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Some basic astronomy
a. The movements of the moon and sun
From the perspective of an observer on earth, the sun and moon and stars are moving around the earth every day. If we look at the sky at night, as the hours pass we will see the moon and stars gradually move west across the sky, seeming to move together. But as several nights go by, we may notice that the position of the moon in relation to the stars moves towards the east.
The extent of this relative movement comes to roughly 13 degrees per day. Thus the moon will complete a full rotation through the belt of stars, called the zodiac, in about one month.
A similar situation is true for the sun. Because the stars are too weak to be seen during the day, we cannot see the sun and the stars simultaneously. But if we could, we would see the sun moving gradually against the background of the stars. The sun, however, moves more slowly than the moon — only about 1 degree each day. So we would have to wait longer to observe the difference. For the sun to come back to the same group of stars on the zodiac takes one year.
b. The definitions of solar and lunar months and years
One can define a month and a year in two basic ways: by the movement of the moon and by the movement of the sun.
i. The solar month and year
The Vedic solar month lasts the time it takes for the sun to traverse a complete sign of the zodiac. The zodiac has twelve signs, so each sign covers an angle of 30 degrees. Because the sun moves across the zodiac by about 1 degree each day, to traverse a complete sign takes about 30 days — more exactly, 30.4 days. Twelve such months make one solar year — that is, a little more than 365 days. In other words, a solar year is the time it takes for the sun to start from any group of stars and return to it. Such a year stays synchronized with the seasons.
ii. The lunar month and year
The lunar month and year are slightly more complex. The Vedic calendar defines the lunar month in terms of the phases of the moon. We know that the phases of the moon change. The moon is sometimes full, sometimes half, and sometimes new, depending on how much of the moon we on earth can see lit up by the sun. When the sun and moon are close to one another on the zodiac, the side of the moon illuminated by the sun will mainly have its back to us. So we will see only a sliver, and most of the moon will seem dark. Then again, when the sun and moon are on opposite sides of the zodiac, the side of the moon we see from earth will be fully illuminated, so we will see a full moon. All other positions of the sun and moon result in the other, intermediate lunar phases.
In the Vaisnava calendar a month starts the day after one full moon and continues through the next full moon. This takes about 29.5 days.
Just as 12 solar months make one solar year, 12 lunar months make one lunar year. Since one lunar month takes 29.5 days, 12 such months will take about 12 times that long — that is, 354 days.
This lunar year is 11 days shorter than the 365-day solar year, so although the month synchronizes with the lunar phases, the year does not synchronize with the seasons. Counting by the solar calendar, every solar year the lunar year will begin 11 days earlier. So, to synchronize the lunar year with the seasons, the Vedic calendar adds an extra month about every third year, according to certain rules. In this way the lunar and solar years stay in synch.
The Pancanga, or the Vedic calendar
The Vedic calendar is called Pancanga. The word Pancanga indicates that the calendar consists of five parts, or tells about five elements. These elements are vara (the day of the week), tithi (the lunar day, or phase of the moon), karana (half a tithi), naksatra (the position of the moon in the zodiac), and yoga (a measurement derived from the positions of the sun and moon). For normal use of the calendar, one need not understand all these elements. But some of them are described as follows.
a. Tithi
As we have discussed, the lunar month marks the time from one full moon to the next. The lunar month is divided into 30 parts, called lunar days, or tithis. The tithis are simply the different phases of the moon. Thus the first tithi starts at the moment when the moon is full — that is, when the angle between the moon and the sun is 180 degrees and it continues until the angle has increased 12 degrees. Then, that much less of the moon seems bright to us: the moon is no longer completely full.
Now the second tithi starts, and it continues until the angle between the sun and moon has increased 12 degrees more. Slightly more of the bright side of the moon now has its back to us, and so the moon is even less full.
When 15 such tithis have passed, the angle between the sun and the moon has increased by 180 degrees. This time the bright side of the moon cannot be seen at all, and so we have a new moon. Then 15 more tithis gradually pass, and the moon again becomes full. When 30 tithis have thus passed, the month ends.
The period when the moon wanes, or decreases in size, is called krsna paksa (“the dark fortnight”), and the period when it waxes, or increases, is called sukla paksa or gaura paksa (“the bright fortnight”). The words Krsna and Gaura used here are specific to the Gaudiya Vaisnava tradition.
Some lunar calendars start the month from the 0-degree position — that is, directly after the new moon. Such calendars are called mukhya candra. Other calendars, such as the one used by the Gaudiya Vaisnavas, start directly after the full moon, with the Krsna paksa. Such calendars are called gauna candra.
