Exact symbolic verification of the rigid-body Roche limit. Starting from the tidal vs self-gravity balance: 2·G·M·r_m/d³ = G·m_m/r_m² with M = (4π/3)·R³·ρ_M and m_m = (4π/3)·r_m³·ρ_m. Cancelling (4π/3)·G and r_m: 2·R³·ρ_M/d³ = ρ_m →…
Exact symbolic verification of the rigid-body Roche limit. Starting from the tidal vs self-gravity balance: 2·G·M·r_m/d³ = G·m_m/r_m² with M = (4π/3)·R³·ρ_M and m_m = (4π/3)·r_m³·ρ_m. Cancelling (4π/3)·G and r_m: 2·R³·ρ_M/d³ = ρ_m →…