Abstract:Several space physics missions that are being designed or flown need spacecrafts flying in a tetrahedron configuration about a highly elliptical reference orbit. At least four spacecrafts can separate space and time, and measure the structural and dynamic parameters of space environment along the mission arc. Based on the orbit element model of relative motion, an analysis was performed to study the influence of four reference orbit elements on the tetrahedron's quality factor and average side length. On the assumption that one spacecraft runs along the reference orbit, a tetrahedron formation optimization design model was proposed, whose design variables are fifteen relative orbit elements of the other three spacecrafts while objective function involves the tetrahedron's quality factor and mean side length. Then, this model is applied in phase I of Magnetosperic MultiScale mission. The results show that a tetrahedron formation with better performance in the mission arc can be found through optimization method while no control is exerted.