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Showing papers on "Gravitational field published in 2003"


Journal ArticleDOI
TL;DR: In this paper, the modified gravity with $R^2$ terms is discussed and it is shown that such a model which has well defined newtonian limit may eliminate the need for dark energy and may provide the current cosmic acceleration.
Abstract: The modified gravity with $\ln R$ or $R^{-n} (\ln R)^m$ terms which grow at small curvature is discussed. It is shown that such a model which has well-defined newtonian limit may eliminate the need for dark energy and may provide the current cosmic acceleration. It is demonstrated that $R^2$ terms are important not only for early time inflation but also to avoid the instabilities and the linear growth of the gravitational force. It is very interesting that the condition of no linear growth for gravitational force coincides with the one for scalar mass in the equivalent scalar-tensor theory to be very large. Thus, modified gravity with $R^2$ term seems to be viable classical theory.

324 citations


Journal ArticleDOI
TL;DR: In this paper, the self-forces of a small mass moving through curved spacetime are decomposed into two parts each of which satisfies the perturbed Einstein equations through O(mu) and includes the ''tail term'' which determines the self force effects of the particle interacting with its own gravitational field, including radiation reaction.
Abstract: The gravitational field of a particle of small mass \mu moving through curved spacetime is naturally decomposed into two parts each of which satisfies the perturbed Einstein equations through O(\mu). One part is an inhomogeneous field which, near the particle, looks like the \mu/r field distorted by the local Riemann tensor: it does not depend on the behavior of the source in either the infinite past or future. The other part is a homogeneous field and includes the ``tail term'': it completely determines the self force effects of the particle interacting with its own gravitational field, including radiation reaction. Self force effects for scalar, electromagnetic and gravitational fields are all described in this manner.

264 citations


Journal ArticleDOI
TL;DR: In this paper, the lowest stationary quantum state of neutrons in the Earth's gravitational field is identified in the measurement of neutron transmission between a horizontal mirror on the bottom and an absorber/scatterer on top.
Abstract: The lowest stationary quantum state of neutrons in the Earth's gravitational field is identified in the measurement of neutron transmission between a horizontal mirror on the bottom and an absorber/scatterer on top. Such an assembly is not transparent for neutrons if the absorber height is smaller than the ``height'' of the lowest quantum state.

246 citations


Journal ArticleDOI
TL;DR: In this article, the authors present new results for the gravitational field of a clustered matter source on the background of an accelerating universe in DGP braneworld gravity, and articulate how these results differ from those of general relativity.
Abstract: The braneworld model of Dvali-Gabadadze-Porrati (DGP) is a theory where gravity is modified at large distances by the arrested leakage of gravitons off our four-dimensional universe. Cosmology in this model has been shown to support both "conventional" and exotic explanations of the dark energy responsible for today's cosmic acceleration. We present new results for the gravitational field of a clustered matter source on the background of an accelerating universe in DGP braneworld gravity, and articulate how these results differ from those of general relativity. In particular, we show that orbits nearby a mass source suffer a universal anomalous precession as large as 5 microarcseconds/year, dependent only on the graviton's effective linewidth and the global geometry of the full, five-dimensional universe. Thus, this theory offers a local gravity correction sensitive to factors that dictate cosmological history.

232 citations


Journal ArticleDOI
TL;DR: In this article, a large class of static, spherically symmetric Lorentzian wormhole metrics is proposed for a brane world. But the wormholes are not symmetric and asymmetric.
Abstract: The condition R=0, where R is the four-dimensional scalar curvature, is used for obtaining a large class (with an arbitrary function of r) of static, spherically symmetric Lorentzian wormhole metrics. The wormholes are globally regular and traversable, can have throats of arbitrary size and can be both symmetric and asymmetric. These metrics may be treated as possible wormhole solutions in a brane world since they satisfy the vacuum Einstein equations on the brane where effective stress-energy is induced by interaction with the bulk gravitational field. Some particular examples are discussed.

