% Bernd Berg Sep 02 2018.
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\centerline{\bf Special and General Relativity (PHZ 4601/5606) Fall 2018 
Solutions} \bigskip

\centerline{\bf Set 3} 

% \begin{figure}[tb] % \vspace{5pc}
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% \caption{for assignment~14.} \label{fig_lader} \vskip -10pt
% \end{figure} \centerline{Potential as function of $z$.}

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\item{\bf 5. Gravitational frequency shift.} 
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Close to the earth surface we have 
$$ \frac{G\,M_E}{R_E} - \frac{G\,M_E}{R_E+h} = 
   \frac{G\,M_E\,h}{R_E} + O\left(R_E^{-2}\right)\,. $$
As $h\ll R_E$ holds, $g\,h$ is a good approximation.
The following Fortran program returns a time difference of 
5.5 micro seconds due to the gravitational frequency shift.
\input gfs.tex

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