\magnification=\magstep1



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


$$
P_{\rm years}^2 \quad = \quad \left(  {1} \over { M_{\rm solar} } \right) {{a_{\rm AU}}}^3
$$

$$
a_{\rm AU}^3 \quad = \quad \left(  M_{\rm solar} \right) {{P_{\rm years}}}^2
$$

$$
M_{\rm planet} \quad = \quad M_{\rm star} \ 
             \left(  { {a_{\rm star}}\over{a_{\rm planet}} } \right)
$$


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

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

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

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


$$
T \quad = \quad {\left( {  { L_{*} } \over { 16 \pi \sigma } } \right)}^{1/4}  \ 
                      {\left( { {1}\over{{a^2}} } \right)}^{1/4}
$$


$$
\eqalign{
 {  {T_{\rm b}} \over {T_{\rm Earth}} } \quad &= \quad
   {\left(  
    { {  { 0.00155 } / { 1.0 } }  \over   { ( { 0.052 } / { 1.0 } } )^2 } 
  \right)}^{1/4} \cr
             \cr
             &= \quad  0.89 
}
$$ 





\bye
