P^{2} = \frac{4π^{2}}{G(M_{s} + M_{p})}(R_{s} + R_{p})^{3}

P^{2} ∼ \frac{4π^{2}}{G(M_{s})}(R_{p})^{3}

a_{c} = \frac{v^{2}}{R_{s}}

a = \frac{GM_{p}}{(R_{s} + R_{p})^{2}}

\frac{R_{p}}{R_{s}} = \frac{M_{s}}{M_{p}} → M_{p} = \frac{M_{s}R_{s}}{R_{p}}

a = \frac{GM_{s}R_{s}}{R_{p}(R_{s} + R_{p})^{2}}

(R_{s} + R_{p}) ≃ R_{p}

a ≃ \frac{GM_{s}R_{s}}{R_{p}^{3}}