Fourth Test of General Relativity: New Radar Result

Abstract

This is the master equation for the evolution of the P representation in the Schrodinger picture. If, as an example, one applies Eq. (17) to the simple caseone has i-which is the well-known equation 4 for the Hamiltonian described by Eq. (18).New radar observations yield a more stringent test of the predicted relativistic increase in echo times of radio signals sent from Earth and reflected from Mercury and Venus. These "extra" delays may be characterized by a parameter X which is unity according to general relativity and 0.93 according to recent predictions based on a scalartensor theory of gravitation. We find that X = 1.02. The formal standard error is 0.02, but because of the possible presence of systematic errors we consider 0.05 to be a more reliable estimate of the uncertainty in the result.General relativity predicts that the round-trip time delay of an electromagnetic wave is influenced by the gravitational potential along the path of the radiation. A test of this prediction involving the transmission of radar signals from Earth to either Mercury or Venus and the detection of the echoes was suggested in 1964.* These echoes are expected on the basis of general relativity to be retarded by solar gravity by an amount 2 A* <=* (4r 0 /c) ln[(r, + r p +R)/(r e + r p -where At, expressed in harmonic coordinates, is the coordinate-time retardation, r 0~ 1.5 km is the gravitational radius of the sun, c is the speed of light far from the sun, r e is the Earthsun distance, r p is the planet-sun distance, and R is the Earth-planet distance. The quantity At is not an observable but is indicative of the magnitude and behavior of the measurable effect as predicted by general relativity. The operational interpretation of the effect has been discussed in detail elsewhere. 3 To test whether or not the echo time-delay data are in agreement with this theory, we may insert an ad hoc multiplicative parameter X on the right side of Eq. (1) and estimate it along with the other unknown parameters that affect the data. 4 This experiment was first performed in 1967 and yielded the result 5 X =0.09 ±0.2 which corre-1132

Classical tests of general relativity: Brane-world Sun from minimal geometric deformation

“…where δφ GR = 6πGM/c 2 a 1 − e 2 is the well-known Schwarzschild precession formula and f (β) ≃ 673.94 β, [31] can thus be ascribed to BW effects, according to Eq. (25).…”

“…(25). Observational data [30,31] yield the bound f (β) ≤ (1.89±2.33)×10 −8 , which constrains β (2.80 ± 3.45) × 10 −11 .…”

Recent astronomical tests of general relativity

“…Testing began in 1967 and after three years of 1 700 measurements by the Haystack and Arecibo Observatories, Shapiro reported γ = 1.03 ± 0.04 (Shapiro et al, 1971). The first measurements made of time dilation with spacecraft were at Mars in 1969.…”

Rotation Effects and The Gravito-Magnetic Approach

“…Shapiro et al [7], [8], [9] verified the influence of the solar mass on signals propagation, however, in weak field approximation, the time of flight does depend also on the angular momentum, and its contribution has the form[10]…”