Histograms of ϕ for U_∞ = 1 (﹩{ \mathcal T }=2﹩) particles at t = 0.1t_S and 1.0t_S, respectively. The planet has mass m_p = 1 × 10⁻⁴M_⊙ and a_p = 1 au, and the corresponding scattering timescale t_S = 3.5 Myr is computed using Equation (58). The initial conditions for the particles are ﹩{{ \mathcal A }}_{0}=1.1﹩, e₀ = 0.854, and i₀ = 2﹩\mathop{.}\limits^{\unicode{x000b0}}﹩9, corresponding to ϕ₀ = 88﹩\mathop{.}\limits^{\unicode{x000b0}}﹩2. The median ϕ during scattering is marked with a red vertical line.