229 citations


Journal ArticleDOI
TL;DR: In this article, a strict separation between the purely geometric concepts on one hand, and the spectroscopic measurement on the other, is made between the pure geometric concepts and the observations made inside gravitational fields.
Abstract: Accuracy levels of metres per second require the fundamental concept of "radial velocity" for stars and other distant objects to be examined, both as a physical velocity, and as measured by spectroscopic and astrometric techniques. Already in a classical (non-relativistic) framework the line-of-sight velocity component is an ambiguous concept, depending on whether, e.g., the time of light emission (at the object) or that of light detection (by the observer) is used for recording the time coordi- nate. Relativistic velocity eects and spectroscopic measurements made inside gravitational fields add further complications, causing wavelength shifts to depend, e.g., on the transverse velocity of the object and the gravitational potential at the source. Aiming at definitions that are unambiguous at accuracy levels of 1 m s 1 , we analyse dierent concepts of radial velocity and their interrelations. At this accuracy level, a strict separation must be made between the purely geometric concepts on one hand, and the spectroscopic measurement on the other. Among the geometric concepts we define kinematic radial velocity ,w hich corresponds most closely to the "textbook definition" of radial velocity as the line-of-sight component of space velocity; and astrometric radial velocity, which can be derived from astrometric observations. Consistent with these definitions, we propose strict definitions also of the complementary kinematic and astrometric quantities, namely transverse velocity and proper mo- tion. The kinematic and astrometric radial velocities depend on the chosen spacetime metric, and are accurately related by simple coordinate transformations. On the other hand, the observational quantity that should result from accurate spectroscopic measurements is the barycentric radial-velocity measure . This is independent of the metric, and to first order equals the line-of- sight velocity. However, it is not a physical velocity, and cannot be accurately transformed to a kinematic or astrometric radial velocity without additional assumptions and data in modelling the process of light emission from the source, the transmission of the signal through space, and its recording by the observer. For historic and practical reasons, the spectroscopic radial-velocity measure is expressed in velocity units as czB ,w herec is the speed of light and zB is the observed relative wavelength shift reduced to the solar-system barycentre, at an epoch equal to the barycentric time of light arrival. The barycentric radial-velocity measure and the astrometric radial velocity are defined by recent resolutions adopted by the International Astronomical Union (IAU), the motives and consequences of which are explained in this paper.

180 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that non-commutative field theories can be seen as ordinary theories in a gravitational background produced by the gauge field with a charge dependent gravitational coupling.

165 citations


Journal ArticleDOI
TL;DR: In this article, a model for relativistic reduction of positional observations with an accuracy of 1 μas is presented, which is expected to be attained in future space astrometry missions.
Abstract: We develop a practical model for relativistic reduction of positional observations with an accuracy of 1 μas, which is expected to be attained in future space astrometry missions. All relativistic effects that are caused by the gravitational field of the solar system and are of practical importance for this accuracy level are thoroughly calculated and discussed. The model includes relativistic modeling of the motion of the observer and modeling of relativistic aberration and gravitational light deflection, as well as a relativistic treatment of parallax and proper motion suitable for the accuracy of 1 μas. The model is formulated both for remote sources (stars, quasars, etc.) and for solar system objects (asteroids, etc.). The suggested model is formulated within the framework of the parameterized post-Newtonian formalism, with parameters β and γ. However, for general relativity (β = γ = 1) the model is fully compatible with the year 2000 IAU resolutions on relativity in celestial mechanics, astrometry, and metrology. The model is presented in a form suitable for implementation in a software system for data processing or simulation. The changes that should be applied to the model to attain an accuracy of 0.1 μas are reviewed. Potentially important relativistic effects caused by additional gravitational fields that are generated outside of the solar system are also briefly discussed.

162 citations


Book
30 Jun 2003
TL;DR: In this paper, the authors discuss the relationship between the Earth's interior and its upper atmosphere, and the two-body problem and the three-body Problem, as well as the dynamical evolution of the solar system.
Abstract: 1. Dynamical Principles.- 2. The Gravitational Field of an Isolated Body.- 3. Planetary Rotation.- 4. Gravitational Torques and Tides.- 5. The Interior of the Earth.- 6. Planetary Magnetism.- 7. Atmospheres.- 8. Upper Atmospheres.- 9. The Sun and the Solar Wind.- 10. Magnetospheres.- 11. The Two-Body Problem.- 12. Perturbation Theory.- 13. The Three-Body Problem.- 14. The Planetary System.- 15. Dynamical Evolution of the Solar System.- 16. Origin of the Solar System.- 17. Relativistic Effects in the Solar System.- 18. Artificial Satellites.- 19. Telecommunications.- 20. Precise Measurements in Space.

