If general relativity holds exactly

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

If general relativity holds exactly, orbital theory predicts that the asteroid Icarus's perihelion should advance by 10.0510.05 arcseconds per century from relativistic geometry alone; this number already includes the factor (2+2γPPN−βPPN)/3(2+2\gamma_{\rm PPN}-\beta_{\rm PPN})/3 evaluated at γPPN=βPPN=1\gamma_{\rm PPN}=\beta_{\rm PPN}=1. Radar ranging over several decades measures the actual advance to be 9.98±0.059.98\pm0.05 arcseconds per century. An independent light time-delay measurement has already fixed γPPN=1\gamma_{\rm PPN}=1 to much higher precision, so it may be taken as exactly 1 here. ((a)) Find the value of βPPN\beta_{\rm PPN} implied by the radar measurement, with its uncertainty. ((b)) State whether this is consistent with general relativity.

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