Ancient Astronomy During Vedic Era

[Guest]

Here is a novel use of astronomy to decipher the Saraswathi Sindhuseals

[Guest]

posted on IC..

http://www.aip.de/~aniket/Saptarshi%20paper.pdf

[dhu]

Scientists discover 500 BC sky map
P Revathi

Hyderabad: When the carving of the Great Bear constellation on a stone, made around 500 BC at Mudumala village in Mahbubnagar district of Andhra Pradesh were discovered, scientists were suitably astounded.

They began to wonder how ancient Indian astrologers could tell exactly how stars and constellations were grouped without the help of modern devices such as the telescope.

The mystery was unravelled when scientists discovered an ancient sky map in Hyderabad.

The sky map, which is probably the oldest in Asia, was carved out by megalithic Indians with astounding accuracy.

<b>The map represents the seven stars also known as the saptarishi mandal, </b>which have for ages been used to pinpoint the North (for the Pole star, located above the North Pole lies opposite the Ursa Major or the Great Bear).

According to Reader, Department of History, Central University Hyderabad, Dr K P Rao, "The discovery of the sky map indicates that from olden days itself the Indians had adequate knowledge of Astronomical science. In fact they used this knowledge to construct monuments based on the directions denoted by stars and constellations."

According to Historians, this is the only sky map to be unearthed in India, probably even South Asia.

Over ages the stone which has the sky map carved on it, is being protected by the local folk.

Eighty menhirs (standing stones) and several hundred smaller stones surround the map. There is a local folklore, which talks about how these stones are cursed men and cattle.

"With this belief the local people do not even dare to cause any damage to the stones and so the sky map remained intact over ages," says Dr Rao.

A detailed study revealed that the megalithic Indians had good knowledge of solar trajectories and the sky map was used to determine the calendar and the seasons with precise information about sun rise-sun set with exact directions.

This information was expected to be used predominantly for agricultural operations.

[Guest]

This isan important paper from the Tata Institute of Fundamental research on the observations in astronomy in ancient India ,in particular the conjunction called Rohini Shaketa Bheda

http://www.tifr.res.in/~vahia/rsb.pdf

Notethe changesin sea level that are reported here.
<img src='http://kosal.us/Astronomy/sealevel.jpg' border='0' alt='user posted image' />

[Hauma Hamiddha]

The native Andean weather-forecasters and shakadhUmA
I was reading the research by Orlove, Cane and Chiang on the native weather forecasters in mountains of Peru and Bolivia. These farmers forecast the auspicious time for planting potatoes by means of a meteorological/astronomical observation. For a week around the summer solstice they start intently observing the skies. At midnight they climb up to the peaks and start observing the Pleiades a few hours before dawn, noting the apparent brightness and “sizes” of the stars in the cluster. Dimmer the Pleiades the less will be the rain in the area around during winter. So if the forecast is dry then the farmers delay planting their potatoes to reduce losses. The fluctuation in the local rainfall is attributable to El Nino. What the researchers found was that if an El Nino was to happen later in winter then it was accompanied by high cirrus clouds in the earlier summer, which caused a dimming of the Pleiades around the summer solstice. This use of the Pleiades as meteorological predictor is an interesting twist to the more general use, in many ancient traditions, of the Pleiades as a calendrical marker to determine various seasonal phenomena and agricultural activities.

This research immediately led me to understand the basis for an ancient tradition recorded in veda of the atharvA~Ngirasa, the shakadhUma sUktaM, which to date has been poorly understood. In the vulgate AV text (commonly considered shaunaka) the sUktaM occurs in 6.128, while in AV-paippalAda it occurs in AV-P 19.24.16-19. The paippalAda version is also appended at the end of the nakShatra kalpa (AV-parishiShTa-1) under the title: “kR^ittikA-rohiNI-madhye paippalAdA mantrAH”. In both texts there are 4 R^ik-s, though they differ somewhat between them. The kR^ittikA-s (Pleiades) have been known in Vedic tradition to possess watery names, which are individually spelled out in the oblations made during the nakShatreShTi: ambA, dulA, nitatnI, abhrayantI, meghayantI, varShayantI and cupuNIkA. It has long been suspected that these names are indicative of their connection with the arrival of monsoons. But were the Pleiades specifically used in weather prognostication in Hindu tradition? Here is where the evidence from the shakadhUma sUktaM comes in. The word shakadhUma is interpreted as smoke (dhUma) from a dung-pat (shaka) fire. But paradoxically we find the AV tradition remembering shakadhUma as a weather-predictor. The word has been rendered as a human weatherman by modern White translators like Whitney and Bloomfield. This is how the late medieval atharva-vedins also seem to have understood the word in ritual context.

