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 / 3 / 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 $M_S\simeq 0.946M_{\odot }$. ThenFor $P=11.6$ days and $V_S=10\mathrm{m}{\mathrm{s}}^{-1}$, these give approximatelyThese 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.