= Solution
Converting luminosity to mass needs a <main-sequence mass-luminosity relation>. Using the near-solar approximation $L/L_\odot\simeq(M/M_\odot)^4$ gives $M_S\simeq0.946M_\odot$. Then
$$
M_P=V_S\left(\frac{PM_S^2}{2\pi G}\right)^{1/3},\qquad a=\left(\frac{GM_SP^2}{4\pi^2}\right)^{1/3}.
$$
For $P=11.6$ days and $V_S=10\,\mathrm{m\,s^{-1}}$, these give approximately
$$
\boxed{M_P\simeq0.107M_J,\qquad a\simeq0.0985\,\mathrm{AU}.}
$$
These estimates retain the circular, edge-on and low-companion-mass assumptions. Adopting a mass-luminosity exponent $3.5$ instead changes the quoted values by about one percent; luminosity alone does not determine a unique stellar mass without such a calibration.
Back to article page
