Astro Insight - Articles

According to the Indian calendar a Tithi is a lunar date, and is one of the five important aspects of an Indian almanac (Panchang – Panch means five and ang means parts). Most of the Indian social and religious festivals are celebrated based on the tithi. Until they left India and went overseas, the Indians didn’t really need to worry about tithi to celebrate their festivals since a tithi in India almost invariably falls on the same day for the entire region of India.

Even after migration to overseas countries, the Indians living overseas would still celebrate their festivals on the same dates as Indians in India would. For those who would argue that behind these festival celebrations, it’s the faith, that is more important than the date of celebration, I’m hundred percent with them. However, the intention here is to provide information for those who want to understand the importance behind the tithi on which Indian festivals are based.

The calendar “date” that we are so familiar with in our daily life is based on the solar calendar. The English calendar is a solar calendar. The basis for the solar calendar is the rotation of the Earth around the Sun. It takes the earth approximately 365 ¼ days to complete its rotation around the Sun. The English calendar that most of us use today divides the 365 days of earth’s period of rotation around the Sun in twelve months. The leap year, which occurs once every four years, accounts for ¼ day per year.

Similar to the solar calendar a lunar calendar is also popular and widely used in the Asian countries such as China, Pacific-rim countries, Middle East countries, and India. The lunar calendar, which is believed to have originated in India, has been around for a very long time, even long before the solar calendar.

The lunar calendar is based on the moon’s rotation around the Earth. The lunar month corresponds to one complete rotation of the Moon around the Earth. Since this period of rotation of moon around the earth varies, the duration of the lunar month also varies. On average, the lunar month has about 29 ½ days. In addition to moon’s rotation around the earth, the lunar year is based on earth’s rotation around the Sun. In general, the lunar year has twelve lunar months totaling to approximately 354 days, thus making the lunar year shorter by about 11 days than the solar year. However, the lunar calendar accounts for this difference by adding an extra lunar month about once every 2 ½ years. The extra lunar month is commonly known as the “Adhik Mas” in India (Adhik means extra and the Mas means month). The concept of this extra month is similar to the “Blue Moon” in the West, which occurs almost about the same time with the same frequency of 2 ½ years.

The Indian lunar year begins on the new moon day that occurs near the beginning of the Spring season. The twelve lunar months are:

As mentioned earlier, to account for the difference between the solar and the lunar year an extra lunar month occurs about every 2 ½ years as the “Adhik Mas”.[1]

According to the Moslem calendar which is widely followed in Middle East and in other Moslem countries the lunar year is strictly based on twelve lunar months of 354 days per year. That’s why their holy month of Ramadan occurs by approximately 11 to 12 days earlier than that in the preceding year.

The solar day (commonly referred as the "date” in western calendar) has a fixed length of 24 hours. The change of date occurs at midnight as per local time or standard time of a given local time zone. Thus, the date changes from midnight to midnight. Similarly the day (as in weekdays) changes from midnight to midnight as per local or standard time for that location. In other words, as per western (or English) calendar the length of day and date is exactly 24 hours, and there is a definite correspondence between the date and the corresponding day of the week.

A lunar day generally begins at sunrise, and the length of lunar day is determined by the time elapsed between the successive sunrises. As per Jewish calendar their lunar day begins at the sunset, and lasts through the next sunset. A lunar day is essentially the same as a weekday. In India the lunar day is commonly referred as “War”. Just like English calendar has seven days for a week, Indian calendar has seven wars for a week. Thus,

The lunar date, however, varies approximately between 22 to 26 hours based on the angular rotation of the moon around the earth in its elliptical orbit. In Indian calendar, the lunar date is referred as “Tithi”. The basis for the length of a lunar date is the angular distance between the sun and the moon as seen from the earth. As the moon rotates around the earth, the angular distance between the sun and the moon as seen from the earth increases from 0 degrees to 360 degrees. It takes one lunar month or about 29 ½ solar days for the angular distance between the sun and the moon to change from 0 to 360 degrees. When the angular distance reaches zero, the next lunar month begins. Thus, at the new moon a lunar month begins, at full moon, the angular distance between the sun and the moon as seen from the earth becomes exactly 180 degrees.

