  We propose a method for determining the two-dimensional orbits of
interstellar matter (ISM) in galactic disks using observed line-of-sight
velocity fields. Although four components, consisting of two of position and
two of velocity, are necessary to determine two-dimensional orbits, the
velocity perpendicular to the line of sight can hardly be determined from
observations. We show that the ISM orbits can be approximately determined by
assuming that (1) the angular momentum is conserved along each orbit, (2) all
orbits are closed in a single rotating frame, and (3) the system is symmetric
through the origin. Since the angular momentum can be estimated on the major
axis of a disk, a velocity perpendicular to the line of sight can be determined
according to the conservation of angular momentum, and thus two components of
velocity are obtained. The ISM orbits can be calculated by solving differential
equations given by an obtained two-dimensional velocity field when a certain
pattern speed is given. The typical deviation from the correct orbit is less
than the observational resolution according to our test calculations for
modeled velocity fields. We applied this method to the observed data of NGC
4569 and obtained possible orbits for this galaxy. Furthermore, we calculated
the mass distribution using our result.
