Source: https://guthlabs.ai/docs/instruments/ground-track-orbital-period-vs-altitude/mechanism/

instrument mechanism / verified-clean

# Ground Track / Orbital Period vs Altitude mechanism

The inspectable method record for Ground Track / Orbital Period vs Altitude, kept separate from implementation and qualification.

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

## Model scope

NEEDS_REVIEW because the exact ambiguity is: the specification claims a rough ground-track repeat but supplies no ground-track-repeat formula, required orbital inputs, or defined repeat output. The period and orbits-per-day formulas are standard only under the stated circular-orbit and unit assumptions.

- The implied circular-orbit formula should be stated explicitly as T = 2π√(a³/μ), with a = Rₑ + h; 'T from Kepler' is underspecified.

- Altitude and orbital period do not determine a ground-track repeat. A repeat calculation also requires at least orbital inclination, Earth's rotation rate, and a specified resonance/repeat criterion; with perturbations, nodal regression and other orbital elements are additionally relevant.

- The stated outputs list period and orbits per day, but the instrument description also claims a rough ground-track repeat without providing a formula or output definition.

- The formula assumes a circular orbit. An altitude alone is insufficient for an eccentric orbit, whose period depends on semimajor axis rather than instantaneous altitude.

## Units and conventions

- Use Earth gravitational parameter μ = 398600.4418 km³/s².

- Use mean/equatorial Earth radius Rₑ = 6378.137 km; altitude must be measured from the same reference radius.

- Use altitude in kilometers in the orbital formula, or explicitly convert meters to kilometers first.

- Compute period T in seconds and orbits per day as 86400/T.

- For the period-input mode, the supplied period is assumed to be in seconds and positive.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "altitude_km": 0,
    "mu_km3_s2": 398600.4418,
    "earth_radius_km": 6378.137
  },
  "expected_outputs": {
    "period_s": 5069.34,
    "orbits_per_day": 17.0436
  },
  "working": "a = Rₑ + h = 6378.137 + 0 = 6378.137 km. T = 2π√(a³/μ) = 2π√(6378.137³ / 398600.4418) ≈ 5069.34 s. Orbits/day = 86400 / 5069.34 ≈ 17.0436."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

A zero supplied period makes the orbits-per-day calculation undefined, and an unspecified altitude unit permits materially different outputs for the same numeric input.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/ground-track-orbital-period-vs-altitude/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/ground-track-orbital-period-vs-altitude/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/ground-track-orbital-period-vs-altitude/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`