\magnification=\magstep2

$$
   P^2  =  { {4 \pi^2} \over {G (M_s + M_p)} }  (R_s + R_p)^3
$$


$$
   P^2  \sim  { {4 \pi^2} \over {G (M_s)} }  (R_p)^3
$$


$$
   a_c  \quad = \quad {{v^2} \over {R_s}}
$$

$$
   a \quad = \quad {{ G M_p } \over {(R_s + R_p)}^2 }
$$

$$
   {{R_p} \over {R_s}} \quad = \quad {{M_s} \over {M_p}}  
         \qquad \rightarrow
         \quad
           M_p \quad = \quad {{{M_s} {R_s}} \over {R_p}}
$$

$$
   a \quad = \quad {{ G M_s R_s } \over {R_p (R_s + R_p)}^2 }
$$

$$
      (R_s + R_p) \quad \simeq \quad R_p
$$

$$
   a \quad \simeq \quad {{ G M_s R_s } \over {R_p}^3 }
$$


\bye
