Observations indicate that interstellar molecular clouds can often be approximated by rotating (polytropic) cylinders. The two limiting configurations -the homogeneous and the isothermal cylinder-are used to obtain analytical solutions valid, at least qualitatively, for the whole range 0 n 1 of permitted polytropic indices. The radius of critically rotating, infinitely long polytropic cylinders has a flat minimum at polytropic index n ¼ 0:854, becoming infinite in the two limiting cases n ¼ 0 and 1. The ratio between the radii of critically rotating and nonrotating polytropic cylinders decreases strongly from 1 if n ¼ 0 to 1.52 if n ¼ 2:04, afterward increasing slowly to exp (1/2) ¼ 1:65 if n ¼ 1. Natural polytropic variables are presented in the Appendix. Subject headingg s: equation of state -hydrodynamics -ISM: kinematics and dynamics

This paper presents trajectories of a spacecraft moving in the gravitational field given by Rein’s model for the restricted three-body problem. For various initial conditions, closed orbits are determined using Maple’s numerical capabilities for ODE. Applications to the Earth-Moon system are considered, with trajectories computed around the stable L4 Lagrangian point.

No abstract

No abstract

No abstract