Particle Swarm Optimization for Orbital Configuration of Satellite Constellations in Geostationary Orbit

The geostationary orbit (GEO), a finite one-dimensional longitudinal resource, has emerged as a critical research focus driven by the rapid development of global communication systems. This scarcity motivates current research efforts toward multi-satellite collocation within single longitudinal slots. This article investigates the optimization design problem of configurations at fixed longitudes in GEO. First, a kinematic model describing the relative fixed-point motion of geostationary satellites was established. Subsequently, the long-term stability conditions of these fixed-point configurations under J2 perturbations were analyzed, with collocation flight stability and passive flight safety formulated as design constraints. The particle swarm optimization (PSO) algorithm was employed to design circular and straight-line spatial configurations, and their corresponding Kepler orbital elements were numerically simulated. Comparative analysis confirmed that circular configurations demonstrate superior stability compared to straight-line configurations.