162 citations


Journal ArticleDOI
TL;DR: In this paper, a new long-wavelength global gravity field model, called EIGEN-2, has been derived in a German/French effort using GPS-CHAMP satellite-to-satellite tracking and on-board accelerometer data over a time span of altogether six months.

159 citations


Journal ArticleDOI
TL;DR: In this paper, it is shown that Friedmann and k-field equations may be analytically integrated for arbitrary K-field potentials during evolution with a constant baryotropic index.
Abstract: We study spatially flat isotropic universes driven by k-essence It is shown that Friedmann and k-field equations may be analytically integrated for arbitrary k-field potentials during evolution with a constant baryotropic index It follows that there is an infinite number of dynamically different k-theories with equivalent kinematics of the gravitational field We show that there is a large "window" of stable solutions, and that the dust-like behaviour separates stable from unstable expansion Restricting to the family of power law solutions, it is argued that the linear scalar field model, with constant function F, is isomorphic to a model with divergent speed of sound and this makes them less suitable for cosmological modeling than the non-linear k-field solutions we find in this paper

Journal ArticleDOI
TL;DR: In this article, regional terrestrial gravity is combined with long-wavelength gravity information supplied by an Earth gravity model to produce a combined geoid effect, which largely cancels the longwavelength features.
Abstract: In a modern application of Stokes’ formula for geoid determination, regional terrestrial gravity is combined with long-wavelength gravity information supplied by an Earth gravity model. Usually, several corrections must be added to gravity to be consistent with Stokes’ formula. In contrast, here all such corrections are applied directly to the approximate geoid height determined from the surface gravity anomalies. In this way, a more efficient workload is obtained. As an example, in applications of the direct and first and second indirect topographic effects significant long-wavelength contributions must be considered, all of which are time consuming to compute. By adding all three effects to produce a combined geoid effect, these long-wavelength features largely cancel. The computational scheme, including two least squares modifications of Stokes’ formula, is outlined, and the specific advantages of this technique, compared to traditional gravity reduction prior to Stokes’ integration, are summarised in the conclusions and final remarks.

Journal ArticleDOI
TL;DR: In this paper, a fast iterative method for gravity field determination from low Earth satellite orbit coordinates has been developed and implemented successfully, which is based on energy conservation and avoids problems related to orbit dynamics and initial state.
Abstract: A fast iterative method for gravity field determination from low Earth satellite orbit coordinates has been developed and implemented successfully. The method is based on energy conservation and avoids problems related to orbit dynamics and initial state. In addition, the particular geometry of a repeat orbit is exploited by using a very efficient iterative estimation scheme, in which a set of normal equations is approximated by a sparse block-diagonal equivalent. Recovery experiments for spherical harmonic gravity field models up to degree and order 80 and 120 were conducted based on a 29-day simulated data set of orbit coordinates. The method was found to be very flexible and could be easily adapted to include observations of non-conservative accelerations, such as (to be) provided by satellites like CHAMP, GRACE, and GOCE. A serious drawback of the method is its large sensitivity to satellite velocity errors. Existing orbit determination strategies need to be altered or augmented to include algorithms that focus on optimizing the accuracy of estimated velocities.

Journal ArticleDOI
TL;DR: In this paper, the total energy of the universe, which includes the energy of both the matter and the gravitational fields, is obtained by using the teleparallel versions of the Einstein and Landau-Lifshitz energymomentum complexes of the gravitational field.
Abstract: The teleparallel versions of the Einstein and the Landau-Lifshitz energy-momentum complexes of the gravitational field are obtained. By using these complexes, the total energy of the universe, which includes the energy of both the matter and the gravitational fields, is then obtained. It is shown that the total energy vanishes independently of both the curvature parameter and the three dimensionless coupling constants of teleparallel gravity.

