Look across the solar system and a clear pattern appears:

• Planets and large moons are round
• Asteroids and small moons are not

This transition is so consistent that it even has a nickname: the “potato radius.”

Why does nature draw this line so cleanly?

In a mechanical framework, the answer is neither gravitational mysticism nor historical accident.
It is a competition between stress and strength.

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Two Competing Effects

Any solid body experiences two opposing mechanical influences:

1. Gravitational (compressive) stress
   Produced by the body’s own mass and size.
2. Material yield strength
   The resistance of the material to permanent deformation.

Shape is determined by which one wins.

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Gravitational Stress Scales with Size

From earlier posts, gravity is understood as stored internal stress.

For a roughly spherical body, the characteristic gravitational stress scales as:$$\sigma_{\text{grav}} \sim \rho g R \sim \rho^2 R^2$$

This is a key result.

• Double the radius → stress increases by four
• Density matters, but size matters more

Small bodies simply cannot build enough internal stress to deform themselves.

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Material Strength Does Not Scale with Size

By contrast, material strength is local.

Rock, ice, and metal have yield strengths that depend on:

• bonding,
• microstructure,
• temperature,

but not on the overall size of the object.

This creates a sharp threshold.

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The Sphericity Condition

A body becomes spherical when:$$\sigma_{\text{grav}} \gtrsim \sigma_{\text{yield}}$$

Below this threshold:

• bumps persist,
• voids remain,
• irregular shapes survive indefinitely.

Above it:

• high points flow,
• low points fill,
• stress redistributes until symmetry emerges.

Sphericity is not imposed—it is the lowest-stress configuration.

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Why the Transition Is Abrupt

Because gravitational stress scales as $R^2$R2, the transition is fast.

There is no long middle ground where objects are “mostly round.”

Once the threshold is crossed:

• deformation accelerates,
• feedback reinforces rounding,
• the body quickly relaxes into a sphere.

This explains why we see:

• very round moons,
• very lumpy asteroids,
• and little in between.

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Why Ice Worlds Round More Easily

Ice has a much lower yield strength than rock.

As a result:

• icy bodies become spherical at smaller radii,
• rocky bodies require larger sizes,
• metallic bodies require even more.

This explains why:

• icy moons are round at sizes where asteroids are not,
• composition matters only through strength, not gravity itself.

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Mountains, Not Perfect Spheres

Even large planets are not perfectly smooth.

Why?

Because once stresses drop below yield:

• deformation stops,
• features “freeze in.”

This sets:

• maximum mountain heights,
• crustal thickness limits,
• and tectonic behavior.

Again, no force laws are needed—just stress balance.

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Why This Matters for Gravity Models

This result reinforces a central theme:

Gravity behaves like pressure in a material, not like attraction in empty space.

The same stress that:

• rounds planets,
• supports mountains,
• and crushes interiors,

also:

• sets surface gravity,
• governs escape,
• and controls orbital behavior.

One mechanism explains many phenomena.

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Key Takeaway

Bodies become spherical when gravitational stress exceeds material strength.

Small bodies stay irregular because they never cross that threshold.
Large bodies round themselves because the medium demands it.

With shape understood as a mechanical outcome, we can now return to a subtler effect—one that shows up not in rocks or orbits, but in time itself.

Why do clocks tick differently on different planets?

That is where we turn next.