Astronomy

Pancanga–The Hindu Almanac
(DRAFT)

"Time creates the sky and the earth. Time creates that past and the future. By Time the sun burns, through Time all beings exist, in Time the eyes see. Time is the lord of all."

This verse from the Atharva-veda (19.54) expresses the importance of time in Hindu culture. In India time is conceived as an unending flow that moves in great cycles. The Matsya Purana speaks of the waters of time. (See: Heinrisch Zimmer, Myths ans Symbols in Indian Art and Civilization Bollingen Series, Princeton University Press, p. 27) Sometimes those waters move in a peaceful way, sometime they move in great and chaotic torrents. So it is with time. The movements of the sun and the moon, and the other celestial bodies are the indication of this flow of time. The Bhagavata Purana describes how the passage of the sun across the atoms on this earth creates the reckoning of time. The record of time is the pancanga wherein the movements of these celestial bodies are precisely recorded. No religious festival, family event, or even a civic affair is performed without first consulting the pancanga to know the favorable movement of this flow of time.

The Sanskrit word "pancanga" is made of two parts: panca and anga. Panca means five and anga means a limb or part. Thus the pancanga is a document made of five parts. These five parts are the tithi (lunar day), the vara (day of the week), the naksatra (lunar mansion), the yoga (luni-solar day) and the karana (half lunar day).

In order to understand these terms it is important to know how astronomers measure the sky. Just as a road map uses miles or kilometers to show distance between cities, so a celestial sky map uses degrees to show apparent distance between celestial objects. Keeping in mind that there are 360 degrees in a circle, it is easy to measure approximate degrees in the sky. Just raise your hand to the sky, and at arm's length, use your hand to measure the degrees in the sky. See the accompaning illustration that shows how the hand can be used to measure degrees in the sky.

At arm's length, for example, the width of the end of the little finger is almost one degree across. Check to see that the moon is about half a little finger in width and therefore can be estimated to be about a half a degree wide. This system is reasonably accurate for men, women and children, since people with smaller hands tend to have shorter arms. Astronomers have used this hand technique for thousands of years to make approximate measurements of the sky. To see how this system can be used to measure a common constellation see the illustration of the sapta-rsi (big dipper) and the star dhruva (polaris) to measure the degrees of separation.

As we begin to discuss the five elements of the Hindu almanac it is important to recognize the importance of the moon in Hindu culture. The basic calendar is primarily a lunar calendar. The lunar day, called a tithi, is all important in selecting a favorable time to begin a certain task. A person's name is often derived from the lunar position in the heavens called a naksatra. The reason for this is simple. In Hindu astrology the moon rules the mind.

Tithi (Lunar Phase)

The first element of the Hindu pancanga is the tithi or lunar phase. This is perhaps the single most important element of the pancanga. It is the building block for the lunar month. Simply stated a tithi is a measurement of 12 degrees of longitudinal separation between the sun and the moon. Another way to put it is to say that a tithi is the daily phase of the moon. For example, at new moon (amavasya) the sun and the moon are separated by zero degrees. We can say they overlap. As they begin to separate the first tithi begins when the sun and the moon have separated by 12 degrees. The moon is now a tiny almost imperceptable sliver. The second tithi begins when they are separated by 24 degrees. The sliver is slightly larger. The third tithi begins when they have separated by 36 degrees. The digit of the moon is new clearly visible. And so it goes until the sun and moon have separated by 180 degrees. This tithi is called full moon, purnima. These first 15 tithis or phases of the moon make up the waxing phases of the moon which in Sanskrit this is called the sukla-paksa. This is the bright side of the lunar month. After purnima, full moon, the tithi begins again counting from one as the longitudanal separation between the sun and the moon decreases back to zero. This is called the waning phase of the moon or in Sanskrit, the krsna-paksa or dark side of the lunar month. At certain times of the month when the sun and moon can both be seen in the sky at the same time you can estimate the tithi by using the hand method to measure the longitudinal separation between the sun and the moon.

The tithis are sequentially numbered from both the points of the new moon as well as the full moon. See the accompaning illustration. In this way, the sukla-paksa, begining with the new moon (amavasya), is followed by the first tithi, then the second tithi, the third tithi and so on up to the 14th tithi. There is no 15th tithi. Instead, this tithi is called full moon (purnima). After the full moon, the waning phase (krsna-paksa) again begins with the first tithi, the second tithi, the third tithi and so on up to the fourteenth tithi followed by the full moon. Afterwards the cycle repeats itself. In this way thirty tithis make up a lunar month, which is known as a masa. Some parts of India begin the month from the full moon whereas other parts begin the month from the new moon. Today, the lunar calendar is still in use throughout the world for Hindu religious purposes.

