The Hindu Lunisolar Calendar
This animation illustrates the basic concepts of the ancient Hindu Lunisolar calendar which is in active use in India even today. By definition, a lunisolar calendar is based on the orbital motion of the Sun and the Moon as observed from the Earth (i.e. in a geocentric model).
Saura Mana
The solar months (Rashis) are nothing but the familiar signs of the Zodiac, labeled in a different language (Sanskrit). A solar day is defined based on the axial rotation of the Earth:
- One sidereal axial rotation is called a Nakshatra Ahoratra.
- Sunrise to sunrise is called a Savana Ahoratra. This is used in practice today in India.
- A lunar month (Masa) starts immediately after New Moon.
- A new fortnight (Paksha) starts immediately after Full Moon.
- Each days (Tithi) is defined as the time required for the Moon to advance 12 successive synodic degrees on its (i.e. relative to the Earth-Sun axis).
- New Moon (i.e. Moon is in conjunction with the Sun) starts a new lunar month and the next fortnight
- Full Moon (i.e. Moon is in opposition to the Sun) starts the next fortnight
- The lunar month in which a Mesha Sankramana occurs is designated the first lunar month (Chaitra). Thus, the lunar new year day (Chandramana Yugadhi) is marked by the New Moon immediately preceding the Sauramana Yugadhi.
- Every lunar month witnesses one and only one sankramana (with the exception noted below).
- Lunar months are shorter than solar months. Observe that at the end of the animation (i.e. end of 1 solar year), the lunar calendar has advanced 11 lunar days (Chitra - Ekadashi) into the next year. Hence, the Hindu calendar introduces an intercalary month (Adhika Masa) approximately every 2.5 solar years to re-synchronize the lunar with the solar calendar (not modeled here). In practice, a lunar month that does not witness a sankramana (i.e. which starts and ends while the sun is traversing a single sign of the Zodiac) is declared an Adhika Masa and labeled with the same name as the lunar month succeeding it. In this animation, Year 2 - Bhadrapada starts and ends entirely in Simha Rashi and hence becomes Adhika Bhadrapada; the next lunar month is the "real" (Nija) Bhadrapada, i.e. Bhadrapada repeats twice in Year 2. This effectively synchronized the lunar calendar with the solar calendar and ensures that a Mesha Sankramana happens in the following Chaitra masa.
- Some lunar days stretch across the commencement of two solar days (i.e. two sun rises); before the moon completes traversing 12 synodic degrees of its orbit (i.e. relative to the Earth-Sun axis), two solar day commencements occur. Both these solar days are labeled with the same Tithi and the second (repeating) Tithi is called Adhika Tithi (extra lunar day). Example: Jyeshta-Shukla-Dashami stretches across two solar days. Hence, when you advance through two days, the Tithi continues to display Dashami.
- Some lunar days start and end between the commencement of two solar days (i.e two sun rises); the Moon traverses 12 synodic degrees of its orbit (i.e. relative to the Earth-Sun axis) between two solar day commencements. Hence, neither of these solar days will be labeled with this Tithi and this Tithi is entirely skilled. Such a Tithi is called Kshaya Tithi (truncated day). Example: Vaishaka-Krishna-Chaturdashi starts and ends between two solar days. Hence, when you advance through two days, the Tithi jumps from Trayodashi to Amavasya (i.e. Chaturdashi is skipped).
- the Tithi of a solar day is determined based on the synodic position of the Moon at the commencement of the solar day