Analysis of Relative Motion of Collocated Geostationary Satellites with Geometric Constraints

This paper investigates the design of the relative motion orbits of geostationary satellites in the presence of geometric constraints. A geometric constraint is defined by a sensor’s pointing direction and field of view. An analyis was made of the underlying geometry of the relative orbits associated to geometric constraints. This resulted in the derivation of novel relations between relative orbital elements and geometric constraints. The paper presents a set of guidelines that can support the design of relative orbits, that use the relations between the orbital elements and constraints. These guidelines are applied in a characteristic example that includes a nadir-pointing sensor and a north-looking star sensor. The focus in this paper is on collocated satellites in geostationary orbits. The results were derived for near-circular orbits, where the satellites share the same mean argument of longitude. The developed relations can likewise be applied for other types of collocated satellites.