One of the greatest points of confusion between Hindu festival dates and the modern solar calendar is that the solar day begins at midnight whereas the lunar tithi can begin at anytime of the solar day. For practical purposes, however, the tithi that is current at sunrise is taken as the prevailing tithi for the day. This means that if a tithi begins just after sunrise and ends before the sunrise of the next day, it is eliminated.This is possible because the tithi can last between 19 to 26 hours due to the changing speed of the earth and moon in their obits. On average a tithi lasts for only 0.95 of a solar day. When this occurs a break in the numerical ordering of the days takes place. These factors cause a lot of confusion between the lunar Hindu calendar and the modern solar calendar.

From an astrological perspective the various tithis are considered either auspicious or inauspicious for different events. In general the sukla-paksa (bright side) is considered condusive to growth, increase and properity and would be selected for such occasions as weddings, moving into new homes or starting businesses, etc. The moon's krsna-paksa (dark side) is considered less favorable. In addition the 8th and 14th tithis, amavasya, as well as the 1st tithi of the sukla-paksa are generally considered inuaspicious. There are of course exceptions to this rule, the most notable of which are the various post funerary rites (sraddhas) that prefer the lunar dark phases. See the article "Hindu Funeral Rites and Ancestor Worship."

Vara (The Day of the Week)

The second element of the Hindu pancanga is the day, vara. In Sanskrit the days of the week are clearly named after seven major astrological influences:

Sunday, the sun, ravi-vara

Monday, the moon, soma-vara

Tuesday, Mars, mangala-vara

Wednesday, Mercury, budha-vara

Thursday, Jupiter, guru-vara

Friday, Venus sukra-vara

Saturday, Saturn, sani-vara

You can still see this astrological influence in the English names, Sunday, Monday and Saturday for the sun, the moon and Saturn respectively. If you examine the French and Spanish words for the days of the week you will see an even greater connection. Astrologically these days are named after these celestial bodies because the influence of that celestial body is said to be prominent on that day. For example, Tuesday, being ruled by Mars, the planet of war, would be a good date to enter into a battle, but not a good day to get married or move into a new home!

Naksatra (Lunar Mansion)

The third element of the pancanga is naksatra. The best way to understand naksatra is to observe the moon some evening. Notice the moon's position in relation to the background of stars. The next evening, at the same time and in the same location, again observe the moon's position in relation to the background of stars. You will see that it has moved consideralably. Use the raised hand technique to estimate how many degrees the moon has moved. The moon has moved somewhere between 10 and 15 degrees. In fact the moon has moved 13 degrees and 20 minutes. The region of the sky that has been displaced by the moon's eastward movement in one day is called a naksatra. In English this known as a lunar mansion. There are 27 such lunar mansions in the 360 degrees the moon travels in one lunar month ( 13.3 x 27 = ~360). In the Hindu Almanac each of these lunar mansions is named after a star or group of stars in each region of the sky.

The naksatra is very important in Hindu culture. At the time of birth a person's horoscope is made and one of the most important items to be known is the naksatra. Many elements of a person's character is thought to be determined by the naksatra. (Remember that the moon stands for the mind in Hindu astrology.) In many regions of India a person's name is based on the naksatra. Perhaps the first syllable of the name is derived from the naksatra. At the time of a puja or religious ceremony a priest will ask for the naksatra of the person performing the religious service so that it can be recited in the opening statement of the puja called a sankalpa. At the time of marriage considerations the naksatras of the both the bride and groom may be compared to check for pschological compatability.

The following is a list of the 27 naksatras along with their western astronomical designations. Note that in some cases it is difficult to determine exactly which western star name corresponds to the naksatras.

