\magnification=\magstep1



$$
P^2 \quad = \quad \left(  {4 \pi^2} \over { GM } \right) {\phantom{a}}^3
$$

$$
{\rm Incoming\ energy\ } \quad = \quad 
        \left(  { {L_{*}} \over{ 4 \pi a^2} } \right) 
        \thinspace \thinspace
        \pi R^2
$$

$$
{\rm Outgoing\ energy\ } \quad = \quad \thinspace 
        \left(  { \thinspace \sigma \thinspace T^4 \thinspace } \right) 
        \thinspace \thinspace \thinspace
        4 \pi R^2
$$

$$
  {
        \left(  { {L_{*}} \over{ 4 \pi a^2} } \right) 
        \thinspace \thinspace
        \pi R^2
  }
   \quad = \quad
  {
        \left(  { \thinspace \sigma \thinspace T^4 \thinspace } \right) 
        \thinspace \thinspace \thinspace
        4 \pi R^2
  }
$$

$$
T^4 \quad = \quad {  { L_{*} } \over { 16 \pi a^2 \sigma } }
$$

$$
\eqalign{
 {  {T_{\rm b}} \over {T_{\rm Earth}} } \quad &= \quad
   {\left(  
    { {  { 0.00155 } / { 1.0 } }  \over   { ( { 0.05 } / { 1.0 } } )^2 } 
  \right)}^{1/4} \cr
             \cr
             &= \quad  0.89 
}
$$ 





\bye
