Once gravity is reinterpreted as a stored stress in a medium, a familiar quantity takes on a very different meaning:

What does it mean to “escape” a planet?

In the standard picture, escape velocity is the speed needed to overcome an attractive force.
In a mechanical picture, escape velocity is something else entirely.

It is a stress-release threshold.

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The Conventional Formula (and the Hidden Assumption)

Escape velocity is usually written as$$v_{\text{esc}}=\sqrt{\frac{2GM}{R}}$$​​

This is typically interpreted as:

“The speed needed so gravity can’t pull you back.”

But this interpretation quietly assumes:

• gravity is a force,
• work must be done against it,
• and potential energy is fundamental.

None of those assumptions are required.

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Recasting Escape as a Material Threshold

If gravity is stored elastic stress, then escape means:

injecting enough kinetic energy to break free of the stress field without the medium pulling the object back into equilibrium.

This is exactly how escape works in ordinary materials.

• Stretch a spring a little → it snaps back
• Stretch it past a threshold → it releases and separates

Escape velocity marks the point where restoring stress can no longer re-capture the defect.

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Where the Square Root Comes From

In a mechanical medium, two energies compete:

• Stored stress energy per unit mass
• Kinetic energy per unit mass

Escape occurs when:$$\frac{1}{2}v^2 \;\gtrsim\; \frac{\text{stored stress}}{\rho}$$​

From Series X.1, stored gravitational stress scales as$$\sigma \sim \rho^2 R^2$$

Dividing by density to get energy per unit mass:$$\epsilon_{\text{stress}} \sim \rho R^2$$

Setting kinetic and stress energies equal gives:$$v^2 \sim \rho R^2 \quad \Rightarrow \quad v \sim R\sqrt{\rho}$$​

This is precisely the same scaling as the classical escape velocity—without invoking force or attraction.

The square root appears because escape compares energy densities, not forces.

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Escape Is Directional Failure

This reframing clarifies something subtle:

• Escape is not “going up”
• It is leaving the stress domain

Once a defect moves fast enough that:

• stress cannot reorganize quickly enough,
• restoring gradients lag behind,
• wave emission cannot re-capture it,

the object decouples from the planetary stress field.

It doesn’t need to “beat gravity forever.”
It only needs to cross the boundary once.

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Why Atmospheres Leak Gradually

This mechanical view immediately explains atmospheric escape.

Gas molecules do not escape all at once because:

• most are far below the stress-release threshold,
• random thermal motion only occasionally exceeds it,
• escape probability is exponential, not binary.

This is why:

• the Moon lost its atmosphere,
• Mars lost much of its own,
• Earth retains a thick one.

Not because of forces—but because of material thresholds.

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Why Escape Velocity Depends on the Surface

Escape velocity is defined at the surface because:

• that is where the stress gradient is steepest,
• stored stress is maximal per unit displacement,
• and failure must occur there first.

Once past the near-surface stress domain, escape becomes progressively easier.

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No Infinite Reach Required

In this framework:

• gravity does not reach to infinity,
• potential energy is not fundamental,
• and nothing “pulls” indefinitely.

The medium enforces capture only within its stress field.
Beyond that, there is nothing left to escape from.

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Key Takeaway

Escape velocity is not about overcoming attraction—it is about exceeding a stress-release threshold.

The familiar formula survives because it compares energies, not because it encodes a force law.

With escape reinterpreted mechanically, the next step follows naturally:

If gravity and escape are stress phenomena, what does it really mean to orbit—and why do orbital speeds take the values they do?

That is where we turn next.