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

instrument / verified-clean

# Ground Track / Orbital Period vs Altitude

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

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

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/ground-track-orbital-period-vs-altitude/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/ground-track-orbital-period-vs-altitude/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/ground-track-orbital-period-vs-altitude/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/ground-track-orbital-period-vs-altitude/qualification/>)

## Ledger state

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

**Area**: Earth & Space (astronomy, orbital mechanics, meteorology, geology, geodesy, oceanography)

**Tranche**: tranche-4

**Evidence ID**: t4-256

**Ledger rows**: 1

No ledger note is attached.

## Review findings

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.

### Formula and scope findings

- 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.

### Unit assumptions

- 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.

## Boundary hardening

**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.

## 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": {
    "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."
}
````

## 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`