How five published almanacs differ on tithi end times, and why

The question

A Tithi is the time the Moon takes to gain twelve degrees of longitude on the Sun. It is a precise astronomical quantity, so it can surprise a reader that two respected almanacs printed for the same city may disagree about when it ends. Before treating such differences as errors, we want a method that explains them.

Why differences arise

We expect four families of cause.

Computational basis. Many almanacs now compute positions from modern ephemerides, an approach usually called drik (seen) ganita. Others keep the parameters of the Sūrya Siddhānta or related texts, a practice sometimes called vakya or traditional computation. Because the classical mean motions and equations of centre differ slightly from modern values, the moment at which the Sun–Moon elongation crosses a multiple of twelve degrees can shift. With the Moon's speed varying between roughly eleven and fifteen degrees a day, a small difference in longitude becomes a difference of many minutes in time.

Location. A tithi ends at the same instant everywhere on Earth. Only the clock reading changes. Almanacs printed for one city are sometimes used in another, and some state times for a reference meridian. Differences of this kind are pure conversion and should vanish once normalised.

Time convention. Older almanacs give times in ghatis and palas counted from local sunrise (one ghati is twenty-four minutes). Converting that to clock time depends on how sunrise was computed: with or without refraction, upper limb or centre of the disc. Two almanacs may agree on the astronomy and still print different clock times.

Printing and transcription. Typographical errors and errors in our own transcription must be checked before anything else is concluded.

The method

1. Choose five almanacs, at least two drik and at least two traditional, all stating a place of computation.
2. Fix one city and twelve dates, one per lunar month, so that the Moon is sampled at different speeds.
3. Transcribe each printed end time twice, independently, and reconcile.
4. Convert every value to IST and to the chosen city, noting the conversion applied.
5. Compute a reference end time from a modern ephemeris for the same location.
6. Record the difference from the reference for each almanac and date.
7. Assign each difference to a cause. If converting location or time convention removes it, it is classified accordingly. Residuals that track the Moon's speed and persist across dates are attributed to computational basis.

What we expect to see†

We expect drik almanacs to agree with each other within a few minutes, with residuals coming mainly from sunrise convention. We expect traditional almanacs to show larger, systematic offsets that change across the year. We do not assume either is "right" for its purpose: a traditional almanac is internally consistent with the rules of the text it follows, and the festival calendar of a community may be bound to it.

Why it matters

Festival dates, kshaya-type omissions of a tithi and the choice of a Muhūrta all depend on these end times. A reader who knows why almanacs differ can read any panchang with more confidence and fewer worries about which one is "wrong". This is also a good exercise in historical astronomy: it shows how classical parameters behave against modern ones, a topic treated at length by David Pingree and, for the Kerala tradition, by K. V. Sarma.

Limits

Five almanacs and one city cannot represent the whole printing tradition. The method compares printed values; it does not inspect the software or tables used to produce them.

† Marked dates or readings are debated among scholars or still being confirmed by our faculty.