Source: https://guthlabs.ai/docs/instruments/synodic-period-calculator/mechanism/

instrument mechanism / verified-clean

# Synodic Period Calculator mechanism

The inspectable method record for Synodic Period Calculator, kept separate from implementation and qualification.

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

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/synodic-period-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/synodic-period-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/synodic-period-calculator/qualification/>)

## 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`