% Bernd Berg Oct 20 2018.
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\centerline{\bf Special and General Relativity (PHZ 4601/5606) Fall 2018 
Solutions} \medskip

\centerline{\bf Set 9} 

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\item {\bf 21. Radar Distance.}
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Let the coordinate times for light-signals from $A$ to $B$ and $B$ to 
$A$ be $\triangle t_{A\to B}$ and $\triangle t_{B\to A}$, respectively. 
The coordinate round-trip time $\triangle t$ for a radio echo is the 
same at $A$ and $B$: $\triangle t = \triangle t_{A\to B} + \triangle 
t_{B\to A}$. But the radar distance is determined with standard clocks:
Radar distance measured at~$A$: $L_A=(c/2)\,\triangle \tau_A =
(c/2)\,\exp(\Phi_A/c^2)\,\triangle t$ and, similarly, $L_B=(c/2)\,
\triangle \tau_B = (c/2)\,\exp(\Phi_B/c^2)\,\triangle t$. Therefore,
$$ \frac{L_A}{L_B} = \frac{\exp(\Phi_A/c^2)}{\exp(\Phi_B/c^2)}\,. $$

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