CALCULATION METHOD

Tithi is calculated by finding the angle between the Moon and the Sun as viewed from Earth.

• We use the Lahiri Ayanamsa for sidereal calculations
• Calculate the longitudes of both the Sun and Moon
• Determine the angular distance between them (Moon phase)
• Divide this angle by 12 degrees (360° ÷ 30 tithis = 12° per tithi)
• The result gives us the current tithi (1-30)
• We predict tithi ending time by calculating when the Moon-Sun angle will reach the next threshold

To ensure accuracy, we perform interpolation calculations at several points and determine the precise moment when the tithi will change.

Nakshatra calculations are based on the Moon's position in the sidereal zodiac, divided into 27 equal parts of 13°20' each.

• Calculate the Moon's longitude in the sidereal zodiac
• Divide the longitude by 13°20' (the span of each nakshatra)
• The result gives us the current nakshatra (1-27)
• We calculate the nakshatra ending time by determining when the Moon will enter the next nakshatra

Our method accounts for the Moon's varying speed in its orbit to accurately predict nakshatra transitions.

Yoga is determined by adding the longitudes of the Sun and Moon and dividing the result into 27 segments.

• Calculate longitudes of both the Sun and Moon
• Add these two longitudes together
• Divide the sum by 13°20' (the span of each yoga)
• The result gives us the current yoga (1-27)
• We predict yoga ending time by determining when the sum will reach the next threshold

Since yoga depends on the movement of both the Sun and Moon, our calculations account for their combined motion to determine transition times.

Karana is half of a tithi, representing the time taken for the angular distance between the Sun and Moon to increase by 6 degrees.

• Calculate the Moon-Sun angle as in tithi calculation
• Divide this angle by 6 degrees to get the karana number (1-60 in a lunar month)
• Apply the correct naming convention:
  • First 7 karanas (Bava to Vishti) repeat 8 times (making 56 karanas)
  • Last 4 karanas (Shakuni, Chatushpada, Naga, Kimstughna) appear only once
• Calculate karana ending time by determining when the Moon-Sun angle will increase by another 6 degrees

Our algorithm accounts for the special pattern of karana repetition near Amavasya and Purnima to ensure accurate calculations.

We calculate the precise times of sunrise and sunset for a given location using astronomical algorithms.

• Utilize the user's latitude, longitude, and timezone
• Apply the Swiss Ephemeris rise/set function which accounts for:
  • Atmospheric refraction
  • The apparent diameter of the Sun
  • Local elevation
• Convert the resulting Julian date to local time

This provides accurate times for the upper limb of the Sun crossing the local horizon.

Similar to sunrise and sunset calculations, but for the Moon:

• Use the Swiss Ephemeris rise/set function for the Moon
• Account for the varying distance of the Moon from Earth
• Handle special cases where moonrise or moonset may not occur on a particular day (in higher latitudes)

Various muhurtas and special time periods are calculated based on divisions of the day:

• Rahu Kaal: Calculated by dividing the daylight hours into 8 parts and selecting the appropriate part based on the day of the week
• Yamgandam: Similar to Rahu Kaal but with a different assignment based on the weekday
• Kulika: Another special time period calculated based on weekday and daylight division
• Abhijit Muhurat: Calculated as ±24 minutes from local midday

The calculation of the current year in the 60-year Jovian cycle:

• Start with the elapsed days since the beginning of Kali Yuga
• Convert to years using the sidereal year length
• Apply mathematical formulas to determine the position in the 60-year cycle
• Map the result to the appropriate named year (e.g., Vikrama, Shukla, etc.)

This calculation includes corrections for precession and other astronomical factors.

While we strive for the highest level of accuracy in our calculations, please note:

• Panchang calculations can vary slightly between different traditions and systems
• Our calculations use the Lahiri Ayanamsa, which is the officially recognized ayanamsa by the Government of India
• The accuracy of location-specific calculations depends on the precision of the latitude and longitude provided
• Very high latitude locations (near the poles) may have special cases for sunrise/sunset and moonrise/moonset
• We regularly update our astronomical algorithms to incorporate the latest research and improvements

Our application uses the following technical components for calculations:

• Swiss Ephemeris library (swisseph): A high-precision astronomical calculation library
• Python's datetime and math modules for time handling and mathematical operations
• Pytz library for accurate timezone handling
• TimezoneFinder for determining the timezone from geographical coordinates
• Custom interpolation algorithms for precise transition time calculations

These components work together to provide accurate, location-specific Panchang calculations for any place on Earth.