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We have derived the mean proper motions and space velocities of 154 Galacticglobular clusters and the velocity dispersion profiles of 141 globular clustersbased on a combination of Gaia DR2 proper motions with ground-basedline-of-sight velocities. Combining the velocity dispersion profiles derivedhere with new measurements of the internal mass functions allows us to modelthe internal kinematics of 144 clusters, more than 90% of the currently knownGalactic globular cluster population. We also derive the initial cluster massesby calculating the cluster orbits backwards in time applying suitable recipesto account for mass loss and dynamical friction. We find a correlation betweenthe stellar mass function of a globular cluster and the amount of mass lostfrom the cluster, pointing to dynamical evolution as one of the mechanismsshaping the mass function of stars in clusters. The mass functions also showstrong evidence that globular clusters started with a bottom-light initial massfunction. Our simulations show that the currently surviving globular clusterpopulation has lost about 80% of its mass since the time of formation. Ifglobular clusters started from a log-normal mass function, we estimate that theMilky Way contained about 500 globular clusters initially, with a combined massof about $2.5 \cdot 10^8$ $M_\odot$. For a power-law initial mass function, theinitial mass in globular clusters could have been a factor of three higher.

Mean proper motions, space orbits and velocity dispersion profiles of Galactic globular clusters derived from Gaia DR2 data