Analytical results of libration zones for apsidal resonances causing orbit flips (left panel) and the numerical results of flipping regions (right panel). The left panel shows four libration zones causing orbit flips (zones 3, 4, 7, and 8). Apsidal resonances with centres at i = 90° cause orbit flips. The right panel shows three distinct regions of orbit flips, located in low-eccentricity, intermediate-eccentricity, and high-eccentricity space.