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Jyotish Library Logic Documentation

This document serves as the technical authority for the jyotish library. It details the mathematical formulas, classical Vedic references, and modern implementation standards used for all astrological calculations.

1. Core Astronomical Foundation

Swiss Ephemeris Integration

The library utilizes the Swiss Ephemeris (SE) for sub-arcsecond precision.

  • Ephemeris Type: SEFLG_SWIEPH (High-precision ephemeris).
  • Coordinate System: Geocentric ecliptic by default. Topocentric positions (SEFLG_TOPOCTR) are calculated when useTopocentric is enabled in CalculationFlags.
  • Precession Adjustment: For sidereal speed (Chesta Bala), a 0.01% correction factor is applied to account for the difference between tropical and sidereal motion rates (~50.3" per year).

Sidereal Conversion (Ayanamsa)

The library converts tropical coordinates to the sidereal frame using precise ayanamsa values.

  • Formula: Sidereal_Longitude = (Tropical_Longitude - Ayanamsa + 360) % 360.
  • Ayanamsa Precision: Time-varying formulas from SE are used.
    • Example: Lahiri (Chitra Paksha) uses the fixed star Spica (α Virginis) as the anchor (coordinate 180°).
  • KP New Ayanamsa (VP291): Used specifically for the KP System, diverging from Lahiri by approximately 6 minutes of arc.

2. Panchanga (The Five Limbs)

Tithi (Lunar Day)

  • Mathematical Formula: Tithi = floor((Moon_Long - Sun_Long) / 12) + 1.
  • End-Time Calculation: Determined using a high-precision binary search (1-minute resolution) to find the exact moment the elongation hits a multiple of 12°.
  • Reference: Surya Siddhanta.

Vara (Weekday Lord)

  • Logic: The planetary ruler of the day based on the sequence: Sun, Moon, Mars, Mercury, Jupiter, Venus, Saturn.
  • Vedic Boundary: The day changes at local Sunrise.
  • Calculation: If Birth_Time < Sunrise_Time, the Vara is of the previous solar day.
  • Reference: Brihat Parashara Hora Shastra (BPHS).

Nakshatra (Lunar Mansion)

  • Division: 360° / 27 = 13°20' per Nakshatra.
  • Formula: Nakshatra = floor(Moon_Sidereal_Long / (13.333333)) + 1.
  • Abhijit Nakshatra: Incorporated for specific rituals and Muhurta (Brahma/Abhijit). Occupies the region between 276°40' and 280°53'20" (the last quarter of Uttarashadha).

Yoga & Karana

  • Yoga: floor((Sun_Long + Moon_Long) / 13.333333) + 1.
  • Karana: Half a Tithi (6°). Includes 7 repeating variable karanas and 4 fixed ones (Kimstughna, Shakuni, Chatushpada, Naga) which occur at specific points in the lunar month.

3. Planetary Strength (Shadbala)

The library implements the complex 6-fold strength system as defined in BPHS, following the numerical models of P.V.R. Narasimha Rao.

Sthana Bala (Positional Strength)

  1. Uchcha Bala: (180 - Distance_from_Deep_Exaltation) / 3. Max = 60 Virupas.
  2. Saptavargaja Bala: Cumulative strength across 7 divisional charts (D1, D2, D3, D7, D9, D12, D30).
    • Own Sign: 30 | Friend: 22.5 | Neutral: 15 | Enemy: 3.75 | Great Enemy: 1.875 units.
  3. Ojayugmarasyamsa: Based on Odd/Even sign and Navamsa placement for masculine/feminine planets.

Kala Bala (Temporal Strength)

  • Natonnata Bala: Day and night strength. Max 60 for Moon/Mars/Saturn at midnight, 60 for Sun/Jupiter/Venus at noon.
  • Ayana Bala: Strength based on Declination (Kranti). Formula: (24 ± Declination) / 48 * 60.
  • Paksha Bala: Lunar phase strength. Benefics gain near Full Moon; Malefics gain near New Moon.

Chesta Bala (Motional Strength)

  • Derived from the planet's daily velocity relative to its average motion.
  • Retrograde planets (speed < 0) receive full Chesta Bala (60).

Functional Phala

  • Ishta Phala: Benefic results. sqrt(Uchcha_Bala * Chesta_Bala).
  • Kashta Phala: Malefic results. sqrt((60 - Uchcha_Bala) * (60 - Chesta_Bala)).

4. Divisional Charts (Varga)

The DivisionalChartService calculates fractional vargas (D1 to D60) and Nadi Amsa (D150).

Key Mapping Rules:

  • Hora (D2): 15° segments. Odd sign: first 15° = Sun (Leo), second 15° = Moon (Cancer). Even sign: reverse.
  • Drekkana (D3): 10° segments. 1st: same; 2nd: 5th from sign; 3rd: 9th from sign.
  • Navamsa (D9): 3°20' segments.
    • Fire Signs: Start from Aries.
    • Earth Signs: Start from Capricorn.
    • Air Signs: Start from Libra.
    • Water Signs: Start from Cancer.
  • Trimsamsa (D30): Uneven mapping per BPHS. Odd signs: 0-5° Mars, 5-10° Saturn, 10-18° Jupiter, 18-25° Mercury, 25-30° Venus. Even signs: reverse order and lords adjusted.
  • Shashtiamsa (D60): 0.5° segments. Odd signs: forward count from current. Even signs: forward count from 9th sign.
  • Nadi Amsa (D150): 150 divisions per sign. Odd signs: forward from Aries; Even signs: backward from Pisces.

