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

instrument mechanism / verified-clean

# Escape Velocity mechanism

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

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

## Model scope

The mathematical formula is correct for escape speed from radial distance r in an ideal two-body model. Verdict is NEEDS_REVIEW because the spec does not explicitly define r = radius + altitude, does not specify units, and leaves the GM-versus-G-and-mass input representation ambiguous. The empty honest_label is not adequate: the product should state that this is idealized two-body escape speed and identify the radius/reference model used for presets.

- The formula v_esc = sqrt(2GM/r) is standard, but the spec does not define how the supplied altitude is incorporated. For a body radius R and altitude h, the required distance is r = R + h, measured from the body's center.

- The formula requires either G and mass M or the gravitational parameter μ = GM; the spec lists GM in its data needs but does not state whether the implementation substitutes μ directly.

- The instrument must constrain mass M > 0, radius R > 0, and altitude h >= 0 unless subsurface locations are intentionally supported.

## Units and conventions

- Use a single consistent unit system, preferably SI: G in m^3 kg^-1 s^-2, mass in kg, radius and altitude in m, and output in m/s.

- Altitude is radial height above the selected reference radius, so r = radius + altitude.

- If using gravitational parameter μ, μ must be in m^3/s^2 and the formula is v_esc = sqrt(2μ/r).

- The listed GM and radius values must correspond to the same body reference model and unit system.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "body": "Earth",
    "gravitational_parameter_m3_per_s2": 398600441800000,
    "radius_m": 6371000,
    "altitude_m": 0
  },
  "expected_outputs": {
    "escape_velocity_m_per_s": 11186.14
  },
  "working": "r = R + h = 6,371,000 + 0 = 6,371,000 m\nv = sqrt(2μ/r) = sqrt((2 × 398,600,441,800,000) / 6,371,000)\n= sqrt(7.972008836 × 10^14 / 6.371 × 10^6)\n= sqrt(1.251296317 × 10^8)\n= 11,186.14 m/s"
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The specification does not define altitude units, sign convention, or required behavior for h<=-R. Inputs at h=-R produce division by zero, and inputs below that limit produce a negative square-root argument. The formula also has no actual physical branch, so domain handling must be implemented explicitly.

## Other records

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