A radar-ranging experiment to a spacecraft passing nearly behind the Sun measures a…

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Schwarzschild spacetime and the tests of general relativity · Schwarzschild spacetime and the tests of general relativity

The Geometry of Gravity, Ch Solar-system tests, the PPN framework and alternative theories

Problem

A radar-ranging experiment to a spacecraft passing nearly behind the Sun measures a round-trip Shapiro delay at closest approach of

250.6\pm0.2\ \mu\mathrm{s}

. General relativity (

\gamma_{\rm PPN}=1

) predicts

250.5\ \mu\mathrm{s}

for the same geometry. The Shapiro delay is proportional to the same factor

\tfrac12(1+\gamma_{\rm PPN})

as the light deflection. ((a)) Find

\gamma_{\rm PPN}-1

implied by this measurement, with its uncertainty. ((b)) State whether the result rules out general relativity.

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