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Orbital Resonance Simulation

Orbit 1 (inner, blue)

Semi-major axis a₁ a₁ = 100

Eccentricity e₁ e₁ = 0.10

Orbit 2 (outer, gold)

Semi-major axis a₂ a₂ = 160

Eccentricity e₂ e₂ = 0.05

Speed ×1.0

Resonance Presets

T₁ = -- yr

T₂ = -- yr

T₂/T₁ = --

Conjunctions: 0

Orbital Resonance — Kepler's Third Law

Two bodies are in mean-motion resonance (MMR) when their orbital periods form a ratio of small integers p:q. This causes periodic gravitational kicks at the same orbital phases, leading to long-term stability or instability depending on the geometry.

Kepler's Third Law: T = 2π √(a³/GM) → T₂/T₁ = (a₂/a₁)^(3/2)

The Galilean moons Io, Europa, Ganymede are in 1:2:4 Laplace resonance — Io is tidally heated to ~100W/m² by forced eccentricity. Neptune-Pluto are in 3:2 resonance. The Kirkwood gaps in the asteroid belt are cleared by 3:1, 5:2, 7:3 resonances with Jupiter. Watch the spirograph (Lissajous) pattern traced when orbits are near resonance.