Exact symbolic verification of the Hill radius. Starting from the force-balance equation at L_1: G·m/r_H² = 3·G·M·r_H/a³. Cross-multiplying: m·a³ = 3·M·r_H³ → 3M·r_H³ − m·a³ ≡ 0 for r_H = a·(m/(3M))^{1/3}. Sympy verification: build r_H…
Exact symbolic verification of the Hill radius. Starting from the force-balance equation at L_1: G·m/r_H² = 3·G·M·r_H/a³. Cross-multiplying: m·a³ = 3·M·r_H³ → 3M·r_H³ − m·a³ ≡ 0 for r_H = a·(m/(3M))^{1/3}. Sympy verification: build r_H…