Ayanāṁśa & Coordinate Systems
The mathematical divergence between the moving Tropical (Sāyana) and fixed Sidereal (Nirayana) zodiacs, axial precession, and the Lahiri ayanāṃśa this engine uses.
Cited for: The Sūrya Siddhānta treats the precession of the equinoxes as a to-and-fro libration of the circle of the asterisms, not a steady drift, and gives a rule for the ayanāṃśa on that basis. Later astronomers took precession as continuous.
1. Tropical (Sāyana) vs. Sidereal (Nirayana)
The fundamental difference between Western astrology and Indian Vedic astrology is the coordinate reference framework:
Tropical Frame (Sāyana)
Anchors 0° Aries to the Vernal Equinox—the intersection point of the celestial equator and the ecliptic. Due to Earth’s axial precession (p ≈ 50.29''/year), the vernal equinox drifts westward across the fixed stars at approximately 1 degree every 71.6 years (completing one cycle every ~25,772 years).
Sidereal Frame (Nirayana)
Anchors the zodiac to fixed stellar landmarks (the 27 Nakshatras). In Indian astronomy, constellations remain stationary relative to the distant stars. The longitudinal offset between the moving vernal equinox and the initial stellar point (0° Sidereal Mesha) is the Ayanāṁśa.
The Fundamental Ayanāṁśa Transform
Parameters & variables
λ_sidereal- Sidereal Longitude: Vedic zodiac degree measured from 0° Mesha(degrees)
λ_tropical- Tropical Longitude: Western equinoctial degree measured from Vernal Equinox(degrees)
Ayanāṁśa- Precession Offset: Angular separation (~24.238° in 2026)(degrees)
2. Comparative Ayanāṁśa Analysis
Several ayanāṃśas are in use among astrologers. This engine uses Lahiri (Chitrāpakṣa), the one the Calendar Reform Committee recommended and the official Indian ephemeris follows. The others are shown for comparison:
| Ayanāṁśa Name | 2026.0 Value | Offset from Lahiri | Stellar Anchor | Status |
|---|---|---|---|---|
| Lahiri (Chitrāpakṣa) SIDM_LAHIRI | 24° 14′ 18″ | 0° 00′ 00″ (Benchmark) | Spica (Chitrā) at exactly 180°00′00″ | Canonical |
| Krishnamurti (KP) SIDM_KRISHNAMURTI | 24° 08′ 26″ | - 0° 05′ 52″ | K.S. Krishnamurti stellar alignment | Alternative |
| B.V. Raman SIDM_RAMAN | 22° 49′ 05″ | - 1° 25′ 13″ | 397 CE zero-precession epoch | Historical |
| Fagan-Bradley SIDM_FAGAN_BRADLEY | 25° 08′ 21″ | + 0° 54′ 03″ | Aldebaran at 15°00′00″ Taurus | Western Sidereal |
| True Chitrā SIDM_TRUE_CITRA | 24° 14′ 12″ | - 0° 00′ 06″ | Apparent astrometric Spica position accounting for proper motion | Astrometric |
The star Chitrā (Alpha Virginis / Spica) is uniquely positioned almost exactly on the ecliptic (celestial latitude β ≈ -2° 03'). By anchoring Spica at precisely 180°00′00″ (the exact cusp between Kanya and Tula), the sidereal zodiac divides into two symmetric hemispheres of 180° each. The vernal equinox coincided with 0° Mesha in 285 CE, making Chitrāpakṣa the most mathematically elegant and historically corroborated anchor.