Orbital Resonance: How Repeating Gravity Rhythms Become Visible

Orbital resonance is one of the most intuitive ways to make gravity feel musical. Two bodies do not need to touch or collide. If their periods repeat in a ratio like 2:1, 3:2 or 5:3, their conjunctions start arriving with a recognizable rhythm.

The Orbital Resonance Atlas Lab turns that rhythm into a visible artifact. It plots orbit trails, marks conjunction chords, traces the resonant angle and reports Hill-spacing diagnostics so the picture is not just orbit art.

The Useful Formula

For a central-mass approximation, the simple relation is P^2 = a^3 / Mstar. Once the inner period is known, a resonance ratio gives the outer period. A 2:1 rhythm means the outer body takes twice as long to orbit as the inner one.

The atlas then tracks theta = p*lambda_outer - q*lambda_inner. When this angle stays in a narrow range, the rhythm is visually coherent. When it circulates widely, the system is closer to a loose commensurability than a tight resonance window.

Why Conjunctions Matter

Conjunctions are the moments when the bodies line up in longitude. A useful visualizer should not merely draw ellipses. It should show where conjunctions happen and whether their geometry repeats. That is why the atlas exports a conjunction CSV, not only a pretty SVG.

Why Hill Spacing Matters

Mutual Hill spacing is a compact way to ask whether two orbiting bodies are too close for comfort. It is not a full stability proof, but it is a valuable warning metric. A resonance map that ignores separation can make a dangerous-looking setup seem elegant.

How To Use The Atlas

1. Open the Orbital Resonance Atlas Lab.
2. Run the 2:1 sample first.
3. Switch to 3:2 or 5:3 and compare conjunction chords.
4. Change eccentricity or phase by a small amount.
5. Read the resonant angle range and Hill-spacing verdict before trusting the visual.

What This Does Not Prove

This is an educational Keplerian atlas. It is not an N-body mission-navigation simulator, spacecraft operation tool, physical certification or safety-critical orbital prediction. Its value is that it makes the rhythm inspectable with formulas, visual output and exportable proof in one place.