\magnification=\magstep1


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


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

$$
{ {d_1} \over {d_2}} \quad = \quad { {m} \over {M} }
$$

$$
{ {m} \over {M} }
\quad = \quad 
{ {d_1} \over {d_2}} 
$$


$$
M \quad = \quad \left( { { 4 \pi^2 a^3 } \over {G P^2} } \right) 
              \thinspace \left[ {{ d_2} \over {d_1 + d_2} } \right]
$$


$$
m \quad = \quad \left( { { 4 \pi^2 a^3 } \over {G P^2} } \right) 
              \thinspace \left[ {{ d_1} \over {d_1 + d_2} } \right]
$$


$$
\gamma \quad \equiv \quad { {m} \over {M} }
$$


$$
{P}^2 \quad = \quad { {4 \pi^2} \over { G M (1 + \gamma) } } 
              \thinspace \thinspace \thinspace  d_1^3 \left( 1 + { {1}\over{\gamma}} \right) ^3
$$

$$
{ { (1 + {{1}\over{\gamma}} )^3 } \over {1 + \gamma} } \quad 
  = 
  \quad  { { G M P^2 } \over { 4 \pi^2 \thinspace d_1^3 } }
$$


$$
{\rm true\ mass\ of\ planet\ } m \quad = 
         \quad { {m_{\rm obs}} \over {\sin (i)} } \quad \ge
          \quad m_{\rm obs} 
$$


$$
{\rm eccentricity\ \ } e \quad = \quad \sqrt{ 1 - {{b^2} \over {a^2}} }
$$

$$
{\rm center\ to\ focus\ \ } f \quad = \quad ae
$$


\bye
