Source: https://guthlabs.ai/docs/instruments/transit-duration-impact-parameter/mechanism/

instrument mechanism / verified-clean

# Transit Duration & Impact Parameter mechanism

The inspectable method record for Transit Duration & Impact Parameter, kept separate from implementation and qualification.

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

## Model scope

The four test vectors evaluate the formula exactly as supplied, including its approximations. The specification needs review because it does not define whether b is normalized, does not state the period input unit, and labels the approximation as circular-orbit-only while omitting additional high-inclination and zero-planet-radius assumptions.

- The stated formula is only a restricted approximation, not the general circular-orbit transit-duration formula. For a planet-to-star radius ratio k and inclination i, the usual first-to-fourth-contact expression is T14=(P/π)·arcsin[(Rs/a)·sqrt((1+k)^2-b^2)/sin(i)], with b=(a/Rs)cos(i).

- The supplied expression omits the planet radius k, so it describes approximately center-to-center or point-planet duration rather than first-to-fourth-contact duration.

- The supplied expression omits the sin(i) denominator. Replacing sin(i) with 1 is a further high-inclination approximation; circularity alone does not justify that omission.

- The definition and units of impact parameter b are ambiguous. The formula requires b to be dimensionless and normalized by stellar radius; a physical impact distance cannot be inserted directly.

- The honest label says only circular-orbit approximation, but should also disclose the zero-planet-radius and sin(i)≈1 assumptions.

## Units and conventions

- P must be supplied in a time unit; the output is in hours, so seconds or other input units require explicit conversion to hours.

- a and Rs must use the same length unit, so Rs/a is dimensionless.

- b is assumed dimensionless, normalized to stellar radius.

- For the supplied approximation, 0≤b≤1 is required for a point-planet transit; the arcsine argument must lie in [-1,1].

- The formula assumes a circular orbit and additionally approximates sin(i)=1 and planet radius k=0.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "period": 72,
    "period_unit": "hours",
    "semi_major_axis": 10,
    "semi_major_axis_unit": "Rs",
    "star_radius": 1,
    "star_radius_unit": "Rs",
    "impact_parameter": 0
  },
  "expected_outputs": {
    "arcsin_argument": 0.1,
    "transit_duration_hours": 2.29566819
  },
  "working": "Rs/a=1/10=0.1. sqrt(1-b^2)=sqrt(1-0^2)=1. Argument=0.1×1=0.1. arcsin(0.1)=0.1001674212 rad. P/π=72/π=22.91831181 h. T=22.91831181×0.1001674212=2.29566819 h."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The specification has no explicit input validation for semi-major axis zero or for the non-transiting regime |b|>1. These inputs produce division-by-zero or non-real square-root results unless the instrument rejects them or selects a no-transit branch.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/transit-duration-impact-parameter/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/transit-duration-impact-parameter/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/transit-duration-impact-parameter/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-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`