CAHC Tutorial · Session 2

Tools for Ancient Indian Astronomy and Cosmography

Session 2 · From Visual Demonstration to Research Workflow

Sunder Chakravarty
CAHC, Jain University

CAHC Tutorial · Session 2

Recap and Roadmap

Session 1 covered

  • Meru — cosmographic visualization
  • Stellarium basics and sky culture
  • Dhruva, Thuban, and precession intuition
  • Sun: daily and annual motion
  • Nakṣatras: stars, shapes, arc-zones
  • Precession as a dating tool — VGJ sun-transit examples

Session 2

  1. Moon and the equinoctial full-moon problem
  2. The dial plot and Maghādi scheme
  3. Eclipses — Parāśara Tantra and NASA/JLEX
  4. Digital tools and CAHC resources
  5. AI-assisted chores
Session 2 extends the same precession arc from the Sun to the Moon, then broadens to the research toolkit.
CAHC Tutorial · Session 2

The Moon Problem

  • Session 1 used the Sun's nakṣatra position to date texts.
  • Session 2 adds the Moon: where is the full moon at the equinox?
  • The Brāhmaṇḍa Purāṇa (BP) ch. 21 gives quarter-nakṣatra precision:
    • Spring equinox full moon at ¼-Kṛttikā (η Tau)
    • Autumn equinox full moon at ¾-Viśākhā (α¹ Lib)

Why this is a dating constraint

  • The equinox point drifts through the nakṣatras via precession.
  • These two stars were in the correct equinoctial sectors only during a specific window.
  • Astropy epoch scan over −2400 to −800 locates that window.

Stellarium demo

The same precession logic — now applied to the full moon rather than the seasonal sun.
CAHC Tutorial · Session 2

BP 21 - The Text

  • Equinoctial full moons in terms of named nakṣatra sectors

  • Day and night are equal - Equinox

  • Sun ¼Kṛttikā, Moon ¾-Viśākhā — Vasanta Full Moon

  • Sun ¾-Viśākhā, Moon head-Kṛttikā — Śarat Full Moon

  • The BP text is in its present form from early CE, but these astronomical statements belong to a much older observational layer.

Stellarium demo

They belong to an observational layer earlier than PT, VGJ, and Lagadha's Jyotiṣa Vedāṅga (around 1350 BCE).
CAHC Tutorial · Session 2

Equinoctial Full Moon - Analysis method

equinoctial full moon chart

  • All full moons in −2400 to −800 are gathered first using Astropy, about 1300 per century.

  • We then select full moons with the Sun within ±1 day of the equinox, about 13 per century.

  • These Full moons are plotted as green dots in chart

    • Vaiśākhī - Spring Eqnx Sun ¼Kṛttikā 0°
    • Kārttikī - Autumn Eqnx Sun ¾Viśākhā 180°

  • The nakṣatra proxy stars are then precessed

    • Red line: drift of η-Tau (Kṛttikā)
    • Blue line: drift of α¹-Lib (Viśākhā)

  • The shaded window ~ 1980–1610 BCE - stars in their equinoctial sectors. The sharper spring equinox constraint ~1700–1600 BCE.

  • ssc/s25-eqfm-search-visualizer.ssc — epoch-by-epoch traversal of 2400–800 BCE candidates

CAHC Tutorial · Session 2

Maghādi scheme - MAU , BP - 1800 BCE

dial ~1800 BCE

Two axes, one dial

  • The N–S axis (MAU): winter solstice in ½-Śraviṣṭhā, summer solstice in Āśleṣā.

  • The E–W axis (BP): spring equinox at ¼-Kṛttikā, autumn equinox at ¾-Viśākhā.

  • Both axes are consistent on a single 27-sector dial — the Maghādi scheme.

Key result

  • Kṛttikā-¼ at spring equinox ≡ Śraviṣṭhā-½ at winter solstice.

  • MAU and BP are the same scheme stated from different starting points.

  • The Maghādi zodiac thus predates the Śraviṣṭhādi zodiac by ~480 years (6°40' of precession).

CAHC Tutorial · Session 2

Śraviṣṭhādi scheme - PT, VGJ ~1300 BCE

dial ~1200 BCE

What has changed

  • Precession has shifted the stars relative to the cardinal axis.
  • By ~1300 BCE, Maghā is no longer visible at the summer-solstice sunrise — the Maghādi anchor is broken.
  • The winter solstice has drifted: the beginning of the Śraviṣṭhā sector now coincides with the solstice point — the Śraviṣṭhādi scheme takes over.
  • This is the regime of PT and VGJ.
Precession rotates the outer star dial. The season boundaries stay fixed.
CAHC Tutorial · Session 2

Seasonal Nakṣatra Drift: 2400 to 1000 BCE

seasonal naks drift
Animation shows precession rotating the star positions through the fixed season-domain framework, −2400 to −1000 BCE.
CAHC Tutorial · Session 2

Stellarium , Astropy - Contrast

  • Stellarium GUI

    • Shows individual cases convincingly.
    • Allows for targeted exploration of specific dates.
    • Scripting is possible but not as efficient as Astropy.

