Kepler's Third Law Calculator mechanism

Model scope

The displayed central-mass formula is standard only in the negligible-orbiting-mass approximation. Because the instrument claims a two-body calculation, omits the secondary mass, and ambiguously describes an inverse 'given T' mode, the specification fails verification.

• For a true two-body system, the standard formula is T²=4π²a³/[G(M+m)], where M and m are both masses; using only central mass M is an approximation valid when the orbiting body's mass is negligible.
• The AU/year relation T²=a³ is valid only for a solar-mass central system under defined astronomical-unit and year conventions; more generally it is T²=a³/(M/M_sun+m/M_sun).
• The output description says 'period T (or a given T)' but does not specify the inverse formula, mode selection, or whether the calculator computes a from an entered T. The inverse formula would be a=[G(M+m)T²/(4π²)]^(1/3).

Units and conventions

• SI mode requires a in metres, G in m³·kg⁻¹·s⁻², masses in kilograms, and T is returned in seconds.
• AU/year mode requires a in astronomical units and T in the selected year convention; using 365.25 days gives 31,557,600 seconds per year.
• The AU/year shortcut assumes the central mass plus orbiting mass is approximately one solar mass; it is not exact for arbitrary central masses.
• Semi-major axis must be nonnegative; an orbital semi-major axis is physically positive, so a=0 is only a mathematical boundary test.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "mode": "SI",
    "a_m": 149600000000,
    "central_mass_kg": 1.989e+30,
    "G_m3_kg_s2": 6.6743e-11
  },
  "expected_outputs": {
    "period_s": 31554100
  },
  "working": "GM=(6.6743×10^-11)(1.989×10^30)=1.32751827×10^20 m³/s². a³=(1.496×10^11)³=3.348071936×10^33 m³. T²=4π²a³/(GM)=39.4784176×(3.348071936×10^33)/(1.32751827×10^20)=9.956×10^14 s². T=√(9.956×10^14)=3.1554×10^7 s≈31,554,100 s."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification exposes hazardous inputs: a=0 is mathematically defined but physically degenerate, central mass M=0 causes division by zero, and a negative semi-major axis produces convention-dependent behavior or a non-real result. The instrument should validate these cases explicitly.

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
• BOUNDARY_HAZARD_CATALOG.json