  Conjunction analysis for resident space objects (RSOs) requires estimating
the range of altitudes that each object can cross, i.e. its space occupancy,
throughout a screening time of, typically, a few days. The work proposes an
analytical method to evaluate the space occupancy of an RSO for a time horizon
of generic duration in a zonal problem model. The method, which allows one to
compute the maximum and minimum occupied orbit radii by solving a quartic
equation, is employed as a basis for the implementation of a new conjunction
filter with a considerable performance improvement compared to the classical
apogee-perigee filter. The effectiveness of the newly proposed filter is
assessed in a low-Earth orbit scenario using a high-fidelity perturbation model
and for a wide range of orbits and conjunction geometries. Finally, the space
occupancy evaluation method is employed as a quick and effective tool to assess
the degree of radial overlap of RSOs in low-earth orbit and its evolution in
the last decade.
