Kepler's Third Law: Orbital Resonance Countdown (2D)

System

Resonance ratio (outer / inner period) 2.000

Inner orbital radius r₁ 1.60 AU

Time speed 1.0×

Phase Dial (body 1 → body 2)

Relative angle
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

This 2D view plots the same Kepler-law resonance from directly above the orbital plane and adds a phase dial that tracks only the relative angle between the inner and second body — the quantity that must return to 0° for the system to realign. A resonant ratio (integer p:q) makes this needle sweep through a fixed, repeating pattern; a detuned ratio makes it drift continuously through every angle, which is the real signature of a non-resonant orbit.

T² = k·r³  →  r = r₁·(T/T₁)^(2/3)
Δθ(t) = θ₂(t) − θ₁(t)   (mod 360°)
resonant:      Δθ(t) repeats exactly every q orbits of body 1
non-resonant:  Δθ(t) never returns to its starting value

Drag to pan the view, scroll (or pinch) to zoom, and click a body to read its period and radius.

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

Drag to pan · scroll to zoom