\magnification=\magstep1

$$
L \quad = \quad ( 4 \pi R^2 ) \thinspace \sigma T^4
$$

$$
L \quad = \quad f \thinspace 4 \pi d^2
$$

$$
R \quad = \quad \left[  {{f d^2}\over{\sigma T^4}} \right]^{1/2}
$$

$$
R \quad = \quad \sqrt{  {{f d^2}\over{\sigma T^4}} }
$$

$$
P^2 \quad = \quad {{ 4 \pi^2} \over {G M} } \thinspace a^3
$$

$$
M \quad = \quad  {{ 4 \pi^2} \over {G P^2}} \ \ a^3
$$

$$
{{\Delta M}\over{M}} \quad = \quad \left( {{\Delta a}\over{a}} \right) ^3 
             \quad = \quad \left( {{\Delta \rm dist}\over{\rm dist}} \right) ^3
$$




\bye
