Kepler's Third Law: Orbital Resonance Countdown (3D)

System

Resonance ratio (outer / inner period) 2.000

Inner orbital radius r₁ 1.60 AU

Time speed 1.0×

Live Readouts

T₁ (inner)

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r ∝ T^(2/3)

Kepler ✓

Status

locking…

Orbits (of inner body) until exact realignment

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Selected body

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How it works

Kepler's third law says a body's orbital period T and orbital radius r obey T² ∝ r³ around a common central mass. Two bodies are in orbital resonance when their periods form a simple integer ratio p:q — they then repeatedly return to the same relative geometry, the mechanism that locks Pluto to Neptune at 3:2 and drives the 1:2:4 Laplace resonance of Jupiter's moons Io, Europa and Ganymede.

T² = k·r³  →  r = r₁·(T/T₁)^(2/3)

resonant:     Tₒᵤₜₑᵣ / Tᵢₙₙₑᵣ = p/q  (small integers)
              → system realigns after q orbits of the inner body
non-resonant: ratio is not a simple fraction
              → the two bodies drift through every relative
                angle and never exactly repeat

Dragging the ratio slider off an exact preset detunes the resonance: the countdown disappears because there is no small integer q that returns the system to its start, and the traced path becomes an open, ever-shifting rosette instead of a closed pattern — the real distinction between a resonant and a non-resonant orbit.

Resonance ratio — sets Tₒᵤₜₑᵣ/Tᵢₙₙₑᵣ directly; the radius of every outer body is then derived from Kepler's law, not set independently.
3-body (Laplace) mode — chains the same ratio twice (T₂=ratio·T₁, T₃=ratio·T₂), reproducing the real 1:2:4 structure of the Galilean moons at ratio = 2.
Click a body — selects it and shows its period and radius.

Central mass Inner body Middle / outer body Outermost body (3-body mode)

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