Accurate light-time correction due to a gravitating mass

Abstract

This work arose as an aftermath of Cassini's 2002 experiment \cite{bblipt03}, in which the PPN parameter $\gamma$ was measured with an accuracy ${\sigma }_{\gamma }=2.3\times 10^{-5}$ and found consistent with the prediction $\gamma =1$ of general relativity. The Orbit Determination Program (ODP) of NASA's Jet Propulsion Laboratory, which was used in the data analysis, is based on an expression for the gravitational delay which differs from the standard formula; this difference is of second order in powers of $m$ -- the sun's gravitational radius -- but in Cassini's case it was much larger than the expected order of magnitude $m^2/b$, where $b$ is the ray's closest approach distance. Since the ODP does not account for any other second-order terms, it is necessary, also in view of future more accurate experiments, to systematically evaluate higher order corrections and to determine which terms are significant. Light propagation in a static spacetime is equivalent to a problem in ordinary geometrical optics; Fermat's action functional at its minimum is just the light-time between the two end points A and B. A new and powerful formulation is thus obtained. Asymptotic power series are necessary to provide a safe and automatic way of selecting which terms to keep at each order. Higher order approximations to the delay and the deflection are obtained. We also show that in a close superior conjunction, when $b$ is much smaller than the distances of A and B from the Sun, of order $R$, say, the second-order correction has an \emph{enhanced} part of order $m^{2}R/b^2$, which corresponds just to the second-order terms introduced in the ODP. Gravitational deflection of the image of a far away source, observed from a finite distance from the mass, is obtained to $O(m^2)$.

4 figures

References in corpus (5)

• The IAU 2000 resolutions for astrometry, celestial mechanics and metrology in the relativistic framework: explanatory supplement
• General post-Minkowskian expansion of time transfer functions
• World function and time transfer: general post-Minkowskian expansions
• Gravimagnetic effect of the barycentric motion of the Sun and determination of the post-Newtonian parameter gamma in the Cassini experiment
• The effect of the motion of the Sun on the light-time in interplanetary relativistic experiments

Cited by in corpus (29)

• Sgr A* and General Relativity
• Testing the No-Hair Theorem with Observations of Black Holes in the Electromagnetic Spectrum
• Relativistic formulation of coordinate light time, Doppler and astrometric observables up to the second post-Minkowskian order
• Testing Theories of Gravity with Planetary Ephemerides
• General relativistic observables of the GRAIL mission
• Light propagation in the field of a moving axisymmetric body: theory and application to JUNO
• Shortcomings of Shapiro delay-based tests of the equivalence principle on cosmological scales
• Direction of light propagation to order G^2 in static, spherically symmetric spacetimes: a new derivation
• Space-Time Reference with an Optical Link
• Time Transfer functions as a way to validate light propagation solutions for space astrometry
• Light propagation in the gravitational field of N arbitrarily moving bodies in 1PN approximation for high-precision astrometry
• The BepiColombo solar conjunction experiments revisited
• 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
• Time transfer functions in Schwarzschild-like metrics in the weak-field limit: A unified description of Shapiro and lensing effects
• Comparison of light-time formulations in the post-Newtonian framework for the BepiColombo MORE experiment
• 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: I. Initial value problem
• Light propagation in 2PN approximation in the field of one moving monopole II. Boundary value problem
• It's Hard to Learn How Gravity and Electromagnetism Couple
• Preliminary Sensitivity Study for a Gravitational Redshift Measurement with China's Lunar Exploration Project
• Kerr-Newman black hole lensing of relativistic massive particles in the weak field limit
• Light propagation in the field of the N-body system and the application in the TianQin mission
• 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
• Total light deflection in the gravitational field of an axisymmetric body at rest with full mass and spin multipole structure
• 2PN/RM gauge invariance in Brans-Dicke-like scalar-tensor theories
• Testing Lorentz symmetry with space-based gravitational-wave detectors
• Numerical evaluation of the exact post-Newtonian parameters in Brans-Dicke and entangled relativity theories