DISTANCE PRESERVED SATELLITE CLUSTERS
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The purpose of this paper is to propose a general solution to the problem of creating a cluster of satellites such that the distance between any pair of them remains constant. We will assume that the orbits are Keplerian and the eccentricities are all small. The motion of satellites are defined in the reference frame of a fictitious satellite with circular orbit by linearized kinematic equations and relative orbital elements. The approach adopted is to eliminate the dependence on the mean anomaly from the expression of the distance. Detailed procedure is classified into three situations by positions of relative orbits: with same center, with same plane, and totally different. The first one is the most common and complicated. The method developed is to solve two quadratic constraint equations for each pair of satellites. It has a significant character of succession which easily allows us to put a large number of satellites into the cluster. The spatial positions of satellites are very special. Some particular situations are introduced. We also briefly analysed how to avoid the perturbing effects of Earth oblateness just by choosing proper parameters. An example has been given, which verified the methods and demonstrated the characters of the cluster.