Mathomathis would like to present an article on Indic Cosmology and Time Keepers by Kosla Vepa – Indic Studies Foundation. The following article is a continuation from the previous article Indic Cosmology | Kosla Vepa | Equatorial Coordinate System | 102.
The TITHI
According to the Indian calendar or Panchangam, Tithi is a lunar date based on the rotation of the moon around the earth, and is one of the five important aspects of an Indian almanac (Panchangam – Panch means five and anga means parts). Most of the Indian social and religious festivals are celebrated on a date corresponding to the original Tithi. The distance between the Sun and the Moon calculated on a daily basis is called Tithi. The positioning and the movements of both Sun and Moon are different (the Sun is much farther away than the moon , and hence it does not make sense to refer to the distance in terms of Miles are meters but in degrees only. As the space which is in the circle shape – is 360 degrees. So in a month there are 30 days ( or Tithis) that will bring us to the 12 degrees per Tithi (360/30) to calculate the distance between the Sun and the Moon. On the New Moon day – that is Amavasya – the distance between the Sun and Moon is only zero (0) degrees and at that time the Moon will have no light. On the full moon day the distance is 180 degree as both Sun and Moon are on opposite positions. So, that shows when the distance between Sun and Moon is 0 – 12 degrees that is defined as Padyami, and when it is 12-24 degrees that is defined as Vidiya ( 2nd day) and when the distance is 24- 36 degrees that day is defined as Tadiya ( third day). There is another specific thing to be noted: the movements of the Sun are slow while the corresponding movements of the Moon are relatively rapid. If one takes the average motion ( mean motion) of Sun, it is 59.1 minutes( 1 degree is equal to 60 minutes) Where as the Moon’s mean motion is about 790.56. So the difference between the Sun and Moon’s motion is 790.56 – 59.1 = 731.46 that is equal to 12.19 degrees.
Whereas to gain the correct Tithi, one should not take the mean motions – one need to take accurate motion to obtain the right time of Tithi. There are functions to obtain this accurate motion to get the right Tithi. In a month there are 30 Tithis- and on an average each Tithi will run for 23.62 hours. But, in many days, the Tithi usually hovering between 20 hours to 26.40 hours – and with this huge fluctuations, one can not depend upon the mean motions and this fluctuation occurs because of the daily changes in the motion of the Moon. The timing of the performance of a particular aspect of a puja associated with a variety of rites and ceremonies is essential for the proper performance of the puja. Such an injunction was a corollary to the assumptions made in the belief system prevalent during the ancient era. As there are many kinds of writers of Panchanga- there is always a difference from one school of thought to another school of thought and the Tithis tend to get overlapped.
WEEK DAYS ( VAARA)
Vaasara, often abbreviated as vaara in Sanskrit-derived languages, refers to the days of the week, which are possibly of Sumerian/Babylonian origin, and bear striking similarities with the names in many cultures: Following are the Hindi and English analogues in parentheses
- Ravi vāsara (ravi-vaara or Sunday; ravi = sun)
- Soma vāsara (som-vaara or Monday; soma = moon)
- Mangala vāsara (mangal-vaara or Tuesday; mangala = Mars)
- Budha vāsara (budh-vaara or Wednesday; budh = Mercury)
- Guru vāsara (guru-vaara or Bruhaspati-vaara or Thursday; vrihaspati/guru = Jupiter)
- Shukra vāsara (shukra-vaara or Friday; shukra = Venus)
- Shani vāsara (shani-vaara or Saturday; shani = Saturn)
Days of the Week are:
- Sunday – Ravi- vasahara Raviwar, Adi, Aditya
- Monday – Somwar (Chandrawar)
- Tuesday – Mangalwar
- Wednesday – Budhwar, Rauhineya, Saumya
- Thursday – Guruwar, Brihaspati
- Friday – Shukrawar, Bhrigu, Bhargava
- Saturday – Shaniwar
There are many variations of these names in the regional languages, mostly using alternate names of the celestial bodies involved. The astonishing fact of the matter is that the system of dividing the week into 7 days is fairly widespread among all geographies and civilizations, and it is difficult to say when it originated . The Indian Panchangam is really an almanac rather than calendar. It is really analogous to the concept of a Farmers almanac that is widely prevalent in the west. The word calendar is itself of Greek origin. The current calendar “date” based on the Gregorian Calendar that we are so familiar with in our daily life is heliocentric and is based on the rotation of the earth around the sun. It takes the earth approximately 365 ¼ days to complete its rotation around the Sun. The 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, the 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 geocentric and 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 lunar month also varies. On average, the lunar month has about 29 ½ days, the period of the lunar Synodic orbit. 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 of approximately 354 days (29.5 *12 ), thus making it 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 “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 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 given below.
