On the usefulness of relativistic space-times for the description of the Earth’s gravitational field

Söffel, M.; Frutos, Francisco

doi:10.1007/s00190-016-0927-4

Cited by 16 publications

(15 citation statements)

References 46 publications

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“…We note that the helioseismology limits are obtained based on the analysis of time variations of the Sun angular momentum and its kinetical energy in the Newtonian framework. Even if a strict approach would require a complete reanalysis of the helioseismology measurements in a non GRT-frame, one can expect a negligeable effect (Soffel and Frutos 2016). As in (Fienga et al 2015), we introduce the parameter Ġ/G through the secular variations of the gravitational mass of the Sun μ/µ with the equation…”

Section: Methodsmentioning

confidence: 99%

Evolution of INPOP planetary ephemerides and Bepi-Colombo simulations

Fienga,

Bigot,

Mary

et al. 2021

Preprint

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We give here a detailed description of the latest INPOP planetary ephemerides IN-POP20a. We test the sensitivity of the Sun oblateness determination obtained with INPOP to different models for the Sun core rotation. We also present new evaluations of possible GRT violations with the PPN parameters β,γ and μ/µ. With a new method for selecting acceptable alternative ephemerides we provide conservative limits of about 7.16×10 −5 and 7.49×10 −5 for β−1 and γ − 1 respectively using the present day planetary data samples. We also present simulations of Bepi-Colombo range tracking data and their impact on planetary ephemeris construction. We show that the use of future BC range observations should improve these estimates, in particular γ. Finally, interesting perspectives for the detection of the Sun core rotation seem to be reachable thanks to the BC mission and its accurate range measurements in the GRT frame.

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Section: Methodsmentioning

confidence: 99%

Evolution of INPOP planetary ephemerides and Bepi-Colombo simulations

Fienga,

Bigot,

Mary

et al. 2021

Preprint

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“…In many astrophysical applications (especially in gravitational-wave astronomy) one needs to make several post-Newtonian approximations for calculating observable effects [39]. For the purposes of relativistic geodesy and celestial mechanics of the solar system the first post-Newtonian approximation is usually sufficient [37] though there are indications that one may soon need a second PN approximation [40] and exact, axially-symmetric solutions of general relativity [41][42][43].…”

Section: The Normal Gravity Field In Classic Geodesy and In General R...mentioning

confidence: 99%

“…The Newtonian gravitational potential V N is given by (40) where the density distribution, ρ(x), is defined in (43) and the integration is performed over the volume bounded by the radial coordinate σ s in (50). The integral can be split in three parts:…”

Section: Newtonian Gravitational Potentialmentioning

confidence: 99%

Normal gravity field in relativistic geodesy

2018

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Modern geodesy is subject to a dramatic change from the Newtonian paradigm to Einstein's theory of general relativity. This is motivated by the ongoing advance in development of quantum sensors for applications in geodesy including quantum gravimeters and gradientometers, atomic clocks and fiber optics for making ultra-precise measurements of the geoid and multipolar structure of the Earth's gravitational field. At the same time, Very Long Baseline Interferometry, Satellite Laser Ranging and Global Navigation Satellite System have achieved an unprecedented level of accuracy in measuring 3-d coordinates of the reference points of the International Terrestrial Reference Frame and the world height system. The main geodetic reference standard to which gravimetric measurements of the of Earth's gravitational field are referred, is a normal gravity field represented in the Newtonian gravity by the field of a uniformly rotating, homogeneous Maclaurin ellipsoid which mass and quadrupole momentum are equal to the total mass and (tide-free) quadrupole moment of the Earth gravitational field. The present paper extends the concept of the normal gravity field from the Newtonian theory to the realm of general relativity. We focus our attention on the calculation of the post-Newtonian approximation of the normal field that is sufficient for current and near-future practical applications. We show that in general relativity the level surface of homogeneous and uniformly rotating fluid is no longer described by the Maclaurin ellipsoid in the most general case but represents an axisymmetric spheroid of the fourth order with respect to the geodetic Cartesian coordinates. At the same time, admitting a post-Newtonian inhomogeneity of the mass density in the form of concentric elliptical shells allows to preserve the level surface of the fluid as an exact ellipsoid of rotation. We parametrize the mass density distribution and the level surface with two parameters which are intrinsically connected to the existence of the residual gauge freedom, and derive the post-Newtonian normal gravity field of the rotating spheroid both inside and outside of the rotating fluid body. The normal gravity field is given, similarly to the Newtonian gravity, in a closed form by a finite number of the ellipsoidal harmonics. We employ transformation from the ellipsoidal to spherical coordinates to deduce a more conventional post-Newtonian multipolar expansion of scalar and vector gravitational potentials of the rotating spheroid. We compare these expansions with that of the normal gravity field generated by the Kerr metric and demonstrate that the Kerr metric has a fairly limited application in relativistic geodesy as it does not match the normal gravity field of the Maclaurin ellipsoid already in the Newtonian limit. We derive the post-Newtonian generalization of the Somigliana formula for the normal gravity field measured on the surface of the rotating spheroid and employed in practical work for measuring the Earth gravitational field anomalies. Finally, ...

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“…The assumptions done in this article to write the metric are simplistic, and for the analysis of a particular experiment, one should use a complete description of the metric around the Earth (see, e.g., [38,61]). This has been done in particular in the context of the detection of the Lense-Thirring effect in the Solar System (see, e.g., [62,63] and the references therein).…”

Section: Ppn Metric Of An Isolated Axisymmetric Rotating Bodymentioning

confidence: 99%