Notion of years and months in the Indian Calender

The Vedic Year

The Vedic year, known as Shravana, consisted of 12 months, each with 30 days, totaling 360 days. This concept is depicted in the Rigveda, where a verse describes the wheel of time with twelve spokes, representing the 12 months, and 720 sons, representing the 360 days and 360 nights. The Yajurveda mentions 12 lunar months called Vatsara, amounting to 354 days. To synchronize this with the solar year of 365.25 days, the eka dasha ratra ceremony was used, accounting for 365 days and leaving an error of 0.25 days.

Five Systems of Year

The Vedic Corpus mentions five systems of year:

1. Samvatsara: The solar year, representing the time taken by the Sun to pass through the 12 zodiacs.
2. Idavatsara: The Shravana year with 12 months of 30 days each, totaling 360 days.
3. Anuvatsara: The lunar year, with each month ending on the new moon day (amavasya).
4. Vatsara: A year with 12 lunar cycles. It's important to note that a lunar year (New Moon to New Moon, 29.5 days) is different from a lunar cycle (27.32 days).
5. Parivatsara: The time taken by Jupiter to pass from one sign of the zodiac to another.

Solar, Shravana, and Lunar Years

A table comparing the Solar, Shravana, and Lunar years shows the differences in their durations:

Yuga Cycle

To reconcile the Solar and Lunar years, the concept of a Yuga was introduced. A Yuga is roughly 5 solar years, equivalent to 61 Shravana months and 62 Lunar months. This accounts for the addition of an extra month (Adhika masa) every two and a half years, bringing the lunar and solar calendars back into alignment.

Solar and Lunar Months

The Surya-siddhanta defines a solar month as the time taken by the Sun to traverse a Rashi. A lunar month (Chandra Masa) is the time interval between two new moons (amavasya to amavasya) or two full moons (purnima to purnima). The difference between the solar and lunar months is corrected through the Adhika masa every two and a half years, ensuring alignment every 5 years.

Pakshas and Tithis

A lunar month is divided into two fortnights (Pakshas):

1. Shukla-paksha: The period when the Moon moves away from the Sun, starting from the new moon (Amavasya) and ending at the full moon (Purnima).
2. Krishna-paksha: The period when the Moon approaches the Sun, starting from the full moon and ending at the new moon.

The concept of Tithi refers to the angular separation between the Sun and the Moon. Each Tithi is approximately 12°, with slight variations depending on the celestial movements.

Vedanga-jyotisha

Vedanga-jyotisha is the first Indian text to provide mathematical algorithms for astronomical calculations, including finding the Tithi, Nakshatra, and Sun's position. These algorithms offer approximate but reasonably accurate results.

Understanding these fundamental elements of the Indian calendar lays the groundwork for comprehending the complex system of timekeeping in the Indian tradition.