This paper addresses the trajectory analysis, mission design, and control law for multiple microsatellites to cooperatively circumnavigate a host spacecraft. This cooperative circumnavigation (CCN) problem is defined to drive a group of networked microsatellites to a predefined planar ellipse concerning a host spacecraft while maintaining a geometric formation configuration. We first design several potential functions to guide the microsatellites to the given planar elliptical orbit with a proper radius. Next, the affine Laplacian matrix is introduced to characterize the desired formation shape of microsatellites. Based on the potential functions and the Laplacian matrix, a CCN control law is finally proposed. Then, the simulation results of eight microsatellites with earth-orbiting mission scenarios are given, where the natural trajectory motion is incorporated which consumes nearly zero-fuel.