Journal ArticleDOI
TL;DR: In this article, a series of two-dimensional hydrodynamic simulations of the rotational collapse of a supernova core in axisymmetry were performed and it was shown that the peak amplitudes of the gravitational wave are mostly within the sensitivity range of laser interferometers such as TAMA and the first LIGO for a source at a distance of 10 kpc.
Abstract: We perform a series of two-dimensional hydrodynamic simulations of the rotational collapse of a supernova core in axisymmetry. We employ a realistic equation of state (EOS) and take into account electron capture and neutrino transport by the so-called leakage scheme. It is an important step to apply the realistic EOS coupled with microphysics to 2D simulations for computing gravitational radiation in rotational core collapse. We use the quadrupole formula to calculate the amplitudes and the waveforms of the gravitational wave assuming Newtonian gravity. With these computations, we extend the conventional category of the gravitational waveforms. Our results show that the peak amplitudes of the gravitational wave are mostly within the sensitivity range of laser interferometers such as TAMA and the first LIGO for a source at a distance of 10 kpc. Furthermore, we find that the amplitudes of the second peaks are within the detection limit of the first LIGO for the source, and first point out the importance of the detection, since it will give us information as to the angular momentum distribution of evolved massive stars.

Journal ArticleDOI
TL;DR: The European Space Agency (ESA) Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission concept has been conceived and designed taking into account multi-disciplinary research objectives in solid Earth physics, oceanography and geodesy based on the unique capability of a gravity gradiometer combined with satellite-to-satellite high-low tracking techniques as mentioned in this paper.
Abstract: Current knowledge of the Earth's gravity field and its geoid, as derived from various observing techniques and sources, is incomplete Within a reasonable time, substantial improvement will come by exploiting new approaches based on spaceborne gravity observation Among these, the European Space Agency (ESA) Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission concept has been conceived and designed taking into account multi-disciplinary research objectives in solid Earth physics, oceanography and geodesy Based on the unique capability of a gravity gradiometer combined with satellite-to-satellite high-low tracking techniques, an accurate and detailed global model of the Earth's gravity field and its corresponding geoid will be recovered The importance of this is demonstrated by a series of realistic simulation experiments In particular, the quantitative impact of the new and accurate gravity field and geoid is examined in studies of tectonic composition and motion, Glaciological Isostatic Adjustment, ocean mesoscale variability, water mass transport, and unification of height systems Improved knowledge in each of these fields will also ensure the accumulation of new understanding of past and present sea-level changes

Journal ArticleDOI
TL;DR: In this article, the point shall move along a geodesic line in the manifold characterised by the line element ds, and the execution of the variation yields the equations of motion of the point: dxα ds2 = ∑ √ √ 6gμνdxμdxν μ, ν = 1, 2, 3, 4, where the gμν stand for functions of the variables x, and in the variation the variable x must be kept fixed at the beginning and at the end of the path of integration.
Abstract: where (1) ds = √6gμνdxμdxν μ, ν = 1, 2, 3, 4, where the gμν stand for functions of the variables x , and in the variation the variables x must be kept fixed at the beginning and at the end of the path of integration. In short, the point shall move along a geodesic line in the manifold characterised by the line element ds. The execution of the variation yields the equations of motion of the point: dxα ds2 = ∑

Journal ArticleDOI
TL;DR: In this article, the authors derived formulas for the gravity potential, field, and field gradient tensor for a polyhedral target body of a spatially linear density medium, and proposed new algorithms of improved error control over existing algorithms for the linear medium.
Abstract: Formulas for the gravity potential, field, and field gradient tensor are derived for a polyhedral target body of a spatially linear density medium. The formulas also define the magnetic potential and field in the case of a medium of spatially linear magnetization. This work generalizes existing solutions for the gravity field of a polyhedral target of linearly varying density.The formulas are analyzed for singularities and for numerical error growth. Error growth with increasing target distance is found to be higher than in the corresponding uniform polyhedral case. Examination of the error sources reveals that some error reduction is possible. On this basis, new algorithms of improved error control over existing algorithms are proposed for the linear medium. Computational results confirm the expected improvement.

