Solution
= Solution
Circular edge-on motion gives $V_s=2\pi a_s/P$ and center-of-mass balance gives $a_s=aM_p/(M_s+M_p)$. Eliminate $a$ using the preceding period relation:
$$
\frac{M_p^3}{(M_s+M_p)^2}=\frac{PV_s^3}{2\pi G}.
$$
Thus $\boxed{M_p^3\simeq PV_s^3M_s^2/(2\pi G)}$ when $M_p\ll M_s$. For a non-edge-on <orbit (dynamical system)>[orbit] the measured <velocity> instead determines $M_p\sin i$ to this accuracy; neglecting eccentricity is also part of the stipulated model.