Escape Velocity Calculator mechanism

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

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