A very-long-baseline radio interferometry campaign measures the deflection of radio…

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 very-long-baseline radio interferometry campaign measures the deflection of radio waves grazing the Sun's limb to be Δϕmeas=1.7502±0.0003\Delta\phi_{\rm meas} = 1.7502 \pm 0.0003 arcseconds, at the same impact parameter for which general relativity (γPPN=1\gamma_{\rm PPN}=1) predicts ΔϕGR=1.75\Delta\phi_{\rm GR} = 1.75 arcseconds exactly. The PPN deflection is Δϕ=12(1+γPPN)×4GM⊙bc2\Delta\phi = \tfrac12(1+\gamma_{\rm PPN})\times\dfrac{4GM_\odot}{bc^2}, with the impact parameter bb and mass M⊙M_\odot the same in both cases. ((a)) Find the value of γPPN−1\gamma_{\rm PPN}-1 implied by this measurement, with its uncertainty. ((b)) State whether this result is consistent with the Cassini bound γPPN−1=(2.1±2.3)×10−5\gamma_{\rm PPN}-1 = (2.1\pm2.3)\times10^{-5} quoted for the light time-delay experiment.

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