\magnification=\magstep1

$$
2 R_A \ + \ 2 R_B \quad = \quad (t_4 - t_1) * (v_A + v_B)
$$

$$
2 R_A \ - \ 2 R_B \quad = \quad (t_3 - t_2) * (v_A + v_B)
$$

$$
R_A \quad = \quad {{1}\over{4}} \ \left[ (t_4 - t_1) + (t_3 - t_2) \right] 
                 \thinspace (v_a + v_b)
$$

$$
R_B \quad = \quad {{1}\over{4}} \ \left[ (t_4 - t_1) - (t_3 - t_2) \right] 
                 \thinspace (v_a + v_b)
$$

$$
P^2 \quad = \quad \left( {{1}\over{m_A + m_B}} \right) \thinspace a^3
$$

$$
{\rm circumference \ C} \quad = \quad v * P \quad = \quad 2 \pi r
$$

$$
{{v_A}\over{v_B}} \quad = \quad {{m_B}\over{m_A}}
$$

$$
\eqalign{
B_{tot} \quad &= \quad 4 \pi R_A^2 \sigma T_A^4 \ + \ 4 \pi R_B^2 \sigma T_B^4 \cr
\phantom{B = } \cr
B_{sec} \quad &= \quad 4 \pi R_A^2 \sigma T_A^4  \cr
\phantom{B = } \cr
B_{pri} \quad &= \quad 4 \pi (R_A^2 - R_B^2) \sigma T_A^4 \ + \ 4 \pi R_B^2 \sigma T_B^4  \cr
}
$$

$$
B_{tot} \ - \ B_{pri} \quad = \quad 4 \pi \sigma R_B^2 T_A^4
$$

$$
B_{tot} \ - \ B_{sec} \quad = \quad 4 \pi \sigma R_B^2 T_B^4
$$


$$
{ {B_{tot} \ - \ B_{pri}}\over{B_{tot} \ - \ B_{sec}} } 
   \quad = \quad 
       \left({{T_A}\over{T_B}}\right) ^4
$$

$$
L \quad = \quad 4 \pi R_A^2 \sigma T_A^4 \ + \ 4 \pi R_B^2 \sigma T_B^4 
$$







\bye
