Synodic Period Calculator mechanism

Model scope

Formula is mathematically correct under its stated assumptions, but the alignment definition and input/data constraints must be made explicit before release.

• The formula 1/S = |1/T1 - 1/T2| is standard for the interval between successive repetitions of the same relative orbital configuration, such as opposition-to-opposition or conjunction-to-conjunction. The phrase "successive alignments" is ambiguous: if conjunctions and oppositions are both counted as alignments, the interval can be half the stated synodic period.
• The specification does not state the required domain constraint that both orbital periods must be positive and finite.
• The planet-picker data source is underspecified: the orbital-period table needs defined values, units, and a source/version.

Units and conventions

• T1 and T2 must use the same time unit; the output S has that same unit.
• Orbital periods are treated as fixed positive heliocentric sidereal periods, using the standard two-body approximation.
• The formula describes repetition of the same relative longitude configuration, not arbitrary geometric alignments.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "body_1": "Earth",
    "T1": 365.256,
    "T1_unit": "days",
    "body_2": "Mars",
    "T2": 686.98,
    "T2_unit": "days"
  },
  "expected_outputs": {
    "synodic_period": 779.934235,
    "unit": "days"
  },
  "working": "S = T1*T2/|T2-T1| = (365.256*686.98)/|686.98-365.256| = 250923.56688/321.724 = 779.934235 days."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The raw arithmetic formula has exploitable failure points at zero periods and equal periods, producing undefined or infinite results. A signed-period interpretation also changes whether an input is valid and can produce a different semantic result unless the convention is explicitly enforced.

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