5. Ashtakavarga

A system of evaluation based on benefic points (Bindus) contributed by the 7 planets and Ascendant.

Reductions (Shodhana):

  1. Trikona Shodhana (Trine Reduction): For each planet's BAV, the lowest bindu count among signs in a trine (e.g., Aries-Leo-Sag) is subtracted from all three.
  2. Ekadhipati Shodhana (Dual-Lordship Reduction):
    • Applied to signs owned by the same planet (excluding Sun/Moon signs).
    • If signs are "Odd Foot" (1, 2, 3, 7, 8, 9), subtract smaller from larger.
    • If "Even Foot", take the minimum non-zero value.
  3. Shodhya Pinda: The final reduced values are multiplied by Rashi Multipliers (1 to 12) and Graha Multipliers to find the net planetary strength.

6. KP System (Krishnamurti Paddhati)

KP is a sub-lord based system emphasizing the "Star Lord" and "Sub-Lord" over the traditional sign-based analysis.

Technical Parameters:

  • Ayanamsa: Strict use of KP New (VP291) Ayanamsa.
  • Houses: Placidus (Semi-arc) house system is mandatory for accurate Sub-Lord boundaries.
  • 249 Sub-Divisions: Each Nakshatra is divided proportionally to the Vimshottari Dasha years (120-year cycle). If a sub-lord boundary crosses a sign boundary (0°, 30°), it is split into two, totaling 249 divisions.
  • Sub-Sub-Lord (SSL): Further refinement dividing the Sub-Lord into 9 further proportional parts.

Significators (ABCD Grading):

The library assigns significators for each planet/house interaction:

  • Grade A: Occupants of the star of the house lord. (Strongest)
  • Grade B: Occupants of the house.
  • Grade C: Houses owned by the planet (Cusp-based ownership).
  • Grade D: Houses owned by the planet's Sign Lord.

7. Advanced Panchang & Muhurta

This section details the newly implemented extended Panchang features, ensuring alignment with both Northern (BPHS) and Southern (Muhurta Chintamani) traditions.

Samvat & Solar Metadata

  • Vikram Samvat: Gregorian Year + 57 (changes at Chaitra Shukla Pratipada).
  • Shaka Samvat: Gregorian Year - 78 (changes at Chaitra Shukla Pratipada).
  • Gujarati Samvat: Vikram Samvat - 1 (lags behind until Kartiki Pratipada).
  • Ayana: Based on Tropical Sun Longitude. long < 180° = Uttarayana, long ≥ 180° = Dakshinayana.
  • Pravishte: Solar date within the current sidereal Rashi (Sun transit).

Muhurta Timing Rules

  • Dur Muhurtam (Default): Divided into 8 equal parts of daytime (BPHS/Northern). One part per day is designated as the "Dur Muhurta" based on the day's ruler alignment.
  • Dur Muhurtam (South Indian): Divided into 15 equal parts (Muhurta Chintamani). Two specific Muhurtas per weekday are designated as inauspicious.
  • Varjyam (Thyajya): The "poisonous" portion of a Nakshatra transit. The start time is calculated as Nakshatra_Start + (Thyajya_Ghati / 60) * Nakshatra_Duration.

Astrological Strength (Balam)

  • Chandrabalam: The strength of the transit Moon relative to the native's Rashi.
    • Strong: 1st, 3rd, 6th, 7th, 10th, 11th from Moon.
    • Moderate: 2nd, 5th, 9th.
    • Weak: 4th, 8th, 12th.
  • Tarabalam: Calculated as (Current_Nakshatra - Birth_Nakshatra + 27) % 9.
    • Resulting index maps to 9 Tara types (Janma, Sampat, Vipat, etc).

Ritual Elements

  • Krishna Paksha Offset: For ceremonial modulo math, Krishna Paksha Tithis (1-15) are mathematically treated as 16-30 to align with Drik Panchang and textual standards.
  • Agnivasa (Fire Residence): (Tithi + Weekday + 1) % 4. Result 0/3 = Earth, 1 = Sky, 2 = Underworld.
  • Shivavasa (Shiva's Residence): A 7-period rotation based on absolute Tithi.

8. Deviations & Clarifications

Feature Implementation Standard Rationale
Rahu/Ketu Mean Node BPHS / Traditional Default set to Mean Node; True Node available as a flag.
Vara Boundary Sunrise Jyotish Standard Day lord must change at Sunrise.
Dur Muhurtam BPHS (1/8th) BPHS Default Set as default for Drik Panchang compatibility; 1/15th available as option.
Ritual Tithis 1-30 numbering Purnimanta/Amanta Offset added in Krishna Paksha for correct modulo outcomes.
Ishta/Kashta sqrt formula PVR Narasimha Rao Adopted from Jagannatha Hora model.

9. Authorities & Texts

  • BPHS: Brihat Parashara Hora Shastra - Core foundation for Shadbala and Northern Muhurta (8-part).
  • Muhurta Chintamani: Primary authority for the 15-part Muhurta division used in the South Indian optional method.
  • Kala Prakashika: Authority for Varjyam and Rahu Vasa calculations.
  • Surya Siddhanta: Primary astronomical authority for Panchanga logic.
  • KS Krishnamurti / P.V.R. Narasimha Rao: Modern references for numerical standardization.