Except for the new moon and the full moon, the names of the tithis are simply counting words: pratipat, dvitiya, trtiya (first, second, third), etc. These names are the same for the tithis occurring during Krsna paksa (the dark period of the moon) and the gaura paksa (the bright period). The new moon is called amavasya, and the full moon purnima.
| Krsna paksa | Gaura paksa | ||
| Tithi | Name | Tithi | Name |
| 1 | Pratipat | 1 | Pratipat |
| 2 | Dvitiya | 2 | Dvitiya |
| 3 | Trtiya | 3 | Trtiya |
| 4 | Caturthi | 4 | Caturthi |
| 5 | Pancami | 5 | Pancami |
| 6 | Sasti | 6 | Sasti |
| 7 | Saptami | 7 | Saptami |
| 8 | Astami | 8 | Astami |
| 9 | Navami | 9 | Navami |
| 10 | Dasami | 10 | Dasami |
| 11 | Ekadasi | 11 | Ekadasi |
| 12 | Dvadasi | 12 | Dvadasi |
| 13 | Trayodasi | 13 | Trayodasi |
| 14 | Caturdasi | 14 | Caturdasi |
| 15 | Amavasya (new moon) | 15 | Purnima (full moon) |
Because the speed of the moon in relation to that of the sun is not constant but varies, a tithi is not a fixed duration of time. Its length fluctuates between 19 and 26 hours. Therefore, since a lunar tithi does not correspond to the 24-hour solar day, a tithi may start at any time of the day.
There are certain tithis on which the followers of the Vedic culture follow various observances or celebrations. On what day is such a tithi to be observed? The general rule is that one will celebrate a tithi on that day whose sunrise falls within the tithi, though sometimes other rules come into effect.
The Ekadasi tithi is especially important, and special rules determine when to observe Ekadasi. Special rules also sometimes apply for festivals such as Sri Krsna Janmastami.
b. Naksatra
As previously mentioned, in the sky the belt of stars called the zodiac is divided into 12 signs, which cover 30 degrees each. There is also a way of dividing the zodiac into 27 parts, which cover 13-1/3 degrees each. These parts are called naksatras.
While moving over the zodiac, the moon continuously passes through these naksatras one by one. In the Vedic calendar, naksatra simply refers to the naksatra within which the moon is present at sunrise on any particular day.
c. Yoga
Tithis and naksatras can easily be understood in relation to the phenomena in the sky. Tithi is the phase of the moon, and naksatra marks the position of the moon. But yoga is not easily understood in a similar way. The yoga is determined by adding the angle or longitude of the sun and moon, reducing the sum to fit in the circle of 360 degrees (by subtracting 360 degrees if needed), and then dividing the resultant number by 13-1/3 degrees. Like the naksatras, the yogas are also 27 in number.
Reasons to follow a lunar calendar
In the Vaisnava calendar the times for various celebrations are determined by the tithi, sometimes with naksatra and other elements of the calendar taken into account.
Most scholars who have analyzed the old Indian calendar systems, both lunar and solar, have concluded that the lunar system is the more ancient.
The lunar phases are known to influence agriculture, and according to scriptures like Manu-samhita (The Law of Manu) they also influence more subtle aspects of human life.
Traditional and modern methods of calculation
Traditionally the astronomical calculations needed to make a Pancanga were done according to one of the astronomical texts such as Surya Siddhanta. The methods described in Surya Siddhanta are basically quite similar to modern astronomical methods for ascertaining the positions of the planets. The main difference is that Surya Siddhanta has a simpler model. Such a model is needed if the calculations are to be done by hand in a practical way.
The methods of Surya Siddhanta could be used by a skillful person at any time, without the need for modern equipment. All that was needed were some observatory instruments that could be built without high technology. These instruments were used regularly to check that the calculations tallied with observable reality. When a difference appeared after some time, corrections were made to the astronomical constants in the formulas. With this system, fairly good results were obtainable even though the astronomical model was simple. Its accuracy cannot be compared to that obtained by modern methods, but for the purpose of astrology and creation of calendars it sufficed.
This computer program uses formulas that give an accuracy of 1 minute of arc for the longitude of the sun and 2 minutes of arc for the longitude of the moon. When determining ending times of tithis these errors can result in a maximum error of 5 minutes of time. The average error is about 3 minutes. Such an error will report an Ekadasi (the eleventh tithi) on the wrong date roughly once every 20 years.