  • Astropy supports repeatable computation

    • Measured example: next 1000 sunrise queries from a fixed Bangalore start JD
    • Astropy/Astroplan: 10.4 s
    • Stellarium script: 19.3 s
    • About 1.85× faster on this repeated-query task
Method Best For
Stellarium GUI Visualisation
Stellarium script Reproducible demo
Astropy scan Exhaustive coverage
AI tools speed up writing the code — not running it. Computation time is physics, not productivity.
CAHC Tutorial · Session 2

Eclipses - Parāśara Tantra

PT eclipse table

  • Parāśara Tantra records eclipse sequences over lunations.

  • The text encodes a periodicity claim: specific lunation counts produce eclipse pairs.

  • Location anchor: Jaipur

Verification with NASA/JLEX

Stellarium support

CAHC Tutorial · Session 2

Meru — Cosmographic Visualization

What it is

  • An interactive 3-D cosmographic visualization of the Meru model.

  • Draws from multiple textual sources — not tied to one text.

  • Built to explore and explain, not to prove.

What it shows

  • Meru as the polar axis of a concentric world model.

  • Dhruva at the apex; the nakṣatra wheel rotating around it.

  • Seasons and geographic zones as concentric rings.

Access

Notes

  • Useful for connecting the textual descriptions of cardinal directions, Dhruva, and the nakṣatra wheel.

  • The same precession intuition from Stellarium applies here in a cosmographic frame.

The app is a visualization aid — it makes an older descriptive cosmology navigable and discussable.
CAHC Tutorial · Session 2

Digital Tools and CAHC Resources

CAHC Search Portal

  • Full-text and metadata search across CAHC-associated papers.
  • Supports keyword and author search.
  • Live demo if time and connectivity allow.

Patra Darpan

  • Digitized journal index covering selected publications
  • An informal, more available repository of papers in our areas
  • Not complete but convenient
  • Patra Darpan

Sanchaya

  • Corpus of Sanskrit texts with text search.
  • Not complete but convenient
  • Example: Useful for locating nakṣatra references across texts.
  • Sanchaya
  • Embedding-based search over CAHC paper abstracts.
  • Surfaces papers by conceptual proximity, not keyword match.
These informal tools reduce the friction of source-chasing — leaving more time for careful reading.
CAHC Tutorial · Session 2

AI-Assisted Chores — What and Why

  • Modern LLMs can help with repetitive scholarly tasks — not replace judgment.
  • Two examples relevant to Jyotiṣa research:
    • Kaṭapayādi decoding — the numerical cipher used in astronomical mnemonics
    • Sanskrit anvaya — unpacking technical sūtra prose into readable order

The guardrail

Always verify. The model is helpful for reducing drudgery and exploratory friction — not for final authority.

  • Errors are plausible-sounding and not self-flagged.
  • Works best with a domain-aware human in the loop.
CAHC Tutorial · Session 2

AI Example 1 — Kaṭapayādi

The prompt

Explain this verse and decode the kaṭapayādi rule it encodes:
नञावचश्च शून्यानि संख्याः कटपयादयः।
मिश्रे तूपान्त्यहल् संख्या न च चिन्त्यो हलस्वरः ॥

What the model returned

  • Full padaccheda and anvaya
  • Mapping table: क=1 … ञ=0, ट=1 … न=0, प=1…म=5, य=1…ह=8
  • Rule for conjunct consonants: only the last consonant counts
  • Directionality note: अङ्कानां वामतो गतिः — digits read right to left
  • Example: भवति → भ(4), व(4), त(6) → reads as 644
Useful as a quick reference check. The mapping table should be verified against a standard commentary.
CAHC Tutorial · Session 2

AI Example 2 — Nidānasūtra Anvaya

The prompt

Parse and give anvaya for Nidānasūtra 5.12 on the Āditya-Saṃvatsara.

The text

त्रयोदशाहं त्रयोदशाहम् एकैकं नक्षत्रम् उपतिष्ठति। अहस्-तृतीयं च नवधा कृतयोः अहोरात्रयोः द्वे द्वे कले च।

What the model returned

  • Padaccheda and anvaya in Sanskrit, then English
  • Derivation: 13 + ⅓ + 2/9 = 122/9 days per nakṣatra
  • Total: 27 × 122/9 = 366 days (6 × 61 = ṣaṇṇava-vargāḥ)
  • Identified navadhā as a 1/9-day unit predating the 60-nāḍī system
The arithmetic derivation is correct and checkable. The unit interpretation (navadhā) is a reasonable scholarly reading — treat as a hypothesis.
CAHC Tutorial · Session 2

Wrap-Up

  • Stellarium makes ancient sky visible and testable.
  • Precession turns visible sky change into a dating instrument.
  • In both sessions, a textual sky description becomes a dating clue:
    • in Session 1 through the Sun,
    • in Session 2 through the Moon.
  • Astropy extends individual visual checks into exhaustive epoch scans.
  • Eclipses can be checked with NASA/JLEX and Stellarium.
  • Digital tools widen the research toolkit.
  • AI helps with drudgery — never with final interpretation.
These tools are most useful when they reduce repetitive effort and leave more time for careful scholarly thinking.

<img src="/Users/sunder/projects/cahc/cahc-utils/presentations/equinoctial-full-moon/bp-२१-१४२-१४९-devanaagari.jpeg" alt="BP 21 text">