P^{2} = \frac{4π^{2}}{G(M + m)} a^{3}

M + m = \frac{4π^{2}}{P^{2}} a^{3}

\frac{d_{1}}{d_{2}} = \frac{m}{M}

\frac{m}{M} = \frac{d_{1}}{d_{2}}

M = (\frac{4π^{2}a^{3}}{GP^{2}} ) [\frac{d_{2}}{d_{1} + d_{2}} ]

m = (\frac{4π^{2}a^{3}}{GP^{2}} ) [\frac{d_{1}}{d_{1} + d_{2}} ]

γ ≡ \frac{m}{M}

P^{2} = \frac{4π^{2}}{GM(1 + γ)} d_{1}^{3} (1 + \frac{1}{γ} )^{3}

\frac{(1 + \frac{1}{γ})^{3}}{1 + γ} = \frac{GMP^{2}}{4π^{2} d_{1}^{3}}

true mass of planet m = \frac{m_{obs}}{sin(i)} ≥ m_{obs} eccentricity e = \sqrt{1 − \frac{b^{2}}{a^{2}}} center to focus f = ae