ii) STELLAR:
1) During the main-sequence, the star's luminosity is generated by converting rest mass
into energy. The fraction of the star's rest mass that is converted over the main-
sequence lifetime is $f$. Show that a star's main-sequence lifetime in terms of its initial
mass $M_*$, assuming the standard mass-luminosity relation $L \propto M^{3.5}$, is given by
$\tau_{MS} = fc^2 \frac{M_\odot}{L_\odot} \left(\frac{M_*}{M_\odot}\right)^{-2.5}$
[6]