Escape Velocity Calculator

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo

Tranche

tranche-4

Evidence ID

t4-011

Ledger rows

1

No ledger note is attached.

Review findings

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.

Formula and scope findings

• 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.

Unit assumptions

• 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.

Boundary hardening

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.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "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."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

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

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json