  The properties of an axisymmetric, stationary gas cloud surrounding a massive
central object are discussed. It is assumed that the gravitational field is
dominated by the central object which is modeled by a nonrelativistic
rotationally-symmetric potential. Further, we assume that the gas consists of
collisionless, identical massive particles that follow bound orbits in this
potential. Several models for the one-particle distribution function are
considered and the essential formulae that describe the relevant macroscopical
observables, such as the particle and energy densities, pressure tensor, and
the kinetic temperature are derived. The asymptotic decay of the solutions at
infinity is discussed and we specify configurations with finite total mass,
energy and (zero or non-zero) angular momentum. Finally, our configurations are
compared to their hydrodynamic analogs. In an accompanying paper, the
equivalent general relativistic problem is discussed, where the central object
consists of a Schwarzschild black hole.