The lunar cycle begins with crescent moon, and the crescent phase lasts till it culminates in the full moon, typically lasting for about 15 days. Then the moon enters in the waning phase until it disappears from the sky by lining up with the Sun. The waning phase also lasts for about 15 days. According to the Indian lunar month, the crescent lunar phase fortnight is called as “Shudha or Shukla Paksha” and the waning phase of the lunar cycle fortnight as “Wadya or Krushna Paksha”. Thus, during Shudha (or Shukla) Paksha the angular distance between the moon and the sun varies from 0 degrees to 180 degrees while that during the Wadya (or Krushna) Paksha from 180 to 0 degrees. If we divide 180 degrees into 15 equal parts, then each part becomes of 12 degrees in length. Thus, this each twelve-degree portion of angular distance between the moon and the sun as it appears from the earth is the lunar date or the Tithi. Tithis or lunar dates in Shudha (or Shukla) Paksha begin with Prathama (first), Dwitiya (second), etc. till we reach the Poornima, the lunar date for the full moon day. Similarly for the waning fortnight lunar cycle or Wadya (or Krushna) Paksha, tithis begin again with Prathama (first), Dwitiya (second), etc. till we arrive Amavasya or the day preceding the new moon. Thus, when we refer to Ramnavami (the birthday of Rama), it’s the Navami (ninth lunar day) of Shudha Paksha of the lunar month Chaitra, or Chaitra Shudha Navami. Similarly, the Gokulashtmi (also called as Janmashtami, the birthday of Krisha) occurs on Shrawan Wadya Ashtami (eighth lunar day of Wadya Paksha of the lunar month Shrawan).

The angular velocity of the moon in its elliptical orbit around the earth continuously varies as it is affected (according to Kepler’s rule) by the relative distance between the earth and the moon, and also by the earth’s relative distance from the sun. As a result, the daily angular speed (the speed of the angle between the moon and the sun as seen from the earth) varies somewhere between 10 to 14 degrees. Since the length of a tithi corresponds to 12 such degrees, the length of a tithi also varies accordingly. Therefore, a tithi can extend over one day (24 hour period) or it can get skipped if two tithis occur in one day.

Since the angular distance between the moon and the sun, as referred here, is always relative to the entire earth, a lunar day or tithi starts the same time everywhere in the world but not necessarily on the same day. Thus, when a certain tithi starts at 10:30 PM in India it also begins in New York at the same time, which is 12 PM (EST) on the same day. Since the length of a tithi can vary between 20 to 28 hours, its correspondence to a War (a weekday) becomes little confusing.

As per the Indian calendar, the tithi for a given location on the earth depends on the angular distance between the moon and the sun relative to the earth at the time of sunrise at that location. Thus, for instance, assume on a November Monday the sunrise in New York city occurs at 8:30 AM (EST). Further assume that at 9 AM (EST) on the same Monday the angular distance between the sun and moon is exactly 12 degrees just following the new moon of the Indian lunar month Kartik. Since the length of a tithi is 12 degrees, the tithi, Kartik Shudha Dwitiya (second day) begins exactly at 9 AM on Monday of that November in New York. However, at the time of the sunrise on that Monday the tithi Dwitiya has not begun. Therefore, the tithi for that Monday for the city of New York is Kartik Shudha Prathama (first day).

On the same Monday morning the sunrise in Los Angeles occurs well past 9 AM (EST). Since the tithi Dwitiya occurs everywhere in the world at the same instant, therefore, for Los Angeles, the tithi for that Monday would be Kartik Shudha Dwitiya.

For the same Monday at 9 AM (EST), it would be 7:30 PM in Mumbai or in New Delhi. Thus, Tithi for that Monday for the city of New York, Mumbai, and New Delhi is Kartik Shudha Prathama (the first day of the Indian lunar month Kartik) while for the regions approximately west of Chicago and St. Louis, the tithi for that Monday is Dwitiya. In other words, the tithi Kartik Shudha Prathama for regions west of Chicago or St. Louis should occur on the preceding day, the Sunday.

Kartik Shudha Prathama (the first day of the Indian lunar month Kartik) also happens to be the first day after Diwali. Most of the Indians celebrate this as their New Year’s day. The Indians living in India, Europe, and in the eastern part of the United States thus should celebrate their New Year on that Monday while regions west of Chicago should on the preceding day, the Sunday.

[1] Adhik Mas occurs only when two amavasyas (no moon day) occur while Sun remains in the same sidereal zodiac sign. For more information on sidereal (or fixed) zodiac system refer to book, “It’s all in Timing”, Jagdish C. Maheshri, Noble House, 1997.