Specific orbital energy change ΔE_orb as a function of normalized pericenter distance r_p/r_t for planets with 10 M_⊕ (left) and 20 M_⊕ (right) cores (a = 1 au). Colored symbols show the energy change after the first (red circles), second (blue squares), and third (green triangles) encounters. The discrete data points are connected by cubic spline interpolations to illustrate the trend. The horizontal dashed line marks ΔE_orb = 0, separating orbital energy gain (above) from loss (below). For both core masses, the peak of positive energy shifts toward larger r_p/r_t with successive encounters, and the three curves converge as r_p/r_t → 2.0, where mass loss becomes negligible. The black cross in the left panel shows a validation run with a = 5 au (all other parameters fixed), confirming that ΔE_orb is insensitive to semimajor axis for highly eccentric orbits.