Some comments on interpreting the Vaisnava calendar
a. Names of years and months
Following Gaudiya Vaisnava tradition, the years are counted from the appearance of Lord Sri Krsna’s incarnation as Lord Sri Caitanya Mahaprabhu. Lord Caitanya is also known as Gaura, so the year is called “Gaurabda,” “the year of Lord Caitanya.” Each month, or “masa,” is known by a name of Visnu. The months, the Sanskrit names by which they are commonly known in India, and their rough equivalents according to the Gregorian calendar are listed as follows:
| 1 | Visnu | Caitra | March-April |
| 2 | Madhusudana | Vaisakha | April-May |
| 3 | Trivikrama | Jyestha | May-June |
| 4 | Vamana | Asadha | June-July |
| 5 | Sridhara | Sravana | July-August |
| 6 | Hrsikesa | Bhadrapada | August-September |
| 7 | Padmanabha | Asvina | September-October |
| 8 | Damodara | Kartika | October-November |
| 9 | Kesava | Margasirsa | November-December |
| 10 | Narayana | Pausa | December-January |
| 11 | Madhava | Magha | January-February |
| 12 | Govinda | Phalguna | February-March |
| 13 | Purusottama | Adhika, or Dvitiya Jyestha | Intercalary month |
b. When to observe Ekadasi
Ekadasi, the eleventh tithi, has special importance. In the scripture Caitanya-caritamrta (Madhya-lila, chapter 24), Lord Caitanya Mahaprabhu instructs Sanatana Gosvami regarding the Vaisnava regulative principles. In text 342 Lord Caitanya says:
“You should recommend the avoidance of mixed [viddha] Ekadasi and the performance of pure Ekadasi. You should also describe the fault in not observing this. One should be very careful as far as these items are concerned. If one is not careful, one will be negligent in executing devotional service.”
As described in the book Hari Bhakti Vilasa, viddha (mixed) Ekadasi takes place when the eleventh tithi starts before sunrise but the tenth tithi still presides at the beginning of brahma muhurta (the auspicious period that starts an hour and a half before sunrise).
On Ekadasi it is traditional to fast. But under certain conditions, called mahadvadasi, one fasts not on the Ekadasi but on the next day, the dvadasi, even though the Ekadasi is suddha, or pure, and not viddha, or mixed. There are eight mahadvadasis.
The calendars produced by this program make it easy to see when to observe Ekadasi. The Ekadasi fast should be observed on the day called suddha (pure) Ekadasi, or alternatively on Mahadvadasi, even if the previous day is called Ekadasi. All this is clarified by the asterisk (*), which indicates a fast, at the right margin of the calendar.
c. “Break fast 05:18 – 09:34” and “Daylight-savings not considered”
To complete the proper observance of Ekadasi, the next morning one should end the fast after the first time given in the calendar and before the second time. The calendar gives these times according to the standard time of the place for which the calendar is made.
During the summer, many locations do not follow standard time, but instead move their clocks an hour ahead (or sometimes more) to make more use of the hours of daylight. So, for example, 5 o’clock in the morning becomes 6 o’clock instead. The Vedic Calendar program does not take such daylight-saving time into account. So for days when your location uses daylight-saving time, you must adjust the times given by the calendar. Generally, this means that when daylight-saving time is in effect you should add an hour to the times given.
d. Double or no tithi
When studying the calendar, you may find that sometimes a tithi is skipped and sometimes one tithi comes on two consecutive days. There is nothing wrong with this. For each day, the calendar just shows which tithi (moon phase) prevails at the time of sunrise. Sometimes a given lunar phase may begin after one sunrise and end before the next, and therefore on the calendar that tithi appears missing. Or sometimes one lunar phase extends throughout two sunrises in a row, and therefore that tithi appears twice.
A person’s birthday is determined by the tithi prevailing at the moment the person was born. Every year thereafter, the day to celebrate as the birthday should be the day whose sunrise occurs during that same tithi. If the tithi prevails on two consecutive sunrises, the sunrise that has the same naksatra as at birth will be the proper day for celebration. If neither sunrise occurs with that naksatra, then the latter of the two days should be chosen. If there is no day whose sunrise occurs during that particular tithi, then the day within which the tithi falls should be chosen as the day of celebration.
Suppose, for example, that a person’s appearance day should be celebrated on dvitiya tithi in the month of Kesava and that for the month of Kesava the calendar lists two dvitiya tithis, one after another. And suppose that the naksatra that prevailed at birth is not present. Then the second dvitiya should be chosen as the day of celebration. If the calendar shows no dvitiya at all, then the appearance day should be celebrated on the day listed as pratipat, because the dvitiya phase of the moon will occur during that day.
e. Sankranti
Sankranti means the time when the sun enters a sign of the zodiac. If you are conversant with astrology, you might wonder why the calendar shows the sun entering the various signs of the zodiac at times different from those given in Western astrology. This is one of the differences between the two kinds of astrology, Western and Vedic. The difference pertains to a certain angle called ayanamsa, which is presently around 23 degrees. The explanation of ayanamsa can be found in books about Vedic astrology.
f. Names for the signs of the zodiac
Here are the Sanskrit names for the signs of the zodiac, alongside their English counterparts.
| SANSKRIT | ENGLISH | |
| 1 | Mesa | Aries |
| 2 | Vrsabha | Taurus |
| 3 | Mithuna | Gemini |
| 4 | Kataka | Cancer |
| 5 | Simha | Leo |
| 6 | Kanya | Virgo |
| 7 | Tula | Libra |
| 8 | Vrscika | Scorpio |
| 9 | Dhanus | Sagittarius |
| 10 | Makara | Capricorn |
| 11 | Kumbha | Aquarius |
| 12 | Mina | Pisces |