1. Asvini–alpha arietis (Hamal)

2. Bharani–41 arietis

3. Krttika–Pleiades

4. Rohini–alpha tauri (Aldebaran)

5. Mrgasirsa–lambda orionis (Bellatrix)

6. Ardra–alpha orionis (Betelgeuse)

7. Punarvasu–beta geminorum (Castor)

8. Pusya–delta canceri (area of M44 Beehive cluster)

9. Aslesa–alpha canceri (sometimes taken as the Hydra or Alphard)

10. Magha–alpha leonis (Regulus)

11. Purvaphalguni–delta leonis (lion's hind)

12. Uttara-phalguni–beta leonis (Denebola)

13. Hasta–gamma or delta corvi (Corvus)

14. Citra–alpha virginis (Spica)

15. Svati–alpha bootis (Arcturus)

16. Visakha–alpha libra

17. Anuradha–delta scorpionis

18. Jyestha–alpha scorpionis (Antares)

19. Mula–lambda scorpionis (near the globular cluster Shaula)

20. Purvasadha–delta sagittarii

21. Uttarasadha–sigma sagittarii (teapot)

22. Sravana–alpha aquilae (Altair)

23. Dhanistha–alpha delphini (Delphinis)

24. Satabhisa–lambda aqurii (Fomalhaut)

25. Purva-bhadrapada–alpha pegasi (Markab)

26. Uttara-bhadrapada–gamma pegasi

27. Revati–delta piscium

(To this group of 27 naksatras, one more naksatra known as abhit is sometimes added. Abhit includes the region of Vega in the constelation of Lyra. This is not on the path of the sun (solar eclipic) as are the other naksatras and so can be ignored.)

This system of 27 naksatra was the original Hindu way of dividing the 360 degrees of the solar ecliptic. The system of the twelve signs of the zodiac, in Sanskrit called rasi, was a later addition to Hindu astronomy.

Yoga (The Luni-solar Day)

The yoga (luni-solar day) is the period during which the combined longitudinal motion of the sun and moon amounts to 13 degrees and 20 minutes. Like the naksatras there are 27 yogas.

Karana (Half Tithi)

The final aspect of the pancanga is karana which is calculated to be 6 degrees of longitudinal separation between the sun and moon. In other words the karana is half a tihi. There are two karanas in each tithi. In total there are eleven karanas that rotate through the 30 tithis that make up the lunar month.

Both a karana and a yoga are similar to a tithi in the sense that they are all a measure of the relationship between the sun and moon. Recall that a tithi was 12 degrees of longitudinal separation between the sun and moon, the yoga is the combined longitudinal motion of the sun and the moon. Here the karana is half the tithi. In Hindu astrology the sun and the moon are both perceived to have a great effect on life, and their motions are precisely calculated.

In addition to these five part of the traditional Hindu calendar the follow other elements may be added.

Masa (Month)

The Hindu year contains twelve lunar months named after the naksatra in which the moon is full:

Caitra (March - April) (citra-naksatra)

Vaisakha (April - May) (visakha-naksatra)

Jyaistha (May - June) (jyestha-naksatra)

Asadha (June - July) (purvasadha-naksatra)

Sravana (July - August) (sravana-naksatra)

Bhadrapada (August - September) (purva-bhadrapada-naksatra)

Asvina (September - October) (asvini-naksatra)

Karttika (October - November) (krttika-naksatra)

Margasirsa or Agrahayana (November - December) (mrgasirsa-naksatra)

Pausa (December - January) (pusya-naksatra)

Magha (January - February) (magha-naksatra) and

Phalguna (February - March) (phalguna-naksatra).

Different parts of India start the year during different months. In general the year begins either in the vernal month of Caitra or in the autumnal month of Karttika.

Rtu (Season)

Traditionally India has six seasons (rtu), each comprised of two months. The six seasons are:

Vasanta (spring, March to May)

Grisma (summer, May to July)

Varsa (rainy, July to September)

Sarad (autumn, September to November)

Hemanta (winter, November to January) and

Sisira (cool, January to March)

Another aspect of the lunar calendar is that its twelve months based on the lunar days (tithis) contain about 354 days. So just as every 4th year on the solar calendar must add an extra day to make up for the discrepancy in the earth's orbit around the sun, so every 30 months the lunar calendar must add an extra month. This leap-month (adika-masa) is generally inserted after the months of Asadha or Sravana and is called either a second Asadha or Sravana. Thus every second or third year contains 13 months. This of course contributes considerably to differences between the lunar and solar calendars. The consequences of these differences makes it hard to reconcile the dates from one calendar to the other without intricate calculations.

Hindu Months and Time Eras

The Hindu Months

In Hindu astrology, as in Western astrology, the zodiac is divided into twelve signs (rasis). Each of the twelve signs is in thirty degree segment of the full zodiac. In addition to the twelve signs, the Hindu zodiac is further divided into twenty-seven naksatras or lunar mansions. Each naksatra is a thirteen degree and twenty minute segment of the zodiac. Specifically, a naksatra is the number of degrees the moon travels across the sky in a twenty-four hour period. The degrees of the twenty-seven naksatras when totaled together equal the three hundred and sixty degrees of the entire zodiac. The names of the Indian months originated from the names of the naksatras where purnima (the full moon) always takes place. Of the twenty-seven naksatras only twelve of them have full moons.
The names of the Hindu months with their corresponding Western periods are as follows:

