Orbital Period (Kepler's 3rd Law) implementation

Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

Record owner

Guth Instruments

Lifecycle

verified-clean

Evidence ID

t4-161

Effect

Computation or source lookup only

Input and validation requirements

• No explicit constraint that semi-major axis must be finite and strictly positive; reject a <= 0 for an orbital-period instrument rather than presenting zero as a valid orbit.
• Reject GM <= 0 and central-body mass <= 0; otherwise the square root is undefined or nonphysical.
• Guard against division by zero if a custom central-body mass or GM is zero.
• Guard against unit mismatch, especially supplying a in kilometres with GM in m³/s² or vice versa; this causes a factor of 1000^(3/2) error in period.
• A mass-only input requires G and consistent SI conversion; a GM preset is preferable because it avoids introducing an additional rounded constant.
• Elliptic-orbit terminology should be explicit: for a two-body bound orbit, a > 0 and the period is independent of eccentricity, but perturbations, oblateness, third bodies, and relativistic effects are ignored.
• The reverse calculation requires T > 0 and GM > 0; it also needs an explicit period-unit conversion before applying the inverse formula.

Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

{
  "inputs": {
    "semi_major_axis": 7000,
    "semi_major_axis_unit": "km",
    "central_body": "Earth",
    "GM": 398600.4418,
    "GM_unit": "km^3/s^2"
  },
  "expected_outputs": {
    "period_s": 5828.52,
    "period_days": 0.06746
  },
  "working": "T = 2π√(a³/GM)\na³ = 7000³ = 343,000,000,000 km³ = 3.43 × 10^11 km³\na³/GM = 343,000,000,000 / 398,600.4418 = 860,510.85 s²\n√(860,510.85) = 927.637 s\nT = 2π × 927.637 = 5828.52 s\nT_days = 5828.52 / 86400 = 0.06746 days"
}

Other records

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