Relativity of GPS measurement

Bahder, Thomas B.

doi:10.1103/physrevd.68.063005

Cited by 42 publications

(60 citation statements)

References 15 publications

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“…An observable is related to the phase comparison between a signal derived from the local oscillator and the received signal, corrected for the frequency difference mainly due to the first order Doppler effect (see Bahder 2003, for details of a similar procedure used in GPS). If we consider a particular bit of the signal that is produced locally at τ p and received at τ a , an observable is a measurement of the local proper time interval between these two events.…”

Section: Relativistic Model For Clocks and Time Transfer Of Acesmentioning

confidence: 99%

Orbit determination for next generation space clocks

Duchayne¹,

Mercier

Wolf³

2009

A&A

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We study the requirements on orbit determination compatible with operation of next generation space clocks at their expected uncertainty. Using the ACES (Atomic Clock Ensemble in Space) mission as an example, we develop a relativistic model for time and frequency transfer to investigate the effects of orbit determination errors. For the orbit error models considered we show that the required uncertainty goal can be reached with relatively modest constraints on the orbit determination of the space clock, which are significantly less stringent than expected from "naive" estimates. Our results are generic to all space clocks and represent a significant step towards the generalized use of next generation space clocks in fundamental physics, geodesy, and time/frequency metrology.

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Section: Relativistic Model For Clocks and Time Transfer Of Acesmentioning

confidence: 99%

Orbit determination for next generation space clocks

Duchayne¹,

Mercier

Wolf³

2009

A&A

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“…This is a combined effect involving, in the general case, entangled contributions of kinematical and gravitational origins. Recently, various aspects of this problem have been discussed, displaying decoupling and in consequence, factorization or partial factorization into gravitational and kinematical (time-dilation-like and classical Doppler shift) contributions [1][2][3] in the case of Schwarzschild spacetime. Nevertheless, as shown long ago by Synge [4], the ratio of the frequencies, the generalized Doppler shift, measured by observer O and sent from source S may be expressed as…”

Section: Introductionmentioning

confidence: 99%

On the nature of cosmological redshift and spectral shift in Schwarzschild-like and other spacetimes

2012

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The kinematical nature of the spectral shift in different types of spacetime, cosmological redshift and frequency shift in Schwarzschild spacetime being the most prominent representatives, has been a subject of recent interest. We demonstrate that the kinematical nature of the spectral shift is an inherent feature of the particular type of spacetimes. The general solution is found: necessary and sufficient conditions for the spectral shift arising from a kinematical origin are formulated. The status of the relative speed is discussed.Keywords Generalized Doppler effect · Relative and recession speeds · Schwarzschild spacetime · Friedmann-Lemaître-Robertson-Walker spacetime

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“…On the other hand, Blanchet et al [3] have determined the time transfer corresponding to each pair of points in space-time by integrating the null geodesic equation [4]. This method has been extended in [5,6] and [7] to determine the time transfer function in higher postNewtonian approximations by using Synge's [4] world function. The use of the world function method for the study of the propagation of light rays avoids the previous calculation of the null geodesic joining the considered points.…”

Section: Introductionmentioning

confidence: 99%

Numerical determination of time transfer in general relativity

Miguel

2007

Gen Relativ Gravit

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This paper determines the travel time of a light ray connecting two points in the space-time solving numerically a two-point boundary value problem by means of the shooting method. For the resolution of this problem multiple precision floatingpoint arithmetic is required. We have studied distinct implementations of the shooting method attending to the way in which the Jacobian appearing at each iteration is approximated. We have shown that by using Magnus expansions to solve the differential equation for the Jacobian, one obtains a better efficiency of the shooting method. Also, a comparison between the numerical results obtained through the application of the shooting method and those derived by Le Poncin-Lafitte et al. (Class Quantum Grav, 21:4463-4483, 2004) from perturbative expansions of the world function is made.

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Relativity of GPS measurement

Cited by 42 publications

References 15 publications

Orbit determination for next generation space clocks

Orbit determination for next generation space clocks

On the nature of cosmological redshift and spectral shift in Schwarzschild-like and other spacetimes

Numerical determination of time transfer in general relativity

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