Journal ArticleDOI
TL;DR: In this article, an algorithm for the determination of the spherical harmonic coefficients of the terrestrial gravitational field representation from the analysis of a kinematic orbit solution of a low earth orbiting GPS-tracked satellite is presented and examined.
Abstract: An algorithm for the determination of the spherical harmonic coefficients of the terrestrial gravitational field representation from the analysis of a kinematic orbit solution of a low earth orbiting GPS-tracked satellite is presented and examined. A gain in accuracy is expected since the kinematic orbit of a LEO satellite can nowadays be determined with very high precision, in the range of a few centimeters. In particular, advantage is taken of Newton's Law of Motion, which balances the acceleration vector with respect to an inertial frame of reference (IRF) and the gradient of the gravitational potential. By means of triple differences, and in particular higher-order differences (seven-point scheme, nine-point scheme), based upon Newton's interpolation formula, the local acceleration vector is estimated from relative GPS position time series. The gradient of the gravitational potential is conventionally given in a body-fixed frame of reference (BRF) where it is nearly time independent or stationary. Accordingly, the gradient of the gravitational potential has to be transformed from spherical BRF to Cartesian IRF. Such a transformation is possible by differentiating the gravitational potential, given as a spherical harmonics series expansion, with respect to Cartesian coordinates by means of the chain rule, and expressing zero- and first-order Ferrer's associated Legendre functions in terms of Cartesian coordinates. Subsequently, the BRF Cartesian coordinates are transformed into IRF Cartesian coordinates by means of the polar motion matrix, the precession–nutation matrices and the Greenwich sidereal time angle (GAST). In such a way a spherical harmonic representation of the terrestrial gravitational field intensity with respect to an IRF is achieved. Numerical tests of a resulting Gauss–Markov model document not only the quality and the high resolution of such a space gravity spectroscopy, but also the problems resulting from noise amplification in the acceleration determination process.

Journal ArticleDOI
TL;DR: In this paper, a cyclic vertical arm movements with an instrumented hand-held load in an airplane undergoing parabolic flight profiles was investigated to determine how humans modulate their grip force when the gravitational and the inertial components of the load force are varied independently.
Abstract: Investigating cyclic vertical arm movements with an instrumented hand-held load in an airplane undergoing parabolic flight profiles allowed us to determine how humans modulate their grip force when the gravitational and the inertial components of the load force are varied independently. Eight subjects participated in this study; four had already experienced parabolic flights and four had not. The subjects were asked to move the load up and down continuously at three different gravitational conditions (1 g, 1.8 g, and 0 g). At 1 g, the grip force precisely anticipated the fluctuations in the load force, which was maximum at the bottom of the object trajectory and minimum at the top. When gravity changed, the temporal coupling between grip force and load force persisted for all subjects from the first parabola. At 0 g, the grip force was accurately adjusted to the two load force peaks occurring at the two opposite extremes of the trajectory due to the absence of weight. While the experienced subjects exerted a grip force appropriate to a new combination of weight and inertia since their first trial, the inexperienced subjects dramatically increased their grip when faced with either high or low force levels for the first time. Then they progressively released their grip until a continuous grip-load force relationship with regard to 1 g was established after the fifth parabola. We suggest that a central representation of the new gravitational field was rapidly acquired through the incoming vestibular and somatic sensory information.

Journal ArticleDOI
TL;DR: In this paper, the energy integral of the motion of a satellite is used to transform satellite velocities into values of gravitational potential, and the derived potential model, TUM-1S, is validated by comparison to ground data and by satellite orbit residuals.
Abstract: [1] In this paper we present results of a global gravity field recovery using half a year of CHAMP data. We use the energy integral of the motion of a satellite to transform satellite velocities into values of gravitational potential. The feasibility of this approach has already been demonstrated by several groups, using CHAMP reduced-dynamic orbits. We show, that the potential recovered from this kind of orbits depends on the a priori gravity field used for orbit determination. Thus, it cannot be excluded that errors present in the prior field propagate into the new CHAMP gravity model. It is the intention of this paper to avoid this dependency through the use of kinematic orbits, which are free from prior information. The derived potential model, TUM-1S, is validated by comparison to ground data and by satellite orbit residuals. It is shown to be comparable in quality to other state-of-the-art gravity field models.

