Equal-probability group visibility criteria for orbit design of surveillance satellite

To address the challenges posed by the large-scale deployment of low-orbit mega-constellations on space situational awareness (SSA), this study proposes an equal-probability group visibility criterion for orbit design of surveillance satellites. First, a solar angle calculation model under the celestial coordinate system is established. The boundary of visibility regions is calculated with maximum solar angle constraint, earth occlusion constraint and earth shadow constraint. Second, for mega-constellation objects sharing identical semi-major axes and orbital inclinations, their periodic distributions in the Ω−u phase plane (right ascension of the ascending node vs. argument of latitude plane) enable visibility regions to be geometrically represented in this two-dimensional (2D) phase space. However, intersection operations of multiple constraint domains under multi-constraint conditions result in fragmented non-connected domains in conventional 2D dynamical representations. A three-dimensional (3D) torus mapping method is introduced to transform disconnected visibility regions in 2D phase planes into closed 3D curves, enabling intuitive visualization and efficient computation of group visibility areas under multiple constraints. Finally, building upon the Ω−u phase plane representation methodology, equal-probability periodic coverage is proposed as the optimization metric. Simulated annealing algorithm is employed to optimize surveillance satellite orbit parameters. The phase plane methodology achieves 6.31 % superior coverage efficiency in space object visibility analysis through systematic screening mechanisms, significantly outperforming traditional spherical surface scanning techniques in orbital pattern optimization.