However, an examination of the word shows that the AV tradition originally hardly implied an earthly weatherman in the term shakadhUma. The sUktaM it self opens by explicitly terms shakadhUma as being made the king of the nakShatra-s (AV-vulgate: “shakadhUmaM nakShatrANi yad rAjAnam akurvata |” AV-P: “yad rAjAnaM shakadhUmaM nakShatrANy akR^iNvata |”). The purpose of him being chosen as the king was to ensure prognostication of fair weather (“bhadrAham asmai prAyaChan”). The presence of the paippalAda form of the text in the nakShatra-kalpa also clearly reiterates the close connection of the weather-predictor shakadhUma with the nakShatras. Realizing that a celestial entity is implied, some people have interpreted shakadhUma to mean the moon (as rAjA of the nakShatra-s) or the Milky Way (due to the “smoky” allegory). But this specific terminology does not describe the moon ever, and the Milky Way is never seen as the leader of nakShatras. The original meaning of shakadhUma becomes clear from the R^ik found only in the AV-P version:
“yad Ahush shakadhUmaM mahAnakShatrANAM prathamajaM jyotir agre |
tan nas satIM madhumatIM kR^iNotu rayiM ca sarvavIraM ni yacchatAm ||”
Here shakadhUma is plainly termed the first born of the great nakShatra-s and the leader of the celestial lights. This shows that shakadhUma was a constellation and the first in the list. Now in the AV nakShatra sUktaM (AV-S 19.7.2) the first in the list is kR^ittikA. The AV nakShatra-kalpa also explicitly states that kR^ittikA is the first of the nakShatra-s: “sa nakShatrANAM prathamena pAvakaH kR^ittikAbhir jvalano no .anushAmyatAm”.
So it is likely that the nakShatra implied by shakadhUma was none other than kR^ittikA. This is further confirmed by Charpentier’s finding that in the medieval desha bhASha lexicon of hemachandra-sUrI (the deshI-nAma-mAlA) he gives dhUma as a synonym for kR^ittikA: dhUmad-dhaya-mahisIo kR^ittikAH | DN-5.63

This leads to one other reference to shakadhUma which is found in the great brahmodaya hymn RV 1.164:
“shaka-mayaM dhUmam ArAd apashyaM viShUvatA para enAvareNa |
ukShANaM pR^ishnim apachanta vIrAs tAni dharmANi prathamAny Asan ||”

Based on its deployment in the pravargya ritual some have commented that the shaka-dhUma here refers to the smoke from the fire on which the mahAvIra pot is being fumigated. This external interpretation is of course for the un-enlightened, for the rahasya-s are concealed beneath the ritual actions described in the mantra. That is exactly what this whole sUktaM is about- astronomical rahasya-s. This becomes very clear from use of a technical astronomical term – viShUvat. In Hindu tradition viShUvat meant equinox [Footnote 1] and in this context clearly means the vernal equinox which formed the middle day of the yearly sattra. So the R^ik means: “From far I saw the shaka-dhUma at the equinoctial point further off from this lower one. The heroes cooked the speckled bullock; these were the first stations.” Thus, the constellation at the vernal equinox (viShUvAn) was being described as shakdhUma. The lower one, the speckled bullock, the first (previous stations) appear to stand for Taurus. Taurus being the prior station stands for where the equinox lay prior to shakadhUma which is currently being described as being at the vishuvAn. Here too shakadhUma implies the Pleiades. This would also suggest that the brahmodaya belongs to the same period as the core AV composition during which the Pleiades lay at the vernal equinox. Not surprisingly it also occurs in the AV-S as sUktaM 19.10
Finally it leads to the issue why the name shaka-dhUma for the Pleiades?
In the AV context the term shaka-dhUma is specifically applied in the context of predicting good weather. With high cirrus clouds it is quite likely that the Pleiades appeared as a smoky patch in the sky, which was then used for weather prognostication. Under this interpretation the AV shakadhUma tradition is likely to be the earliest surviving record of weather prognostication based on the appearance of the Pleiades. Unfortunately, the original AV tradition is completely dead, hence only experimental verification can test the effectiveness of the method.

While the original AV tradition does not survive, we know from the much later Hindu meteorological traditions recorded in the kR^iShi parAshara that such knowledge did survive in different forms. For example, the KP23 gives a crude formula to determine the nature of the El Nino effects. KP24-25 describes clouds associated with the cycle and mentions the puShkara (cirrus) clouds that appear to prognosticate droughts. KP33 indicates that the predictions were refined using wind-vanes to measure wind direction/speed and predict rain several months later.

