Planetary Cleavage Mechanics: Why the Moon Can Structurally Fracture While the Earth Cannot

Description / Abstract: Terrestrial seismology is governed by strict dissipation bounds: on Earth, seismic intensity scales (such as the Japan Meteorological Agency JMA Intensity 7, peak ground acceleration PGA ≥ 4.0 m/s^2) describe localized surface shaking rather than global planetary failure. Because Earth possesses an active convective mantle, asthenospheric hydrous fluid lubrication, a molten outer core, and dynamic plate boundaries, seismic energy attenuates rapidly through viscoelastic damping (quality factor Q_Earth ≈ 100–300), preventing whole-planet rupture. In contrast, the Moon represents a fundamentally different planetary mechanical archetype: a cold, desiccated, monolithic brittle body with an ultra-thick lithosphere (h_lith ≈ 1,000 km) occupying over 80% of its volume, surrounded by an intensely scattering megaregolith with virtually zero fluid damping. This monograph establishes the theoretical formulation and geomechanical proofs demonstrating that the Moon is susceptible to catastrophic macro-scale cleavage and structural bifurcation under critical energy thresholds that Earth would absorb plastically: (1) We analyze Apollo Passive Seismic Experiment telemetry, proving that the Moon exhibits extreme seismic quality factors (Q_Moon ≈ 3,000–10,000), causing seismic reverberations to sustain undamped constructive resonance for hours ("ringing like a bell"); (2) We derive global thermal contraction stress profiles showing that billions of years of interior secular cooling have locked the lunar lithosphere into a pre-stressed state analogous to tempered glass, laced with global lobate thrust scarps; (3) Applying Linear Elastic Fracture Mechanics (LEFM) and Griffith brittle cleavage criteria, we prove that when stress intensity factors exceed critical fracture toughness (K_I ≥ K_Ic ≈ 2.4 MPa·m^1/2), dynamic crack propagation accelerates to the Rayleigh wave velocity (v_R ≈ 3.4 km/s), establishing self-sustaining planar cleavage across the lunar diameter in approximately 17 minutes; and (4) We calculate the critical energy threshold for hemispheric cleavage (E_cleave ≈ 10^23–10^24 J), which is five orders of magnitude lower than the gravitational binding energy (E_bind ≈ 1.2 × 10^29 J). We prove that aggressive industrial initiatives (e.g., Artemis nuclear subsurface explosive engineering or high-energy mining) introduce catastrophic bifurcation risks, mandating immediate planetary defense treaties.