Source: https://guthlabs.ai/docs/instruments/angular-size-physical-size/mechanism/

instrument mechanism / verified-clean

# Angular Size ↔ Physical Size mechanism

The inspectable method record for Angular Size ↔ Physical Size, kept separate from implementation and qualification.

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

## Model scope

The stated formula is standard for the small-angle approximation, and the honest label correctly identifies that limitation. Review is required because angular units, diameter-versus-radius semantics, validity bounds, and zero/invalid-input behavior are not fully specified.

- The small-angle relation θ = size/distance is correct only when θ is small and size is the full physical diameter corresponding to the full angular diameter.

- For larger angular sizes, the exact full-diameter relation is θ = 2·atan((size/2)/distance); the specification does not state the allowable small-angle range.

- The input units for angular size are unspecified even though the formula requires radians.

## Units and conventions

- Angular size θ must be in radians before applying the formula; degrees must be converted using θ_rad = θ_deg·π/180, and arcseconds using θ_rad = θ_arcsec·π/(180·3600).

- Physical size and distance must use the same linear units.

- size is assumed to mean full linear diameter, and angular size is assumed to mean the corresponding full angular diameter.

- The geometry is Euclidean and the object is sufficiently distant for the small-angle approximation.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "physical_size_km": 3474,
    "distance_km": 384400
  },
  "expected_outputs": {
    "angular_size_rad": 0.00903746098
  },
  "working": "θ = size/distance = 3474 km / 384400 km = 0.00903746098 rad."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

A zero-distance input produces an undefined angular size and must be rejected; additionally, an angular-size unit ambiguity can change the computed physical size from approximately 1.74533 m to 100 m.

## Other records

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