OURANOS · the celestial · the sky, measured · kept by URANIA

THE ROCHE LIMIT ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP

A moon that wanders too close to its planet gets torn apart — not by crashing, but by TIDES. The planet pulls harder on the moon’s near side than its far side, and inside a critical distance (the Roche limit) that stretching beats the moon’s own gravity holding it together. The debris spreads into a RING. It’s why Saturn has rings and no big close moon. Slide the moon inward past the limit.

◆ LIT▲ AMBER
◧ THE MEASURE · 2D
◍ TORN INTO A RING · 3D · too close, and tides shred the moon
◆ THE FOURTH · 4D · a tesseract turns
◐ THE SHADOW · one dimension down
👶 THE TODDLER CORNER — one fat tap
distance
Roche limit
2.4 R
tidal vs gravity
INTACT?

◆ LIT — exact / checkable

The Roche limit is the distance within which a body held together only by its own gravity is torn apart by TIDAL forces from a larger body. Tides arise from the DIFFERENCE in gravitational pull across the moon (stronger on the near side); when the satellite is closer than d ≈ 2.44·R·(ρᵧ/ρᵐ)⁵Ÿ (for a fluid body; R and ρ are the planet’s radius and density), that differential stretch exceeds the moon’s self-gravity and it disintegrates into a ring of debris — which is why planetary rings sit inside the Roche limit and large moons orbit outside it. A fail-loud self-check throws unless, inside the limit, the tidal force exceeds the moon’s self-gravity. ◆ real celestial mechanics, node-verified.

▲ AMBER — the figure

The fluid Roche limit (~2.44 R; a rigid body survives closer, ~1.26 R); real disruption depends on the moon’s strength and spin — the tides-beat-self-gravity-inside-the-limit mechanism is exact.

OURANOS: the sky is a laboratory you may only look at — so we learned to weigh it with light.  — URANIA
David Lee Wise / ROOT0 / TriPod LLC  ·  the observatory, with AVAN