Source: https://guthlabs.ai/docs/instruments/escape-velocity-calculator/mechanism/

instrument mechanism / verified-clean

# Escape Velocity Calculator mechanism

The inspectable method record for Escape Velocity Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

NEEDS_REVIEW: the exact ambiguity is whether radius is center-to-object distance or surface radius/altitude, and what units are accepted. The honest_label is "n/a" but should disclose the Newtonian, spherical-body, outside-surface assumptions and the ignored effects of rotation and atmosphere.

- The formula v_esc=√(2GM/r) is the standard Newtonian escape-speed formula for a test object at radius r outside a spherically symmetric body, or for an ideal point mass. The spec does not state that radius means center-to-object distance or that the object is outside the body's effective surface.

- For a position inside an extended body, using the body's total mass in this formula is generally incorrect; the mass distribution and gravitational potential are required.

- The formula is nonrelativistic and should not be presented as physically exact when the result approaches the speed of light.

- Preset mass/radius values require a defined table version and reference values; NASA/JPL fact sheets can contain differing radius definitions and rounding.

## Units and conventions

- G=6.67430×10^-11 m^3 kg^-1 s^-2.

- Mass must be in kilograms and radius must be in meters before substitution; the output is in meters per second.

- Radius means center-to-object distance, not altitude above the surface. If altitude is supplied, surface radius must be added first.

- Mass is treated as concentrated spherically or the object is outside a spherically symmetric body.

- The result ignores atmosphere, drag, rotation, launch-site latitude, and other bodies.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "mass": 5.9722e+24,
    "radius": 6371000,
    "mass_unit": "kg",
    "radius_unit": "m",
    "G": 6.6743e-11
  },
  "expected_outputs": {
    "escape_velocity": 11186.2,
    "unit": "m/s"
  },
  "working": "v=√(2GM/r)=√[(2)(6.67430×10^-11)(5.9722×10^24)/(6.371×10^6)]; 2G=1.33486×10^-10; (1.33486×10^-10)(5.9722×10^24)=7.972050892×10^14; divide by 6.371×10^6=1.2513029×10^8 m^2/s^2; √(1.2513029×10^8)=1.11862×10^4 m/s≈11186.2 m/s."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

Zero radius creates division by zero and negative radius creates a square-root domain error. A calculator without explicit positive-radius validation can return Infinity, NaN, or an exception instead of rejecting the input. The radius-versus-altitude convention can also produce materially different valid outputs.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/escape-velocity-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/escape-velocity-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/escape-velocity-calculator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`