\magnification=\magstep1


$$
Q_{\rm scatter} \quad = \quad {{8}\over{3}} \thinspace
         {\left( {{2 \pi a}\over{\lambda}} \right)}^4 \thinspace
         {\left[ {{n^2 - 1}\over{n^2 + 1}} \right]}^2
$$


$$
{\rm energy\ absorbed\ per\ second\ } \quad = \quad
     Q_{\rm abs} \ \varepsilon c \   
       ( \pi a^2 ) \thinspace
$$

$$
Q_{\rm abs} \quad  \simeq \quad 0.8 \thinspace 
        {\left( {{a}\over{0.1 \thinspace \mu{\rm m}}} \right)}^{0.85}
$$

$$
{\rm energy\ radiated\ per\ second\ } \quad = \quad
     Q_{\rm emit} \   ( 4 \pi a^2 )  \   
     \sigma T^4
$$


$$
Q_{\rm emit} \quad  \simeq \quad 3.2 \times 10^{-4}  \thinspace 
        {\left( {{a}\over{0.1 \thinspace \mu{\rm m}}} \right)} \thinspace
         {\left[ {{T}\over{20 \thinspace {\rm K}}} \right]}^2
$$


$$
\left( {\rm 1 - albedo} \right) \thinspace 
   {F} \thinspace \left( \pi R^2 \right) \thinspace 
   \quad = \quad
\left( {\rm emissivity } \right) \thinspace 
       \left( 4 \pi R^2 \right) \thinspace \sigma T^4 \thinspace 
$$


$$
\quad 0.8 \thinspace 
        {\left( {{a}\over{0.1 \thinspace \mu{\rm m}}} \right)}^{0.85}
  \thinspace
    \left( 10^{-13} \  c \right) \thinspace
    \left( \pi a^2 \right) 
       \quad = \quad 
                           3.2 \times 10^{-4}  \thinspace 
        {\left( {{a}\over{0.1 \thinspace \mu{\rm m}}} \right)} \thinspace
         {\left[ {{T}\over{20 \thinspace {\rm K}}} \right]}^2
      \thinspace
        \left( 4 \pi a^2 \right) 
      \thinspace
        \sigma T^4 
$$

$$
L \quad = \quad ({\rm Area}) \thinspace \sigma T^4 \quad = \quad
             (4 \pi r^2) \thinspace \sigma T^4 
$$

\bye