Journal ArticleDOI
Lorenzo Iorio1
TL;DR: In this paper, the classical secular precessions of the node Ω and the perigee ω of an Earth artificial satellite induced by the even zonal harmonics of the static part of the geopotential up to degree l = 20.
Abstract: In this paper we calculate explicitly the classical secular precessions of the node Ω and the perigee ω of an Earth artificial satellite induced by the even zonal harmonics of the static part of the geopotential up to degree l = 20. Subsequently, their systematic errors induced by the mismodelling in the even zonal spherical harmonics coefficients Jl are compared to the general relativistic secular gravitomagnetic and gravitoelectric precessions of the node and the perigee of the existing laser-ranged geodetic satellites and of the proposed LARES. The impact of the future terrestrial gravity models from CHAMP and GRACE missions is discussed as well. Preliminary estimates with the recently released EIGEN-1S gravity model including the first CHAMP data are presented.

Journal ArticleDOI
TL;DR: In this article, the equations of general relativistic magnetohydrodynamics (MHD) in 3 + 1 form were assembled for evolving numerically a MHD fluid in a dynamical spacetime characterized by a strong gravitational field.
Abstract: We assemble the equations of general relativistic magnetohydrodynamics (MHD) in 3 + 1 form. These consist of the complete coupled set of Maxwell's equations for the electromagnetic field, Einstein's equations for the gravitational field, and the equations of relativistic MHD for a perfectly conducting ideal gas. The adopted form of the equations is suitable for evolving numerically a relativistic MHD fluid in a dynamical spacetime characterized by a strong gravitational field.

Journal ArticleDOI
TL;DR: In this article, the spectral element modeling of seismic wave propagation at the global scale is considered and a new formulation inside the fluid which allows to account for an arbitrary density stratification is proposed.
Abstract: This paper deals with the spectral element modeling of seismic wave propagation at the global scale. Two aspects relevant to low-frequency studies are particularly emphasized. First, the method is generalized beyond the Cowling approximation in order to fully account for the effects of self-gravitation. In particular, the perturbation of the gravity field outside the Earth is handled by a projection of the spectral element solution onto the basis of spherical harmonics. Second, we propose a new formulation inside the fluid which allows to account for an arbitrary density stratification. It is based upon a decomposition of the displacement into two scalar potentials, and results in a fully explicit fluid-solid coupling strategy. The implementation of the method is carefully detailed and its accuracy is demonstrated through a series of benchmark tests.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the optimal regularization in the context of the processing of satellite gravity gradiometry (SGG) data that will be acquired by the GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) satellite.
Abstract: The issue of optimal regularization is investigated in the context of the processing of satellite gravity gradiometry (SGG) data that will be acquired by the GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) satellite. These data are considered as the input for determination of the Earth’s gravity field in the form of a series of spherical harmonics. Exploitation of a recently developed fast processing algorithm allowed a very realistic setup of the numerical experiments to be specified, in particular: a non-repeat orbit; 1-s sampling rate; half-year duration of data series; and maximum degree and order set to 300. The first goal of the study is to compare different regularization techniques (regularization matrices). The conclusion is that the first-order Tikhonov regularization matrix (the elements are practically proportional to the degree squared) and the Kaula regularization matrix (the elements are proportional to the fourth power of the degree) are somewhat superior to other regularization techniques. The second goal is to assess the generalized cross-validation method for the selection of the regularization parameter. The inference is that the regularization parameter found this way is very reasonable. The time expenditure required by the generalized cross-validation method remains modest even when a half-year set of SGG data is considered. The numerical study also allows conclusions to be drawn regarding the quality of the Earth’s gravity field model that can be obtained from the GOCE SGG data. In particular, it is shown that the cumulative geoid height error between degrees 31 and 200 will not exceed 1 cm.

Journal ArticleDOI
TL;DR: In this paper, the essential features of the experiments responsible for the current limits on new effects in the range from a few microns to a few centimeters, and discuss prospects for the near future.

