Someone argues: "The measured advance of Mercury's perihelion

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

Someone argues: "The measured advance of Mercury's perihelion,

42.98\pm0.04

arcseconds per century, agrees with the general-relativistic prediction of

43.0

arcseconds per century. Since the PPN formula for the advance is

\Delta\varpi_{\rm PPN} = 43.0\,\frac{2+2\gamma_{\rm PPN}-\beta_{\rm PPN}}{3}\ \text{arcsec/century},

and this number comes out right only for

\gamma_{\rm PPN}=1

and

\beta_{\rm PPN}=1

, the perihelion measurement on its own proves that

\gamma_{\rm PPN}=1

and

\beta_{\rm PPN}=1

separately." ((a)) Explain what is wrong with this reasoning. ((b)) Find a second pair of values

(\gamma_{\rm PPN},\beta_{\rm PPN})

, with

\gamma_{\rm PPN}\neq 1

, that reproduces the same measured advance to within the quoted precision, and state which other solar-system measurement rules this pair out.

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