
\magnification=\magstep2

$$
\eqalign{
E_A \quad = \quad \gamma_A m c^2 \cr
E_B \quad = \quad \gamma_B m c^2 \cr
}
$$

$$
{ { \gamma_A } \over { \gamma_B } } \quad = 
$$

$$
 { \gamma_A } \quad = \quad   \gamma_B  \thinspace \left ( 
            \phantom{2.88323} \right )
$$


$$
t_A \quad = \quad {{ D } \over {v_A} }
$$

$$
\gamma \quad = \quad {{ 1} \over {\sqrt{1 - {{v^2}\over{c^2}} } } } 
          \qquad \rightarrow \qquad 
     v \quad = \quad c \thinspace \sqrt{ 1 - {{1}\over{\gamma^2}} } 
$$

$$
\eqalign{
t_A \quad &= \quad {{ D } \over {c} } 
        { {1} \over {\sqrt{1 - {{1}\over{\gamma^2} } } } } \cr
\cr
          &= \quad t_0
        { {1} \over {\sqrt{1 - {{1}\over{\gamma^2} } } } } \cr
}
$$

$$
t_A \quad = \quad t_0  \thinspace \thinspace + \thinspace \thinspace 
              {{1}\over{2}} \thinspace t_0 
             \thinspace {{1}\over{\gamma_A^2}}
$$

$$
t_B \quad = \quad t_0  \thinspace \thinspace + \thinspace \thinspace 
              {{1}\over{2}} \thinspace t_0 
             \thinspace {{1}\over{\gamma_B^2}}
$$

$$
t_B - t_A \quad = \quad
          {{{1}\over{2}} \thinspace t_0 } 
                \thinspace
               \left ( ?? \thinspace - \thinspace ?? \right )
$$

$$
\eqalign{
t_B - t_A \quad &= \quad
          {{{1}\over{2}} \thinspace t_0 } 
                \thinspace
               \left ( {{1}\over{\gamma_B^2}} 
                       ( 1  - 
                        {{1}\over{1.73^2}} )   \right ) \cr
\cr
          \quad &= \quad
          {{{1}\over{2}} \thinspace t_0 } 
                \thinspace
                       ( 0.6648 ) 
                \thinspace 
               \left ( {{1}\over{\gamma_B^2}}  \right ) \cr
}
$$



\bye
