A proposed gyroscope satellite in circular orbit around Jupiter would measure the…

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 proposed gyroscope satellite in circular orbit around Jupiter would measure the geodetic precession of its spin axis. General relativity (

\gamma_{\rm PPN}=1

) predicts a magnitude

\Omega_{\rm GR}=200.0\ \mathrm{mas\,yr^{-1}}

for the proposed orbit. In the PPN framework the same precession is

\Omega = \dfrac{1+2\gamma_{\rm PPN}}{3}\,\Omega_{\rm GR}

, where

\Omega_{\rm GR}

is defined so that it already contains the factor evaluated at

\gamma_{\rm PPN}=1

, namely

(1+2)/3=1

. The mission returns a measured precession

\Omega_{\rm meas}=199.5\pm0.8\ \mathrm{mas\,yr^{-1}}

. ((a)) Find

\gamma_{\rm PPN}-1

and its

1\sigma

uncertainty from this result. ((b)) Using twice the

1\sigma

uncertainty as the two-standard-deviation bound on

|\gamma_{\rm PPN}-1|

, derive the corresponding lower bound on the Brans-Dicke coupling

\omega_{\rm BD}

. ((c)) State whether this bound is stronger or weaker than a Cassini-type time-delay bound of

\omega_{\rm BD} > 4\times10^4

, and explain why in terms of the two experiments' precisions.

Browse the problem library