Mathematical prototypes for collocating geostationary satellites

Collocating geostationary satellites sharing the same position is much demanded for satellite operation recently,the separation strategies are adopted to safeguard the satellites collocated of leaving the relative distance beyond collision with different sets of orbit parameters.This paper presents the mathematical prototypes which establish the allowable relative distance with uncertainty of orbital determination(OD),as well as the orbital element offset for each pair of collocated satellites,and puts forward algorithms to build such relationship to face the challenge of putting three satellites sharing the same position,the algorithms to allocate the longitude,eccentricity and inclination for each satellite are also given to ascertain that the mathematical prototypes are the guide specification to design collocation strategy for geostationary satellites.