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Cluster flight algorithms enable the operation of multiple satellites within given distance bounds for long periods of time. Synchronizing the states of the satellites in the cluster is important for both cluster establishment and cluster keeping. This paper offers two distributed orbit control laws with fixed-magnitude thrust for satellite cluster flight based on mean-orbital elements. These controllers are capable of synchronizing the convergence of orbital elements among all satellites. Intersatellite communication is represented by weighted digraphs, and the related stability properties of the closed-loop control system are examined. Global asymptotic stability is proven for the first controller using nonsmooth analysis, whereas the second controller is shown to be only locally asymptotically stable. Furthermore, it is proven that chattering in the thrust direction is unavoidable when using fixed-magnitude thrusters and continuous weights. The occurrence of chattering is analyzed with respect to constant weights and time-varying weights. Two approaches are suggested to mitigate chattering: fast-varying weights and thrust modulation. Numerical simulations are performed to validate the analysis.

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