Journal ArticleDOI
TL;DR: In this paper, a strategy for the combination of satellite, airborne and ground measurements is presented, based on ideas independently introduced by Sjoberg and Wenzel in the early 1980s and has been modified by using a quasi-deterministic approach for the determination of the weighting functions.
Abstract: Satellite gravity missions, such as CHAMP, GRACE and GOCE, and airborne gravity campaigns in areas without ground gravity will enhance the present knowledge of the Earth’s gravity field. Combining the new gravity information with the existing marine and ground gravity anomalies is a major task for which the mathematical tools have to be developed. In one way or another they will be based on the spectral information available for gravity data and noise. The integration of the additional gravity information from satellite and airborne campaigns with existing data has not been studied in sufficient detail and a number of open questions remain. A strategy for the combination of satellite, airborne and ground measurements is presented. It is based on ideas independently introduced by Sjoberg and Wenzel in the early 1980s and has been modified by using a quasi-deterministic approach for the determination of the weighting functions. In addition, the original approach of Sjoberg and Wenzel is extended to more than two measurement types, combining the Meissl scheme with the least-squares spectral combination. Satellite (or geopotential) harmonics, ground gravity anomalies and airborne gravity disturbances are used as measurement types, but other combinations are possible. Different error characteristics and measurement-type combinations and their impact on the final solution are studied. Using simulated data, the results show a geoid accuracy in the centimeter range for a local test area.

Journal ArticleDOI
TL;DR: In this article, the energy conservation method is used to estimate the gravity potential at satellite altitude, considering the tidal potential from the sun and the moon, the explicit time variation of gravity potential in inertial space and loss of energy due to external forces.
Abstract: . The energy conservation method is based on knowledge of the state vector and measurements of nonconservative forces. This is or will be provided by CHAMP, GRACE and GOCE. Here the analysis of one month of CHAMP state vector and accelerometer data is described. The energy conservation method is used to estimate the gravity potential at satellite altitude. When doing so we consider the tidal potential from the sun and the moon, the explicit time variation of the gravity potential in inertial space and loss of energy due to external forces. Fast Spherical Collocation have been used to estimate a gravity field model to degree and order 90, UCPH2002 04. This gravity field model is compared to EGM96 and EIGEN-2. The largest differences with respect to EGM96 are found at those places where the gravity data used to determine EGM96 had the largest uncertainty. EIGEN-2 and UCPH2002 04 are similar, though there are some differences in Antarctica and Central Asia.

Journal ArticleDOI
TL;DR: In this article, the authors investigate the practical implementation of Taylor's three-dimensional potential reconstruction method using weak gravitational lensing, together with the requisite reconstruction of the lensing potential, and create catalogues of galaxies sampling this distortion in 3D, with realistic spatial distribution and intrinsic ellipticity for both ground-based and space-based surveys.
Abstract: We investigate the practical implementation of Taylor's three-dimensional gravitational potential reconstruction method using weak gravitational lensing, together with the requisite reconstruction of the lensing potential. This methodology calculates the 3D gravitational potential given a knowledge of shear estimates and redshifts for a set of galaxies. We analytically estimate the noise expected in the reconstructed gravitational field taking into account the uncertainties associated with a finite survey, photometric redshift uncertainty, redshift-space distortions and multiple scattering events. In order to implement this approach for future data analysis, we simulate the lensing distortion fields due to various mass distributions. We create catalogues of galaxies sampling this distortion in three dimensions, with realistic spatial distribution and intrinsic ellipticity for both ground-based and space-based surveys. Using the resulting catalogues of galaxy position and shear, we demonstrate that it is possible to reconstruct the lensing and gravitational potentials with our method. For example, we demonstrate that a typical ground-based shear survey with redshift limit z = 1 and photometric redshifts with error Δz = 0.05 is directly able to measure the 3D gravitational potential for mass concentrations ≥10 1 4 M O . between 0.1 ≤ z ≤ 0.5. and can statistically measure the potential at much lower mass limits. The intrinsic ellipticity of objects is found to be a serious source of noise for the gravitational potential, which can be overcome by Wiener filtering or examining the potential statistically over many fields. We examine the use of the 3D lensing potential to measure mass and position of clusters in 3D, and to detect clusters behind clusters.

Journal ArticleDOI
TL;DR: In this article, a viscous flow exterior to a circular cylinder rotating about its horizontal axis in a vertical gravitational field is considered, when the mean film thickness is small compared with the...
Abstract: Freesurface viscous flow exterior to a circular cylinder rotating about its horizontal axis in a vertical gravitational field is considered. When the mean film thickness is small compared with the ...