Roche Limit Calc

TIDAL DISRUPTION

PHYSICS THRESHOLD:

The Shatter Point

When a celestial body gets too close to a planet, the tidal forces overcome its internal gravity, tearing the body apart into debris.

CRITICAL RADIUS

147,000KM

Distance for icy objects.

STABILITY STATUS

DISRUPTED

Objects turn into rings.

Roche Sync

Tidal Disruption Mapping. Analyzing the 147,000 km "Shatter Constant" where moon integrity fails. The Oat monitors the Density Ratio to track ring formation boundaries.

💥 Shatter: Tidal Force > Self-Gravity.
💍 Rings: Permanent Debris Corridor.
📐 Limit: Approx. 2.44 Planetary Radii.

Oat ROCHE SYNC

⚡

SYNC STATE

SHATTER

TIDAL SYNC ACTIVE

ROCHE BUFFER BREACHED

Shatter Sync

Tidal Tension Mapping. Analyzing the $d^3$ gradient constant that overcomes internal gravity. The Oat monitors the Tension Ratio to track moon disintegration events.

💥 Force: Tidal Gradient > Self-Gravity.
📐 Scaling: $1/d^3$ Disruption Law.
💍 Outcome: Debris Dispersion (Ring Formation).

Oat SHATTER SYNC

💥

SYNC STATE

SHATTER

TENSION SYNC ACTIVE

GRAVITY BUFFER EXCEEDED

Limit Sync

Anti-Accretion Mapping. Analyzing why the 147,000 km Roche boundary prevents moon formation. The Oat monitors the Shear Constant to track ring stability.

💍 Zone: A, B, and C Rings (Inside Limit).
📐 Force: Tidal Shear > Particle Gravity.
✨ Result: Permanent Brilliance / No Moon.

Oat LIMIT SYNC

🚫

MOON FORMATION

BLOCKED

SHEAR SYNC ACTIVE

ROCHE BUFFER SECURE

Destruction Sync

Structural Failure Mapping. Analyzing the 147,000 km collapse constant where internal moon gravity fails. The Oat monitors the Stress Ratio to track tidal disassembly.

❄️ Result: Billions of Ice Fragments.
📏 Boundary: 147,000 km Limit.
⚖️ Physics: Tidal Stress > Material Strength.

Oat DESTRUCTION SYNC

🧊

STRUCTURAL STATE

SHATTERED

COLLAPSE SYNC ACTIVE

COHESION BUFFER EXPIRED

Fluid Sync

Hydrostatic Limit Mapping. Analyzing the 2.44x radial constant for non-rigid celestial bodies. The Oat monitors the Density Ratio to track fluid tidal disruption.

🌊 Physics: Hydrostatic Equilibrium Failure.
📐 Coefficient: 2.44 (Fluid) vs 1.26 (Rigid).
💍 Result: Rapid Ring Dispersion.

Oat FLUID SYNC

💧

SYNC STATE

FLUID

ROCHE SYNC ACTIVE

DEFORMATION BUFFER SECURE

Paper

ROCHE LIMIT ANALYSIS 🌌

Randomized: 5 Questions from our 50-item Gravity Bank.

Sources

THE FLUID LIMIT

For a non-rigid body (like a loose pile of ice), the Roche limit is roughly 2.44 Rₚ (ρₘ/ρₛ)¹/³. For Saturn, this is about **147,000 km**.

DERIVATION MATH

Coefficient: 2.44