The dynamics of a point-like mass body in the central plateau of a collapsing protostellar cloud

The collapse of a spherically symmetric, self-gravitating, isothermal, protostellar cloud has been described in terms of hydrodynamics by several authors. One of the solutions found provides initially flat behaviour of the density in the cloud's interior. (This specific interior herein is referred to as "the central plateau".) This paper gives an analytical solution - in the form of a power series - of the equations of motion of a test point-like mass body, located within the central plateau. The solution reducing computational time can be useful in studying the dynamics of a huge number of bodies in a collapsing protostellar cloud (in studying the dynamics of cometary nuclei in the collapsing protosolar nebula, for example).