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 “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 the 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 usually begins at sunrise, and the length of lunar day is determined by the time elapsed between the successive sunrises. As per the 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 “V[W]ar”. Just as the English calendar has seven days for a week, the Indian calendar has seven vara’s for a week. Thus, The lunar day, however, varies approximately between 22 to 26 hours based on the angular rotation of moon around the earth in its elliptical orbit. In the Indian calendar, the lunar date is referred as “Tithi”. The basis for the length of a lunar date is geocentric and is defined as the angular distance between the sun and the moon as seen from the earth. As the moon rotates around the earth, the relative 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 that phase 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 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 “ Krishna 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 Krishna 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 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 full moon day. Similarly for the waning fortnight lunar cycle or Wadya (or Krishna) Paksha, tithis begin again with Prathama (first), Dwitiya (second), etc. till we arrive Amavasya or a day before 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 Krishna) occurs on Shravana Vadya Ashtami (eighth lunar day of Vadya Paksha of the lunar month Shrawana).
The angular velocity of moon in its elliptical orbit around the earth varies continuously as it is affected (according to Kepler’s Law) 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 angular change between the moon and the sun as seen from the earth) varies somewhere between 10 to 14 degrees per day. 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 shortened if two Tithis occur in one 24 hour 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 at 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 Vara (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 sunrise in New York city occurs 8:30 AM (EST). Further assume that at 9 AM (EST) on Monday the angular distance between the sun and moon is exactly 12 degrees just following the new moon of the Indian lunar month Karthika. 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 sunrise on that Monday the tithi Dwitiya has not begun. Therefore, the tithi for that Monday for 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 Karthik Shudha Dwitiya.
For the same Monday at 9 AM (EST), it would be 7:30 PM in Mumbai or New Delhi. Thus, Tithi for that Monday for city of New York, Mumbai, and New Delhi is Karthik Shudha Prathama (the first day of Indian lunar month Karthik) while for most of the regions west of Chicago or St. Louis the Tithi for that Monday is Dwitiya. In other words, the Tithi Karthik Shudha Prathama for regions west of Chicago or St. Louis should occur on the preceding day, the Sunday. Karthik Shudha Prathama (the first day of Indian lunar month Karthik) also happens to be the first day after Diwali. Most of the Indians celebrate this as their New Year ’s Day. Indians living in India, Europe, and eastern part of the United States thus should celebrate their New Year on that Monday while regions west of Chicago should celebrate on the preceding day, the Sunday. (Based on description by Jagdish C. Maheshri October 12, 2000 [1] Adhik Mas occurs only when two amavasyas )
The Days of the indian Lunar Synodic Month
SL No Krishna paksa (Dark fortnight) Waning moon Gaura or Shukla paksa (bright fortnight) Lightening moon Deity and properties
1 Pratipata Pratipata The presiding deity of the first lunar day in Brahma and is good for all types of auspicious and religious ceremonies
2 Dvitiya Dvitiya Vidhatr rules this lunar day and is good for the laying of foundations for buildings and other things of a permanent nature.
3 Trtiya Trtiya Visnu is the lord of this day and is good for the cuttings of one's hair and nails and shaving.
4 Caturthi Caturthi Yama is lord of the 4th lunar day, which is good for the destruction of one's enemies, the removal of obstacles, and acts of combat.
5 Pachami Pachami The Moon rules this day, which is favorable for administering medicine, the purging of poisons, and surgery.
6 Shasthi Shasthi Karttikeya presides over this day and is favorable for coronations, meeting new friends, festivities, and enjoyment.
7 Saptami Saptami The 7th lunar day is ruled by Indra; one may begin a journey, buy conveyances, and deal with other such things as a movable nature.
8 Ashtami Ashtami The Vasus rule this day, which is good for taking up arms, building of one's defenses, and fortification.