Footnote 1: In his kArika on Ishvara-pratyabhij~nA the Kashmirian tantric utpala-deva makes the following statement:
prANa-apAna-mayaH prANaH pratyekaM sUpta-jAgratoH |
tach-Ched-AtmA samAna-akhyaH sauShupta viShuvatsv-iva ||
The metabolism in both the sleeping and waking states is comprised of prANa and apAna processes. Both are suspended in the deep sleep state when the samAna process functions, like what happens on the equinox.
Here the word viShuvan (equinox) is used metaphorically to explain that state of equality or balance when the prANa and apAna are suspended in the deep sleep state.
Report on Orlove, Cane and Chiang’ work:
http://earthobservatory.nasa.gov/Study/S...oudsCrops/

[Guest]

Separating Chaff and Grain
by <i>Sreenadh OG</i>

[Guest]

My ideas on the development of astronomy in India through the millennia are slowly taking shape. ' Clearly the words of William Brennand (Hindu astronomy are apropos here.

Upon the antiquity of that (Hindu Astronomy ) system it may be remarked, that no one can carefully study the information collected by various investigators and translators of Hindu works relating to Astronomy, without coming to the conclusion that . long before the period whe Grecian learning founded the basis of knowledge and civilization in the West, India had its own store of erudition. Master minds, in those primitive ages, thought out the problems presented by the ever recurring phenomena of the heavens, and gave birth to the ideas which were afterwards formed into a settled system for the use and benefit of succeeding Astronomers, mathematicicans and Scholiasts, as well as for the guidance of votaries of religion .
No system, no theory, no formula concerning those phenomena could possibly have spruing suddenly into existence into existence, at the call or upon the dictation of a single genius. Far rather , is it to be supposed that little by little, and after many arduous labors of numerous minds, and many consequent periods passed in the investigation of isolated phenomena, a system could be expected to be formed into a general science concerning them

He belongs to the very small group of English indologists and mathematicians who felt that tjhe astronomical traiditon of indi awas very ancient and tht it ook severl ahundreds of years to make the observations necessary to achieve the precision that the Indians did in the measurement of varous astronomical constants such as the sidereal year and the sidereal month. Le me recaop sime defintions here before we go on.


Hindu Cosmology & the Celestial Timekeepers Introduction
In order to understand the Indic approach to history, one must understand the cosmology and the calendar of the Hindu. The calendar and the cosmos have always played a large part in the consciousness or weltanschuung of the Hindu and he spent a large portion of his observational powers in deciphering the universe around him. In this he was not alone, as we know now that other ancient civilizations, such as the Babylonian, the Egyptian and the Chinese had similar interests and a curiosity about the heavens. But the answers the Indic came up with were quite prescient for his time and the resulting numbers were far more accurate than the European world realized or knew, even millennia after the Indic discovered these periodicities. The extraordinary allergy that the Occidentals, with a few notable exceptions, have exhibited to the study of the Indic mathematical tradition, and when they have done so, the vehemence with which they have denied the autochthonous origin of the Indic intellectual traditions, is astonishing to say the least. The consistency with which the Occidental denied the Indic contributions is exemplified in the writings of various Indologists such as Whitney , Bentley , Moriz Winternitz Albrecht Weber , W W Rouse Ball, G R Kaye, Thibaut and continues on till today in the works of David Pingree . There were exceptions such as Brennand, Playfair, Colebrooke.
John Playfair













