Panchangam Reference

Surya Siddhanta mean-motion longitudes ​

astronomy.surya-siddhanta-longitudes

A bounded transcription of mean-motion and manda corrections produces solar and lunar longitudes for the Surya Siddhanta engine.

Assurance ​

LevelCurrent statement
Documented and traceableYes — the canonical record includes the process and a worked example.
Regression or reproduction checkedLinked to 1 repository test file(s).
Independently source-supportedNot independently verified at this level; current behavior is regression-pinned.

Computation method ​

Method type: formula

Compute mean longitude from elapsed Kali-epoch days and revolution counts, then apply one variable-circumference manda correction for the Sun and Moon.

Process ​

  1. Subtract the code epoch, including the Ujjain longitude adjustment, to obtain Kali ahargana.
  2. Convert ahargana and the body's revolution count into a normalized mean longitude.
  3. Compute anomaly from the fixed solar apogee or moving lunar apogee.
  4. Interpolate the manda epicycle circumference between its even- and odd-quadrant values.
  5. Subtract the arcsine manda correction and normalize to 0-360 degrees; subtract Sun from Moon for elongation.

Formulae ​

Mean motion and manda correction ​

text
K = JD - epoch
L_mean = (K * revolutions / 1577917828 * 360) mod 360
A = (L_mean - apogee) mod 360
C = C_even - (C_even - C_odd) * abs(sin A)
manda = asin((C / 360) * sin A)
L_true = (L_mean - manda) mod 360
  • K: Kali ahargana in days
  • A: anomaly
  • C: interpolated epicycle circumference in degrees
  • L_true: returned longitude

Worked example ​

Hyderabad sunrise, 2026-06-11 ​

Inputs

  • UT Julian day: 2461202.5077662035
  • Sun revolutions: 4,320,000
  • Moon revolutions: 57,753,336

Calculation

  1. Apply the mean-motion formula with the Sun constants and solar apogee 77.333 degrees.
  2. Apply it again with the moving lunar apogee and lunar epicycle constants.
  3. Compute elongation as (Moon - Sun) modulo 360.

Result

  • Sun: 55.6206770967 degrees
  • Moon: 0.5772516191 degrees
  • Elongation: 304.9565745224 degrees

Method notes ​

  • The direct floating-point formula is a bounded modern transcription, not a complete traditional procedure.
  • The ayanamsa constructor argument is validated but does not alter these longitudes.

Contract ​

Owning layer: engine-core
Claim kind: deterministic-fact
Time basis: Julian day relative to the engine's Kali epoch constants.

Inputs ​

  • Julian day

Outputs ​

  • solar longitude
  • lunar longitude
  • Moon-Sun elongation

References and evidence ​

Evidence classes: astronomical, textual
Verification states: partially_verified, engine_pinned

The algorithm family is source-traced in part; production outputs remain regression-pinned rather than independently compared.

surya_siddhanta.mean_motion_manda ​

Evidence class: textual
Verification state: partially_verified
Locator: Chapter I verses 29-34 and 53 for revolution counts and mean place; chapter II verses 29-39 for anomaly, epicycle dimensions and the manda equation
Last reviewed: 2026-08-27
Scope: Supports the mean-motion and manda-correction algorithm family and the Sun/Moon revolution and epicycle constants. The implementation uses direct floating-point trigonometry, a fixed code epoch and simplified apogee treatment; this claim does not make it a complete textual transcription or independently verify its modern Panchangam outputs.

Sources ​

panchangam.non_drik_engine_outputs ​

Evidence class: astronomical
Verification state: engine_pinned
Locator: tests/test_surya_siddhanta_engine.py and tests/test_vakya_engine.py

Scope: Regression tests preserve the current Surya Siddhanta and Vakya Pancha-Anga and sky-event outputs. No independent published-Panchangam comparison set is registered, so engine-pinned output must not be described as externally verified.

Sources ​

  • No external source is registered for this claim.

The complete machine-readable source registry is available in provenance.json. A regression fixture or same-code reproduction is not independent verification.

Reproduce and review ​

Run the linked tests, then the complete offline contract:

bash
python tools/verify_project.py

Public surfaces ​

  • python-library
  • mcp
  • ics
  • website
  • generated-data

Limitations ​

  • This is not a complete textual transcription; direct floating-point trigonometry and simplified epoch/apogee constants intentionally differ from a full traditional procedure and from modern Drik positions.

Implementation ​

This route is generated from computations.json. Edit the registry and canonical reference prose in the same pull request as a behavior change.