One of the quiet surprises of planetary science is how simple surface gravity really is.

Despite very different compositions, temperatures, and histories, the surface gravity of a rocky body is largely determined by just two quantities:

its average density and its radius

No force laws are required to see this.
No inverse-square attraction needs to be assumed.

The result falls directly out of mechanics.

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A Familiar Result, Reached a Different Way

In conventional physics, surface gravity is written as$$g = \frac{GM}{R^2}$$

But mass $M$ can be written as$$M = \frac{4}{3}\pi \rho R^3$$

Substituting gives$$g = \frac{4}{3}\pi G \rho R$$

This is usually treated as a mathematical coincidence.

In a mechanical-medium picture, it is not a coincidence at all.
It is the core insight.

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Gravity as a Stress Gradient

If gravity is not a force pulling inward, but a response of a medium under compression, then surface gravity represents something very specific:

the rate at which internal stress changes near the surface

Inside a spherical body:

• each layer supports the weight (stress) of layers above it,
• stress increases smoothly toward the center,
• the surface value reflects the total internal stress gradient.

Mechanically, the surface acceleration scales as$$g \;\sim\; \frac{\text{internal stress}}{\rho R}$$​

For a roughly uniform body, internal stress itself scales with $\rho^2 R^2$, giving$$g \;\propto\; \rho R$$

This is not a force balance.
It is a material response.

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Why Composition Barely Matters

This immediately explains a puzzling observation:

• Earth and Mercury have very different compositions
• Mars and the Moon have very different internal histories

Yet bodies with similar density–radius products have similar surface gravity.

Why?

Because:

• gravity depends on bulk stress, not chemistry,
• chemical structure averages out,
• only density (how much medium is displaced) and size (over what distance) matter.

The medium does not care what the defect is made of—only how much of it exists and how far stress must propagate.

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Putting Numbers on It

Let’s compare a few bodies using only density and radius.

Body	Radius (km)	Density (kg/m³)	$\rho R$ (scaled)	Surface g (m/s²)
Earth	6371	5514	high	9.81
Moon	1737	3344	low	1.62
Mars	3390	3933	medium	3.71
Mercury	2440	5427	medium	3.70

Mars and Mercury have nearly identical surface gravity—not because they share mass, composition, or history, but because ρR is nearly the same.

That agreement is not tuned.
It is structural.

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Why Radius Enters Linearly

The linear dependence on radius is especially important.

If gravity were a force emanating from the center, we might expect more complicated behavior. Instead:

• each additional layer adds stress,
• stress accumulates linearly with depth,
• the surface gradient reflects total integrated stress.

This is exactly how pressure behaves in ordinary materials.

Planetary gravity behaves like pressure in a very large object.

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What This Explains Immediately

This single relation explains:

• why small asteroids have almost no gravity
• why super-dense but tiny objects don’t dominate
• why gravity grows smoothly with planetary size
• why “surface gravity” is a meaningful concept at all

None of this requires spacetime curvature or action-at-a-distance.

It follows from mechanics.

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Key Takeaway

Surface gravity is not a force law—it is a stress gradient.

For spherical bodies, that gradient depends only on:

• how dense the body is, and
• how large it is.

Everything else is secondary.

With this result in hand, we can now ask the next natural question:

If gravity is a stored stress, what does it mean to “escape” it—and why does escape speed take the form it does?

That is where we turn next.