Particle trajectories in a two-dimensional steady state reconnection field geometry are studied in order to understand phase space density variations near the magnetopause and in the geomagnetic tail. Charged particles are traced back in time from a spacecraft position until they are in the source or inflow region for an entire gyroorbit. The inflow regions for the dayside magnetopause are the magnetosheath and the closed field lines inside the magnetosphere. The inflow regions for the magnetotail are the lobes north and south of the central plasma sheet. Using Liouville's theorem and known distribution functions in the source regions, the distribution function at the spacecraft can be calculated. Unlike previous studies of ''remote sensing,'' this one is in two dimensions and includes a perpendicular electric field. The question of whether ''trapped'' distribution functions can exist on ''open'' field lines on the dayside magnetopause is examined as well as the signatures of reconnection in the geomagnetic tail. We find that ''trapped'' distributions which have a peak at or near 90¿ pitch angle can exist on topologically ''open'' field lines. Thus the observations of such distributions in the low-latitude boundary layer do not establish that this layer is on closed field lines. In the tail the omnidirectional flux of keV ions should show a minimum in the center of the plasma sheet at distances up to about 25 RE earthward of the neutral line. Since no such minimum is apparent in the ISEE data, we conclude that the neutral line in the tail is generally tailward of 50 RE. We also find that adiabatic theory cannot be used as a means for visualizing or predicting the orbits of charged particles in these complex magnetic field topologies. In fact, we find that some orbits are chaotic in the sense that particles which start at nearly the same place in phase space follow entirely different and exponentially (in time) diverging orbits. These rather unintuitive results suggest that there is no simple or general method for interpreting pitch angle distributions observed near magnetospheric boundary layers which are magnetically connected to a neutral line. ¿ American Geophysical Union 1989