General post-Minkowskian expansion and application of the phase function

Qin, Cheng-Gang; Shao, Cheng-Gang

doi:10.1103/physrevd.96.024003

Cited by 6 publications

(6 citation statements)

References 28 publications

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“…From the expressions of gravitational delay in Ref. [67,68,69], we can obtain direct the derivatives. Inserting these derivatives into Eq.…”

Section: The Frequency Shift Between High Earth-orbiting Satellitesmentioning

confidence: 99%

“…∆ ME represents the contribution of the mass monopole, ∆ Jn represents the contributions from the mass multipole moments, and ∆ s represents the contribution of the vector potential. Since these three terms have been determined by some works [66][67][68], we will direct use the previous results to the calculations for frequency shift. Here, we will focus on the second term ∆ tidal .…”

Section: The Frequency Shift Between High Earth-orbiting Satellitesmentioning

confidence: 99%

“…In order to calculate the frequency shift due to the gravitational delay, the derivatives of the terms ∆ ME , ∆ Jn and ∆ s should be determined. From the expressions of gravitational delay in [66][67][68], we can obtain direct the derivatives. Inserting these derivatives into equation (26), we estimate frequency shift due to gravitational delay for TianQin mission (table 1).…”

Section: The Frequency Shift Between High Earth-orbiting Satellitesmentioning

confidence: 99%

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Relativistic tidal effects on clock-comparison experiments

Qin

Tan

Shao

2019

Class. Quantum Grav.

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We consider the relativistic tidal effects on frequency shift of clockcomparison experiments. The relativistic formulation for frequency shift and time transfer is derived in the gravitational field of a tidal, axisymmetric, and rotating Earth. With the help of Love numbers describing the tidal response of solid Earth, we formulize the mathematical connection between tidal effects from the ground-based clock-comparison experiments and the local gravity tides from the gravimeters, which in turn provides us an approach to eliminate tidal influences on clock comparison with the local gravity tides data. Moreover, we develop a method of the perturbed Kepler orbit to determine relativistic effects of clock comparison for space missions, which allows more precise calculations comparing to the conventional method of unperturbed Kepler orbit. With this perturbed method, it can give the perturbation of relativistic effects due to the orbital changes under the influences of tidal forces, Earth's oblateness etc. In addition, as the applications of our results, we simulate tidal effects in frequency shift for the clock comparison on the ground and also give some estimates for TianQin mission and GPS.

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“…From the expressions of gravitational delay in Ref. [67,68,69], we can obtain direct the derivatives. Inserting these derivatives into Eq.…”

Section: The Frequency Shift Between High Earth-orbiting Satellitesmentioning

confidence: 99%

Section: The Frequency Shift Between High Earth-orbiting Satellitesmentioning

confidence: 99%

Section: The Frequency Shift Between High Earth-orbiting Satellitesmentioning

confidence: 99%

See 1 more Smart Citation

Relativistic tidal effects on clock-comparison experiments

Qin

Tan

Shao

2019

Class. Quantum Grav.

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“…The method has been demonstrated by Poncin-Lafitte et al [7,8]. When we only consider the case of n ≤ 2, the solution of eikonal equation is expressed as [8,29] ϕ (1)…”

Section: Acknowledgmentmentioning

confidence: 99%

“…These require us to rigorously determine the light propagation in the field of Solar System. In the DSX formalism [27,28], relativistic phase in the field of N-body system can be derived from solving the eikonal equation [26,29]. Different from classical treatment in the static field, the influences of the N-body-system velocity, acceleration, gravitational interaction and tidal deformation also are determined in this formalism.…”

Section: Introductionmentioning

confidence: 99%

Light propagation in the field of the N -body system and its application in the TianQin mission

et al. 2019

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Given the high-precision modern space mission, a precise relativistic modeling of observations is required. By solving the eikonal equation with the post-Newtonian approximation, the light propagation is determined by the iterative method in the gravitational field of an isolated, gravitationally bound N-body system. Different from the traditional N bodies that are independent with each other in the system, our system includes the velocities, accelerations, gravitational interactions and tidal deformations of the gravitational bodies. The light delays of these factors then are precisely determined by the analytical solutions. These delays are significant and are likely to reach a detectable level for the strong gravitational fields, such as binary pulsars and some gravitational wave sources. The result's application in the vicinity of the Earth provides a relativistic framework for modern space missions. From the relativistic analysis in the TianQin mission, we find the possible tests for the alternative gravitational theories, such as a possible determination for the post-Newtonian parameter γ in the level of some scalar-tensor theories of gravity.

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