Example of Pacman orbit. Top row: relative coordinates between BHs during the Jacobi capture. The reference frame is centered on the most massive BH and rotates with it. The binary Hill radius is marked by the dotted circle. Bottom row: the black line represents the binding energy (E_b) per unit mass of the binary (M_tot = M₁ + M₂), with negative values shown in the colored area. The black marker indicates the point when the energy becomes negative. The blue curve represents the relative distance (d_rel) between the BHs. The binary Hill radius is indicated by a dashed blue line.