9 Navami Navami The Serpent rules this day, with is suitable for killing enemies, acts of destruction, and violence.
10 Dashami Dashami The day is ruled by Dharma and is auspicious for acts of virtue, religious functions, spiritual practices, and other pious activities.
11 Ekadasi Ekadasi Rudra rules this day; fasting, devotional activities, and remembrance of the Supreme Lord are very favorable.
12 Dvadashi Dvadashi The Sun rules this day, which is auspicious for religious ceremonies the lighting of the sacred fire, and the performance of one's duties.
13 Trayodashi Trayodashi The day is ruled by Cupid and is good for forming friendships, sensual pleasures, and festivities.
14 Caturdashi Caturdasi Kali rules this day suitable for administering poison and calling of elementals and spirits.
15 Amavasya (new moon) Purnima (full moon) The Vasve-devas rule the New Moon suitable for the propitiation of the Manes and performance of austerities.
The Nakshatra and the Key Role it plays in Vedic Astronomy
This calendar has been modified and elaborated, but because it is based on the stars (Nakshatras) visible to the naked eye, and on the visible Lunar phases, it is more accurate than any others of the past. The actual moments when Lunar months begin, can easily be checked by the regular appearances of Solar eclipses, and the middle moment of a Lunar month — Poornima or full moon — can similarly be verified by the more frequent Lunar eclipses. Hence the Hindu calendar, not requiring special instruments for its rectification, has maintained great accuracy for thousands of years. The oldest calendar is probably the Vedic calendar among the languages referred to as IE languages; at first lunar, later with solar elements added to it. The sister Avesta calendar is similarly first Lunar, but later only Solar. Both these calendars (the oldest in the IE universe) are influenced by the prehistoric calendars of the first and second root races at the North Pole and its surroundings, as they reckon with days and nights lasting six months. It was the impression of knowledgeable Indologists such as William Brennand that the Hindus have been observing and recording the the motion of the moon, the sun and the seven planets along a definite path that circles our sky, now known as the ecliptic, and is marked by a fixed group of stars clustered around this ecliptic. The moon afforded the simplest example.
Indic Cosmology | Indian Nakshatra
| Number | Western Zodiac name | Sidereal | Deity | Sector in deg,min | Meaning |
|---|---|---|---|---|---|
| 1 | Beta Arietis | Aswini (Asvayjau) | Asvinau | 00 00 13 20 | A Horse’s head |
| 2 | 41 Arietis | ApaBharani | Yama | 13 20 26 40 | Yoni or Bhaga |
| 3 | Eta Tauri | Karthika | Agni | 26 40 40 00 | Razor |
| 4 | Alpha Tauri | Rohini | Prajapati | 40 00 53 20 | A wheel carriage |
| 5 | Lamda Orionis | Mrigasira | Soma | 53 20 66 40 | The head of an antelope |
| 6 | Alpha Orionis | Aridra | Rudra | 66 40 80 00 | A gem |
| 7 | Beta Geminorum | Punarvasu | Aditi | 80 00 93 20 | A house |
| 8 | Delta Cancri | Pushya | Brihaspati | 93 20 106 40 | An arrow |
| 9 | Alpha Cancri | Aslesha | Sarpah | 106 40 120 00 | A wheel |
| 10 | Alpha Leonis | Magha | Pitarah | 120 00 133 20 | Another house |
| 11 | Delta Leonis | Purva Phalguni | Aryaman (Bhaga) | 133 20 146 40 | A bedstead |
| 12 | Beta Leonis | Uttara Phalguni | Bhaga (Aryaman) | 146 40 160 00 | Another bed stead |
| 13 | Gamma Virginis | Hasta | Savitar | 160 00 173 20 | A hand |
