Relativistic tidal effects on clock-comparison experiments

Abstract

We consider the relativistic tidal effects on frequency shift of clock-comparison 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.

References in corpus (46)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• An Optical Lattice Clock with Accuracy and Stability at the $10^{-18}$ Level
• An atomic clock with $10^{-18}$ instability
• Systematic evaluation of an atomic clock at 2e-18 total uncertainty
• Atomic clock performance beyond the geodetic limit
• Single-Ion Atomic Clock with $3\times 10^{-18}$ Systematic Uncertainty
• Hunting for topological dark matter with atomic clocks
• Geodesy and metrology with a transportable optical clock
• Frequency ratio of two optical clock transitions in ${}^{171}$Yb${}^{+}$ and constraints on the time-variation of fundamental constants
• Searching for dilaton dark matter with atomic clocks
• Ultra-stable optical clock with two cold-atom ensembles
• The IAU 2000 resolutions for astrometry, celestial mechanics and metrology in the relativistic framework: explanatory supplement
• Improved limit on a temporal variation of $m_p/m_e$ from comparisons of Yb${}^{+}$ and Cs atomic clocks
• Real-time geopotentiometry with synchronously linked optical lattice clocks
• Experimenting an optical second with strontium lattice clocks
• Searching for an oscillating massive scalar field as a dark matter candidate using atomic hyperfine frequency comparisons
• A transportable optical lattice clock with $7\times 10^{-17}$ uncertainty
• Test of special relativity using a fiber network of optical clocks
• Quantum Tests of the Einstein Equivalence Principle with the STE-QUEST Space Mission
• Relativistic theory for time and frequency transfer to order c^{-3}
• Brillouin amplification supports $1\times 10^{-20}$ accuracy in optical frequency transfer over 1400~km of underground fibre
• General post-Minkowskian expansion of time transfer functions
• A transportable 40Ca+ single-ion clock with $7.7\times 10^{-17}$ systematic uncertainty
• Frequency transfer via a two-way optical phase comparison on a multiplexed fiber network
• Two-Way Optical Frequency Comparisons Over 100km Telecommunication Network Fibers
• Time transfer and frequency shift to the order 1/c^4 in the field of an axisymmetric rotating body
• World function and time transfer: general post-Minkowskian expansions
• Relativistic formulation of coordinate light time, Doppler and astrometric observables up to the second post-Minkowskian order
• Atomic Clock Ensemble in Space (ACES) data analysis
• Analysis of Sun/Moon Gravitational Redshift tests with the STE-QUEST Space Mission
• Gravitomagnetism and Relative Observer Clock Effects
• Quantum network of neutral atom clocks
• Influence of mass multipole moments on the deflection of a light ray by an isolated axisymmetric body
• General relativistic observables of the GRAIL mission
• Relativistic Corrections for Time and Frequency Transfer in Optical Fibres
• Spinning test particles and clock effect in Kerr spacetime
• Light propagation in the field of a moving axisymmetric body: theory and application to JUNO
• Circular Holonomy and Clock Effects in Stationary Axisymmetric Spacetimes
• Direction of light propagation to order G^2 in static, spherically symmetric spacetimes: a new derivation
• A Search for New Physics with the BEACON Mission
• Time Transfer functions as a way to validate light propagation solutions for space astrometry
• New method for determining the light travel time in static, spherically symmetric spacetimes. Calculation of the terms of order $G^3$
• Atomic clocks and dark-matter signatures
• Light propagation in the gravitational field of N arbitrarily moving bodies in the 1.5PN approximation for high-precision astrometry
• Light propagation in the gravitational field of one arbitrarily moving pointlike body in the 2PN approximation
• Light propagation in 2PN approximation in the field of one moving monopole II. Boundary value problem

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• Testing Lorentz symmetry with space-based gravitational-wave detectors
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