Equilibrium on the Eddington capture sphere. Trajectories of particles returning to the Eddington sphere (X = 5, k = 1.5) are shown for four initial velocity perturbations: v^φ ≡ xdφ/dτ = 0.12,v^r ≡ dx/dτ = 0 (thick green continuous line), v^φ = 0.20,v^r = 0 (thin blue continuous line), v^φ = 0.12,v^r = 0.10 (thick red dashed line) and v^φ = 0.12,v^r = −0.10 (extra thick violet dashed line). Also shown is a tangential escape trajectory (in thick brown) with initial v^φ = 0.32,v^r = 0.