| 14 | Alpha Virginis(spica) | Chitra | Indra (Tvastr) | 173 20 186 40 | A pearl |
| 15 | PI Hydrae | Swati | Vayu | 186 40 200 00 | A piece of Coral |
| 16 | Beta Librae | Vishaka | Indragni | 200 00 213 20 | A festoon of leaves |
| 17 | Delta Scorpi | Anuradha | Mitra | 213 20 226 40 | An oblation to the Gods |
| 18 | Alpha Scorpi | Jyeshta | Indra (Varuna) | 226 40 240 00 | A rich ear ring |
| 19 | Lamda Scorpi | Moola | Pitarah | 240 00 253 20 | The tailof a fierce lion |
| 20 | Delta Sagittari | Poorvashad | Aapah | 253 20 266 40 | A couch |
| 21 | Delta Sagittari | Uthrashad | Visvedevah | 266 40 280 00 | The tooth of a wanton elephant, near which lies thekernel of the springataca nut |
| 22 | Beta Capricornus | Sravana | Visnu | 280 00 293 20 | The three footed step of vishnu |
| 23 | Alpha DelphiniDelta capricornus | Dhanishta (Sravistha) | Vasavah | 293 20 306 40 | A tabor |
| 24 | Lamda Aquar | Satabhishaj | Varuna | 306 40 320 00 | A circular jewel |
| 25 | Alpha Pegasi | Poorvabhadrapada (prosthapada) | Aja Ekapad | 320 00 333 20 | A two faced image |
| 26 | Alpha Andromeda | Uttrarabhadra | Ahirbudhya | 333 20 346 40 | Another couch |
| 27 | Zeta Piscium | Revathi | Pusan | 346 40 360 00 | A small sort of tabor |
Indic Cosmology | Values of the Lunar Sidereal orbit and the lunar synodic orbit
| Comparisons | Lunar Orbit Sidereal | Lunar Orbit Synodic |
|---|---|---|
| AD 2000.0 | 27.32166156 | 29.53058888 |
| AD 498 | 27.3216638 | 29.530591 |
| Àryabhata | 27.321668 | 29.530582 |
| Paulisa Siddhanta | 27.321673 | 29.530587 |
| Surya Siddhanta | NA | 29.530587946 |
- Kimstughna
- Shakuni
- Chatushpād
- Nāgava
- Bava
- Bālava
- Kaulava
- Taitula
- Garajā
- Vanijā
- Vishti (Bhadrā)
| Rashi (Sura Maasa) [Solar Months] | Ritu (Season) | Gregorian Months | Zodiac |
| Mesha | Vasant (spring) | March/April | Aries |
| Vrushabha | April/May | Taurus | |
| Mithuna | Grishma (summer) | May/June | Gemini |
| Karka | June/July | Cancer | |
| Simha | Varsha (monsoon) | July/August | Leo |
| Kanya | August/Septemeber | Virgo | |
| Tula | Sharada (autumn) | September/October | Libra |
| Vruschika | October/November | Scorpious | |
| Dhanu | Hemant (autumn-winter) | November/December | Sagittarius |
| Makara | December/January | Capricornus | |
| Kumbha | Shishir (Winter-Spring) | January/February | Aquarius |
| Meena | February/March | Pisces |
- Vishkambha
- Prīti
- Āyushmān
- Saubhāgya
- Shobhana
- Atiganda
- Sukarman
- Dhriti
- Shūla
- Ganda
- Vriddhi
- Dhruva
- Vyāghāta
- Harshana
- Vajra
- Siddhi
- Vyatīpāta
- Varigha
- Parigha
- Shiva
- Siddha
- Sādhya
- Shubha
- Shukla
- Brāhma
- Māhendra
- Vaidhriti
| ASTRONOMIC AUTHORITY | Àryabhata (from Clarke and Kay) | Surya Siddanta | 2007 |
| Years in Cycle ,MY | 4,320,000 | 4,320,000 | 4,320,000 |
| Rotations,R | 1,582,237,500 | 1,582,237,828 | |
| Mean Rotations of the earth in a Sidereal year R/KY=1 +DSiYr | 366.2587565 | ||
| Lunar Orbits one MY | 57,753,336 | 57,753,336 | |
| Days in a Sidereal month, DSiM = 1577917500/57753336 = 27.32166848 | |||
| Kaye notes 57,753,339 lunar orbits rather than 57,753,336 per Clarke | |||
| Synodic Months MSyn in a MY | 53,433,336 | 53,433,336 | |
| Days in a synodic month DSynM = 1,577,917,500/53,433,336=29.53058181 days | |||
| Mercury | 17,937,920 | 17,937,060 | |
| Venus | 7,022,388 | 7,022,376 | |
| Mars | 2,296,824 | 2,296,832 | |
| Jupiter | 364,224 | 364,220 | |
| Saturn | 146,564 | 146,568 | |
