How Tithi is Calculated: The Astronomy of Lunar Days
By Siddhartha Banerjee • Panjika Science Contributor
In the Bengali Panjika and general Vedic astrology, a Tithi (তিথি) is a lunar day. Unlike a Gregorian solar day (which lasts 24 hours), a Tithi is determined by the celestial relationship between the Sun and the Moon.
The Mathematical Definition
A Tithi represents a $12^\circ$ increase in the longitudinal separation between the Moon and the Sun, as viewed from the Earth.
A complete lunar cycle (from one New Moon to the next) is $360^\circ$ and takes approximately 29.5 days. Because $360^\circ / 12^\circ = 30$, there are exactly 30 Tithis in a lunar month.
The Formula
$$\text{Tithi Number} = \left\lfloor \frac{\lambda_{moon} - \lambda_{sun} + 360 \pmod{360}}{12^\circ} \right\rfloor + 1$$
Where:
- $\lambda_{moon}$ is the sidereal longitude of the Moon.
- $\lambda_{sun}$ is the sidereal longitude of the Sun.
The resulting integer (1 to 30) identifies the specific Tithi.
The Two Pakshas (Fortnights)
The lunar month is split into two halves:
- Shukla Paksha (Waxing Phase): Tithis 1 to 15. The Moon grows brighter, culminating in the 15th Tithi: Purnima (Full Moon).
- Krishna Paksha (Waning Phase): Tithis 16 to 30. The Moon grows darker, culminating in the 30th Tithi: Amavasya (New Moon).
Frequently Asked Questions
Can a Tithi be skipped or doubled?
Yes! Because the Moon moves faster near its perigee and slower near its apogee, a Tithi can last anywhere from 19 to 26 hours. If a Tithi starts after sunrise and ends before the next sunrise, it is skipped (Kshaya Tithi). If it spans two sunrises, it is doubled (Adhika Tithi).
Why is Tithi important for festivals?
Most Bengali festivals, including Durga Puja and Kali Puja, are celebrated on the day when the required Tithi is prevailing at a specific time of day (such as sunrise, afternoon, or midnight).