General post-Minkowskian expansion of time transfer functions

Teyssandier, P.; Poncin-Lafitte, Christophe Le

doi:10.1088/0264-9381/25/14/145020

Cited by 100 publications

(184 citation statements)

References 16 publications

(41 reference statements)

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“…Various concepts and techniques being useful to develop the 1-order RPS have been found in previous papers, among them, we may point out the definition and uses of the world function (Synge, 1931;Bahder, 2001;Bini et al, 2008;San Miguel, 2007) and the time transfer function, the form of this last function in the S-ST (Teyssandier and Le Poncin-Lafitte, 2008), and a method to find the user position coordinates by using the time transfer function (Čadež and Kostić, 2005;Čadež et al, 2010;Delva et al, 2011). Here, this last method is modified by using the analytical formula derived by Coll et al (2010) -instead of numerical iterations-to work with photons moving in M-ST The Earth's center is at rest in the asymptotic M-ST; hence, the S-ST may be considered as a perturbation of the asymptotic M-ST with a static metric g αβ = η αβ +s αβ , where η αβ is the Minkowski metric, and s αβ are perturbation terms depending on GM ⊕ /R, where R is the Schwarzschild radial coordinate.…”

Section: Relativistic Positioning In S-st: the 1-order Rpsmentioning

confidence: 99%

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Approaches to relativistic positioning around Earth and error estimations

Puchades

Sáez

2016

Advances in Space Research

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In the context of relativistic positioning, the coordinates of a given user may be calculated by using suitable information broadcast by a 4-tuple of satellites. Our 4-tuples belong to the Galileo constellation. Recently, we estimated the positioning errors due to uncertainties in the satellite world lines (U-errors). A distribution of U-errors was obtained, at various times, in a set of points covering a large region surrounding Earth. Here, the positioning errors associated to the simplifying assumption that photons move in Minkowski space-time (S-errors) are estimated and compared with the U-errors. Both errors have been calculated for the same points and times to make comparisons possible. For a certain realistic modeling of the world line uncertainties, the estimated S-errors have proved to be smaller than the U-errors, which shows that the approach based on the assumption that the Earth's gravitational field produces negligible effects on photons may be used in a large region surrounding Earth. The applicability of this approach -which simplifies numerical calculations-to positioning problems, and the usefulness of our S-error maps, are pointed out. A better approach, based on the assumption that photons move in the Schwarzschild space-time governed by an idealized Earth, is also analyzed. More accurate descriptions of photon propagation involving non symmetric space-time structures are not necessary for ordinary positioning and spacecraft navigation around Earth.

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Section: Relativistic Positioning In S-st: the 1-order Rpsmentioning

confidence: 99%

“…It has been proved that T S may be expanded as follows [see Teyssandier and Le Poncin-Lafitte (2008) and references cited therein]:…”

Section: Relativistic Positioning In S-st: the 1-order Rpsmentioning

confidence: 99%

Approaches to relativistic positioning around Earth and error estimations

Puchades

Sáez

2016

Advances in Space Research

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“…In this paper, we will revisit the role of the cosmological constant Λ in terms of the time transfer function recently proposed in [28,29], which is originally related to Synge's world function Ω(x A , x B ) and which enables us to circumvent the integration of the null geodesic equation. In Section 2, we will briefly summarize the time transfer function method.…”

Section: Introductionmentioning

confidence: 99%

Effect of the Cosmological Constant on Light Deflection: Time Transfer Function Approach

Arakida

2016

Universe

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Abstract:We revisit the role of the cosmological constant Λ in the deflection of light by means of the Schwarzschild-de Sitter/Kottler metric. In order to obtain the total deflection angle α, the time transfer function approach is adopted, instead of the commonly used approach of solving the geodesic equation of photon. We show that the cosmological constant does appear in expression of the deflection angle, and it diminishes light bending due to the mass of the central body M. However, in contrast to previous results, for instance, that by Rindler and Ishak (Phys. Rev. D. 2007), the leading order effect due to the cosmological constant does not couple with the mass of the central body M.

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“…This formulation has been proposed in [11] and it has been justified in the small impact parameter regime by much more theoretically rooted derivations in [5], [14] and [1]. Figure 4 shows that the order 2 correction is relevant for our experiment, especially when there is a superior conjunction with a small impact parameter of the radio wave path passing near the Sun.…”

Section: Shapiro Effectmentioning

confidence: 81%

Light-time computations for the BepiColombo Radio Science Experiment

Tommei

Milani²,

Vokrouhlický³

2010

Celest Mech Dyn Astr

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The radioscience experiment is one of the on board experiment of the Mercury ESA mission BepiColombo that will be launched in 2014. The goals of the experiment are to determine the gravity field of Mercury and its rotation state, to determine the orbit of Mercury, to constrain the possible theories of gravitation (for example by determining the post-Newtonian (PN) parameters), to provide the spacecraft position for geodesy experiments and to contribute to planetary ephemerides improvement. This is possible thanks to a new technology which allows to reach great accuracies in the observables range and range rate; it is well known that a similar level of accuracy requires studying a suitable model taking into account numerous relativistic effects. In this paper we deal with the modelling of the space-time coordinate transformations needed for the light-time computations and the numerical methods adopted to avoid rounding-off errors in such computations.

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General post-Minkowskian expansion of time transfer functions

Cited by 100 publications

References 16 publications

Approaches to relativistic positioning around Earth and error estimations

Approaches to relativistic positioning around Earth and error estimations

Effect of the Cosmological Constant on Light Deflection: Time Transfer Function Approach

Light-time computations for the BepiColombo Radio Science Experiment

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