In this paper an algorithm for estimating the low-Earth-orbit space object population and distribution from measurements taken by a vertical, staring narrow beam radar is developed and validated. The radar measures the altitude, inclination, and radar cross section of each object which passes through the beam. Validation of the algorithm is achieved by simulating the orbits of the objects in the North American Aerospace Defense Command (NORAD) data base, determining those which pass through a vertical staring radar and by estimating the population and distribution of the NORAD data base from the altitude, inclination, and radar cross section of those which pass through. The effects of the assumptions made in developing the algorithm and measurement errors are discussed. An estimate of the operational time of the radar needed to achieve a specified accuracy in the space object population is also developed.
Nomenclature h= orbit altitude / = orbit inclination N = number of objects in population A^st = estimated number of objects in population r = orbit radius T = orbit period T m -measurement time a -Earth central angle subtended by radar j8 = radar beamwidth 6j = latitude of radar A = expected rate of objects through radar beam X* = measured rate of objects through radar beam