$\Omega ^B$ and $\Omega ^0$ from MACHOs and Local Group Dynamics

We obtain restrictions on the universal baryon fraction, $f_B = \Omega_{B}/ \Omega_{0}$, by assuming that the observed microlensing events towards the Large Magellanic Cloud are due to baryonic MACHOs in the halo of the Galaxy and by extracting a bound to the total mass of the Milky Way from the motion of tracer galaxies in the Local Group. We find a lower bound $f_B > 0.29^{+0.18}_{-0.15}$ . Consistency with the predictions of primordial nucleosynthesis leads to the further constraint on the total mass density, $\Omega_{0} \lesssim {0.2}$