\magnification=\magstep1

$$
2.512 \times 2.512 \times 2.512 \times 2.512 \times 2.512 
  \quad = \quad (2.512)^5 \quad  = \quad 100
$$

$$
(m_1 - m_2) \quad = 
    \quad 2.5 \thinspace \log_{10} \left( {{I_2}\over{I_1}} \right) 
    \quad = 
    \quad -2.5 \thinspace \log_{10} \left( {{I_1}\over{I_2}} \right) 
$$

$$
\left( {{I_1}\over{I_2}} \right) \quad = \quad
       10^{-0.4(m_1 - m_2)} 
   \quad = \quad
       10^{0.4(m_2 - m_1)} 
$$


$$
{\rm star\ at\ distance\ d\ } \qquad \Rightarrow \qquad I_1 \quad = \quad {{L}\over{4 \pi d^2}}
$$

$$
{\rm star\ at\ distance\ D\ } \qquad \Rightarrow \qquad I_2 \quad = \quad {{L}\over{4 \pi D^2}}
$$

$$
{{I_1}\over{I_2}} \quad         = \quad {{1/d^2}\over{1/D^2}} 
                          \quad = \quad {{D^2}\over{d^2}}
$$

$$
m \quad = \quad ZP - 2.5 \log_{10} I_1 
    \quad = \quad
                ZP - 2.5 \log_{10} \left( {{L}\over{4 \pi d^2}} \right) 
$$

$$
M \quad = \quad ZP - 2.5 \log_{10} I_2 
    \quad = \quad
                ZP - 2.5 \log_{10} \left( {{L}\over{4 \pi D^2}} \right) 
$$

$$
{\rm if\ D\ =\ 10\ pc} \qquad \Rightarrow \qquad (m - M) \quad = \quad ??
$$

$$
(m - M) \quad = \quad 5 \log_{10}(d) \ - \ 5 \log_{10}(D) 
$$
    
$$
(m - M) \quad = \quad 5 \log_{10}(d) - 5
$$


\bye 
