Gravitational Binding Energy and the Threshold for Destroying a Planet

Gravitational binding energy is the energy required to disperse all of a body's mass to infinity against its own self-gravity. For an Earth-mass planet, this is approximately **2.5 × 10³² joules**. Below this threshold, you can wound a planet — melt the surface, eject a continent, even spin off a moon — but the bulk reaccretes under gravity. Only at or above the binding-energy threshold does the body truly cease to exist. Scale benchmarks show how extreme this number is: - Hiroshima atomic bomb: 6 × 10¹³ J (10⁻¹⁹ of Earth's binding energy) - Tsar Bomba (largest H-bomb ever detonated): 2 × 10¹⁷ J (10⁻¹⁵) - All Cold War nuclear arsenals combined: ~10¹⁹ J (10⁻¹³) - Chicxulub impactor (dinosaur killer): ~4 × 10²³ J (10⁻⁹) - Sun's total radiative output per second: 3.8 × 10²⁶ J (10⁻⁶) - Theia impact (Moon-forming collision): ~10³¹ J (about 4% of binding energy) - **Earth gravitational binding energy: 2.5 × 10³² J** - Supernova total energy output: ~10⁴⁴ J (a trillion times Earth's binding energy) The **Theia benchmark** is the most instructive: a Mars-sized impactor (~6000 km diameter) hitting early Earth at ~15 km/s — the closest event in Earth's actual history to "planet destruction" — delivered only 4% of binding energy. It melted the surface and ejected enough material to form the Moon, but left Earth coherent. Real planetary destruction requires Theia × 25+ or a cosmic-tier directed weapon. A clean tunnel through a planet does effectively nothing structurally. A 10m-wide tunnel through Earth removes about 10⁻¹² of the mass (a trillionth — like a sewing needle through a basketball). Even a 1 km-wide vaporized tunnel only delivers ~7.5 × 10²³ J (about 2x Chicxulub, still 10⁻⁹ of binding energy). The pressure gradient (Earth's core sits at ~360 GPa, rock fails at ~GPa) collapses any tunnel at the speed of sound in rock within milliseconds. Real mechanisms that can actually disperse a planet: Theia-class impactors stacked 5+ times; relativistic kill vehicles (the Kzinti Lesson — 1000 tons at near-lightspeed delivers binding-energy-scale kinetic energy); ~3 million tons of antimatter; stellar disruption during the host star's red-giant phase (the polluted white dwarf signature shows that 25-50% of white dwarfs have accreted former planets); a close supernova (under 0.1 light-year); tidal disruption by a black hole; or cosmic-tier directed energy weapons.