  We combine the equations of motion that govern the dynamics of galaxies in
the local volume with Bayesian techniques in order to fit orbits to published
distances and velocities of galaxies within $\sim 3$ Mpc. We find a Local Group
(LG) mass $2.3\pm 0.7\times 10^{12}{\rm M}_\odot$ that is consistent with the
combined dynamical masses of M31 and the Milky Way, and a mass ratio
$0.54^{+0.23}_{-0.17}$ that rules out models where our Galaxy is more massive
than M31 with $\sim 95\%$ confidence. The Milky Way's circular velocity at the
solar radius is relatively high, $245\pm 23$ km/s, which helps to reconcile the
mass derived from the local Hubble flow with the larger value suggested by the
`timing argument'. Adopting {\it Planck}'s bounds on $\Omega_\Lambda$ yields a
(local) Hubble constant $H_0=67\pm 5$km/s/Mpc which is consistent with the
value found on cosmological scales. Restricted N-body experiments show that
substructures tend to fall onto the LG along the Milky Way-M31 axis, where the
quadrupole attraction is maximum. Tests against mock data indicate that
neglecting this effect slightly overestimates the LG mass without biasing the
rest of model parameters. We also show that both the time-dependence of the LG
potential and the cosmological constant have little impact on the observed
local Hubble flow.