Naksatra

Hindu Month

Western Month

Visakha
Vaisakha
April-May

Jyestha
Jyaistha
May-June

Purva-asadha
Asadha
June-July

Sravana
Sravana
July-August

Purva-bhadrapada
Bhadra
August-September

Asvini
Asvina
September-October

Krttika
Kartika
October-November

Ardha
Agrahayana
November-December

Pusya
Pausa
December-January

Magha
Magha
January-February

Uttara-phalguni
Phalguna

February-March

Citra
Caitra
March-April

Hindu Time Eras

India has many time eras. In general there are two kinds of eras: those named after prominent religious leaders and those named after kings. In addition, there are two annual time periods that mark the beginning of an era: the month of Caitra (March-April) and the month of Karttika (October-November). In the north the custom is to begin each year with Caitra (March-April) and each month with the full moon. But in the south and in Gujarat the years begin with Karttika (October-November) and the months with the new moon. The two most important eras are the Sakabda and the Samvat.
The Sakabda or Salivahana era (AD 78), now used throughout India, is the most important of all. It has been used not only in many Indian inscriptions but also in ancient Sanskrit inscriptions in Indochina and Indonesia. The reformed calendar promulgated by the Indian government from 1957 is reckoned by this era. It is variously alleged to have been founded by the Hindu king Salivahana. To reduce Saka dates to dates AD, 78 must be added for a date within the period ending with the day equivalent to December 31 and 79 for a later date.
The Samvat or Vikrama era (58 BC) is said in the Jain book Kalakacaryakatha to have been founded after a victory of King Vikramaditya over the Sakas. But some scholars credit the Scytho-Parthian ruler Azes with the foundation of this era. It is sometimes called the Malava era because Vikramaditya ruled over the Malava country, but it was not confined to this region, being widespread throughout India. The years reckoned in this era are generally indicated with the word vikramasamvat, or simple samvat. To reduce Vikrama dates to dates AD, 57 must be subtracted from the former for dates before January 1 and 56 for dates after.
The Bengali era is also known as the Laksmana era (AD 1119) said to have been founded by the king Laksmanasena of Bengal and still used throughout Bengal and preserved until modern times. To convert Bengali era to AD, 593 years must be added. The Caitanya era starts from the appearance of Caitanya Mahaprabhu in 1486. To convert the Caitanya era to dates AD add 1486 years to the Caitanya date. The Caitanya dating system is only in use by Caitanya Vaisnavas.

HIndu dates are usually given in the order: month, paksa and tithi, thus Caitra, sukla 7 means the seventh day from the new moon of the month of Caitra.

Rahu and Ketu–The Invisible Planets

Why do Hindus believe that the mythological demons Rahu and Ketu cause solar eclipses?

In Hindu mythology there is a wonderful story that describes how the gods and the demons once formed an alliance to produce a nectar that could give them immortality. This is the story of the churning of the milk-ocean and the descent of Lord Visnu as the Kurma avatara, the divine tortoise. When the nectar that was churned from this ocean was being served to the gods, a demon, disguised as a god, sat between the Sun and the Moon in an attempt to procure the nectar. When he was detected by the Sun and the Moon, Lord Visnu immediately severed his head from his body. Unfortunately, it was not fast enough, for the demon had already tasted a small quantity of the nectar and had become immortal. Ever since, this demon is said to wreak vengeance on the Sun and Moon whenever they come near. The head of this great demon is known as Rahu and his tail is known as Ketu.

In Hindu astrology Rahu and Ketu are known as two invisible planets. They are enemies of the Sun and the Moon, who at certain times of the year (during conjunction or opposition) swallow the Sun or the Moon causing either a solar or a lunar eclipse. In Sanskrit this is known as grahanam or seizing.
What perhaps sounds like a childish story is a powerful metaphor for what actually happens when an eclipse takes place. Rahu and Ketu are the astronomical points in the sky respectively called the north and south lunar nodes.
To the observer on earth, the paths of the sun and the moon appear to be two great circles projected on the celestial sphere (see the diagram). The sun’s path, the solar ecliptic, makes a complete revolution in one year. At the same time, the moon’s circular path is completed in about one month. Every month the moon will overtake the sun which moves more slowly. This is called new moon or in Sanskrit, amavasya. Usually the moon’s path passes above or below the sun’s path and no eclipse occurs. But, periodically the moon overtakes the sun at the place where their paths intersect. This causes the sun or the moon to be hidden from the earth’s view and is thus called a solar or lunar eclipse. These places of intersection are the north and south lunar nodes, or as they are referred to in Hindu mythology, Rahu and Ketu. Therefore, in the symbolic language of mythology, Rahu and Ketu are said to “swallow up” the Sun and the Moon. The ancient Hindu observers of the sky were aware of the cause of the solar and lunar eclipses and so described the process in the language of metaphor.