Quantization and symmetry in periodic coverage patterns with applications to earth observation

Analytical approaches based on an idealized physical model and concepts from number theory show that in periodic coverage patterns, uniquely defined by their revolution numbers R (orbital) and N (rotational), the subnodal points are earth-fixed, and they divide the equator into R equal segments of length s. The ascending subsatellite trace crosses each point once (only) each period. The descending subnodal points coincide with the ascending points if the integers N and R have like parity, and bisect the intervals between them if opposite. The interval between consecutive unidirectional crossings is Ns. Symmetries extend the equatorial results to all parallels of latitude. Complete periodic patterns of traces exhibit an overall symmetry, with trace intersections confined to discrete coordinate values which are quantized in longitude (basic s-unit) and symmetric in latitude.