Empirical Earth · Gravity, Buoyancy & the Air

Why everything big enough is a sphere — the “potato radius”

The claim

“If gravity makes planets round, why are asteroids lumpy?”

What is measured

A body rounds up once its own gravity overcomes the strength of its material. That crossover is the “potato radius,” a few hundred kilometers across (~400 km icy, ~600 km rocky). Smaller bodies stay irregular; larger ones are forced into balls. Earth, at ~12,742 km, lies about thirty times beyond that line, so it cannot be anything but round. The lumpy asteroids beside the round planets are the same split gravity predicts.

What would show this is wrong

finding large bodies well above ~1,000 km that are permanently flat or irregular rather than spheroidal, or small bodies well below the threshold consistently rounded with no gravity to do it. Neither is observed: the round/irregular divide tracks size and composition just as self-gravity requires.

Sources

  1. The roundness threshold, with examples. Self-gravity rounds a body once it overcomes the material’s strength: Mimas (396 km) is the smallest round body, Proteus (420 km) the largest irregula link
  2. The “potato radius.” Lineweaver & Norman derive the radius at which a body’s gravity overcomes its yield strength and it turns from potato-shaped to spherical — about 300 km for rock and ~20 link
  3. How big to be round. Self-gravitation pulls a body round above roughly 200 km in radius if icy, or ~400 km if rocky; Mimas is the smallest body rounded this way, while larger but stronger as link
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