  General Relativity yields an analytical prediction of a minimum required mass
of roughly $\sim 0.08-0.09 M_{\odot}$ for a star to stably burn sufficient
hydrogen to fully compensate photospheric losses and, therefore, to belong to
the main sequence. Those objects below this threshold (brown dwarfs) eventually
cool down without any chance to stabilize their internal temperature. In this
work we consider quadratic Palatini $f(\mathcal{R})$ gravity and show that the
corresponding newtonian hydrostatic equilibrium equation contains a new term
whose effect is to introduce a weakening/strenghtening of the gravitational
interaction inside astrophysical bodies. This fact modifies the General
Relativity prediction for this minimum main sequence mass. Through a crude
analytical modelling we use this result in order to constraint a combination of
the quadratic $f(\mathcal{R})$ gravity parameter and the central density
according to astrophysical observations.
