Tithi calculation
How the Sun–Moon elongation becomes one of thirty lunar-day divisions without depending on ayanāṁśa.
Calculation contract · released 2026-08-18
Definition
A tithi is one 12° interval of normalized geocentric Moon-minus-Sun ecliptic longitude, counted through waxing and waning halves.
Calculation procedure
Compute tropical apparent geocentric Sun and Moon longitudes at the same instant, normalize Moon minus Sun, divide by 12°, and retain fraction and boundary distance.
Required inputs
- Sun and Moon longitude in the same frame
- Instant
- Boundary policy
Maha convention
Maha numbers thirty absolute intervals and separately records pakṣa, within-pakṣa index, fraction, and near-boundary status.
Uncertainty and edge cases
Because the same ayanāṁśa cancels from both longitudes, tithi is unchanged by tropical-to-sidereal zero-point conversion; ephemeris differences still matter.
What this does not establish
A calculated tithi does not establish that an activity is favorable.
Authoritative references
These sources establish the calculation vocabulary, data product, or transformation convention. They do not establish astrological interpretation.
- Astronomy Engine
Don Cross (cosinekitty) · 2.1.19
Locally computed Sun and Moon positions derived from the VSOP87 and JPL-derived lunar theories, together with rise and set times, at the accuracy stated in the library documentation.
Boundary: Positions are computed in process rather than fetched from an authority, so a fact citing this source carries a digest over the computed values and not over a provider response body. Its accuracy is adequate for calendrical work and is not a substitute for a Horizons query where sub-arcsecond agreement matters.
- Swiss Ephemeris general documentation
Astrodienst AG · 2.10 documentation, checked 2026-08-18
An independent ephemeris implementation, supported reference choices, house calculations, and its dual-license boundary.
Boundary: Maha does not bundle or call Swiss Ephemeris in production. Frozen conformance results are validation evidence, not permission to redistribute its software or data.