Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2015 / S2 / 1 / 2 / Solution

Kepler's third law is $P^2=4{\pi }^2{a}^3/[G(M_S+M_P)]$, with $a$ the semimajor axis of the relative orbit. For a circular edge-on orbit, the star's speed is $V_S=2\pi a_S/P$, and the centre of mass relation gives $a_S=a{M}_P/(M_S+M_P)$. Cubing the speed expression and eliminating $a$ yieldsFor $M_P\ll M_S$, this reduces toWithout the edge-on assumption, a factor ${\sin }^{3}i$ multiplies the numerator, explaining the minimum-mass degeneracy of the radial-velocity method.