Orbital Period (Kepler's 3rd Law)

Inspectable records

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

t4-161

Ledger rows

1

No ledger note is attached.

Review findings

The displayed formula is standard and correct under the stated two-body approximation. The catalog claim is incomplete because reverse computation is advertised but its inverse formula and input constraints are absent. The specification therefore needs review before release.

Formula and scope findings

• The forward formula T² = 4π²a³/(GM) is correct for an ideal two-body Keplerian orbit when a is the semi-major axis and GM is the standard gravitational parameter of the central body.
• The specification claims computation in reverse (semi-major axis from period), but does not provide the inverse formula a = (GMT²/(4π²))^(1/3).
• The input is described as central body mass, while the formula requires GM. The implementation must either multiply mass by G or accept GM directly; this distinction is not specified.
• The formula assumes a bound Keplerian orbit with a > 0. It is not valid as an unrestricted calculator for a = 0 or non-orbital trajectories.

Unit assumptions

• Use one consistent unit system: a in metres, GM in m³/s², and T in seconds; or a in kilometres, GM in km³/s², and T in seconds.
• If central body mass M is supplied instead of GM, use G = 6.67430 × 10^-11 m³ kg^-1 s^-2 and convert a to metres.
• Reported days are T/86400, using exactly 86400 s per day.
• Reported years require a declared convention; the test vectors use the Julian year of 365.25 days = 31557600 s.
• For preset bodies, values should be identified as GM values, not merely masses, and should use a documented JPL/IAU epoch or reference source.

Boundary hardening

Recorded hazards

• 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.

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": {
    "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"
}

Related workflows

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