Time delay in the quadrupole field of a body at rest in 2PN approximation

Abstract

The time delay of a light signal in the quadrupole field of a body at rest is determined in the second post-Newtonian (2PN) approximation in harmonic coordinates. For grazing light rays at Sun, Jupiter, and Saturn the 2PN quadrupole effect in time delay amounts up to 0.004, 0.14, and 0.04 pico-second, respectively. These values are compared with the time delay in the first post-Newtonian (1PN and 1.5PN) approximation, where it turns out that only the first eight mass-multipoles and the spin-dipole of these massive bodies are required for a given goal accuracy of 0.001 pico-second in time-delay measurements in the solar system. In addition, the spin-hexapole of Jupiter is required on that scale of accuracy.

arXiv comment34 pages, 1 figure

References in corpus (22)

• An ${}^{27}$Al${}^{+}$ quantum-logic clock with systematic uncertainty below $10^{-18}$
• The IAU 2000 resolutions for astrometry, celestial mechanics and metrology in the relativistic framework: explanatory supplement
• Lunar laser ranging: the millimeter challenge
• Quantum Physics Exploring Gravity in the Outer Solar System: The Sagas Project
• A Preliminary Jupiter Model
• ASTROD and ASTROD I -- Overview and Progress
• Astrometric and Timing Effects of Gravitational Waves from Localized Sources
• Constraining the angular momentum of the Sun with planetary orbital motions and general relativity
• Odyssey: a Solar System Mission
• On the Gravitomagnetic Time Delay
• Constraining Saturn's Core Properties by a Measurement of Its Moment of Inertia - Implications to the Cassini Solstice Mission
• Numerical versus analytical accuracy of the formulas for light propagation
• Propagation of Light in the Field of Stationary and Radiative Gravitational Multipoles
• Precession, nutation, and space geodetic determination of the Earth's variable gravity field
• LATOR Covariance Analysis
• Light propagation in the gravitational field of N arbitrarily moving bodies in 1PN approximation for high-precision astrometry
• New method for determining the light travel time in static, spherically symmetric spacetimes. Calculation of the terms of order $G^3$
• Light propagation in the gravitational field of N arbitrarily moving bodies in the 1.5PN approximation for high-precision astrometry
• The physics of rotational flattening and the point core model
• Light propagation in 2PN approximation in the monopole and quadrupole field of a body at rest: Initial value problem
• Post-linear metric of a compact source of matter
• APOLLO clock performance and normal point corrections

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