth Satellite ◽  
Theoretical Curve ◽  
Orbital Inclination ◽  
Small Eccentricity ◽  
Earth’S Atmosphere ◽  
The Earth ◽  
Earth’S Gravitational Field ◽  
Good Agreement

Besides the perturbations due to the gravitational field of the earth, the rotation of the earth’s atmosphere produces a perturbing force on a satellite which affects the motion of its orbital plane. Theoretical formulae are derived for the rotation of the orbital plane about the earth’s axis and the change in orbital inclination of a near-earth satellite of small eccentricity (< 0.2) due to the influence of the atmosphere. It is assumed that the atmosphere is spherically symmetrical and has a density which varies exponentially with altitude. Comparison of the theoretical changes in orbital inclination show reasonably good agreement with those estimated from kinetheodolite observations, although the need for a slightly steeper theoretical curve is indicated. Although the rotation of the orbital plane is small, allowance must be made for it when making estimates of the harmonics of the earth's gravitational field.

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