AbstractIn this paper we present a fully hydrodynamical treatment of the stationary isothermal accretion problem onto a moving gravitating point mass. The derivation is purely analytical. We find that the accretion rate is more than a factor of 50 higher than the accretion rate derived from the partially non-hydrodynamical treatment by Hoyle and Lyttleton (1939) or Bondi and Hoyle (1944). This result may have some bearing on the evolutionary tracks of young pre-Main Sequence stars still embedded in their parent protocluster cloud. We discuss the work by Federova (1979) who investigated the pre-Main Sequence evolution of degenerate low mass ‘stars’ with strong accretion of protocluster cloud material. We suggest that the stars which lie below the Main Sequence in young clusters could strongly accrete matter at the pre-Main Sequence stage.