Colebrooke









Sir William Jones



Albrecht Weber



Winternitz



The resulting illiteracy on the part of the western scholar on matters pertaining to India was lethal to the understanding of their own history and leaves Occidental historians, the task of explaining why there was no progress in Europe between the time of the Greek contribution to the mathematical sciences and the flowering of the renaissance resulting in the Keplerian paradigm shift. We are compelled to remark that the sudden explosion of knowledge that took place during the renaissance, occurred shortly after the Jesuits sent 70 scholars to Malabar in the 1500’s. The conventional wisdom in the West was that they were sent to teach the Indics the finer points of the occidental civilization. In reality it turns out, they were sent to learn a whole host of topics such as navigation, mathematical techniques including trigonometry, and the Indian approach to calendrical astronomy. In short the Jesuits embarked on a systematic study of the Indic episteme, since it was obvious that the Indics had made considerable advances, which the Jesuits were quick to realize were far advance of their own that . We are in the process of chronicling the study of those individuals who in turn studied India or studied subjects in which the Indics had great proficiency, beginning with ancient Babylon to the British , to understand the role that India and the Indic episteme played in the renaissance of Europe
We view the study of history and philosophy of science as central to the understanding of any civilization and its ethos. And hence we make no apology for the emphasis on science, and especially on Astronomy in our study of history.
The Ancient Vedics seemed to have an obsession for precision as well as a fascination for large numbers. They also subscribed to the notion that the planet earth and the solar system were of immense antiquity without a beginning, in contrast to the creationist theories propounded by many in the west till recently. A combination such as this makes an excellent prerequisite for time keeping and for devising a useful and practical calendar. So, they turned to the sky and began to decipher the meaning behind the various cycles they observed. Let us see how they went about developing a calendar that would convey a lot of information merely by knowing the day of the month, after constant observation of the sky both during the day and the night over centuries. The result was a highly efficient and accurate calendar. The added bonus of such a system is the usefulness of the recordings of ancient astronomy to decipher the age at which various events took place.
The basic information they used for purposes of time keeping were the motions of the sun and the moon relative to the earth. So far nothing unusual, as did all the other ancients. The cycles they used apart from the day, the week, the fortnight, and the month are shown in Table 1.
Table I
1 60 year Jovian cycle/ 360 year ‘divine cycle
2 2700 year cycle of the Sapta Rishi or the Ursa Major
3 26000 year cycle of the asterisms called the Great Year or the precession cycle
4 432,000 year cycle called a yuga (= duration of Kaliyuga)
5 4,320,000 year cycle known as the Maha Yuga
6 Kalpa, the cycle consisting of 4.32*10**9 years

But first we give a brief history of Indic astronomy, to put the astronomical discoveries in the proper context within the larger canvas of Indic history. Contrary to the conventional wisdom of occidental versions of the Indic narrative, India had a very strong and consistent tradition of scholarship in the so called exact sciences of antiquity (as Neugebauer called them) such as astronomy and mathematics. The list of famous astronomers and mathematicians is staggering in quantity, in the quality of the contributions, as well as the time span over which it occurred. We list in Table 2 significant contributers

Let us establish the coordinate systems first. Everyday the celestial sphere appears to turn as the earth rotates, causing the daily rising and setting of the sun, stars and other celestial objects. (vide Figure 1)



Figure 2 The celestial sphere showing the ecliptic and its inclination to the celestial equator
ecliptic क्रांतिवृत (Kranthivruth )
(ēklĬp´tĬk, Ĭ-) , the great circle on the celestial sphere that lies in the plane of the earth's orbit (called the plane of the ecliptic). Because of the earth's yearly revolution around the sun, the sun appears to move in an annual journey through the heavens with the ecliptic as its path. The ecliptic is the principal axis in the ecliptic coordinate system . The two points at which the ecliptic crosses the celestial equator are the equinoxes. The obliquity of the ecliptic is the inclination of the plane of the ecliptic to the plane of the celestial equator, an angle of about 23 1/2 °. The constellations through which the ecliptic passes are the constellations of the zodiac .

Figure 3 The Ptolemaic Armillary sphere,
The Armillary sphere was also the model used by the Indics, even though Aryabhata was aware that the earth was spinning on its axis and that it was a heliocentric system where the earth was merely a planet. Even today, we use a coordinate system that is geocentric while observing the planets and the rest of the solar system, simply because that is the easiest way to study the sky,
equinox वसंत संपत (Vasanth Sampat) Vernal equinox
(ē´kwĬnŏks) , either of two points on the celestial sphere where the ecliptic and the celestial equator intersect. The vernal equinox, also known as “the first point of Aries,” is the point at which the sun appears to cross the celestial equator from south to north. This occurs about Mar. 21, marking the beginning of spring in the Northern Hemisphere. At the autumnal equinox, about Sept. 23, the sun again appears to cross the celestial equator, this time from north to south; this marks the beginning of autumn in the Northern Hemisphere. On the date of either equinox, night and day are of equal length (12 hours each) in all parts of the world; the word equinox is often used to refer to either of these dates. The equinoxes are not fixed points on the celestial sphere but move westward along the ecliptic, passing through all the
constellations of the zodiac in 26,000 years. This motion is called the precession of the equinoxes . The vernal equinox is a reference point in the equatorial coordinate system
Equatorial coordinate system
The most commonly used astronomical coordinate system for indicating the positions of stars or other celestial objects on the celestial sphere is the Equatorial coordinate system . The celestial sphere is an imaginary sphere with the observer at its center. It represents the entire sky; all celestial objects other than the earth are imagined as being located on its inside surface. If the earth's axis is extended, the points where it intersects the celestial sphere are called the celestial poles; the north celestial pole is directly above the earth's North Pole, and the south celestial pole directly above the earth's South Pole. The great circle on the celestial sphere halfway between the celestial poles is called the celestial equator; it can be thought of as the earth's equator projected onto the celestial sphere. It divides the celestial sphere into the northern and southern skies. An important reference point on the celestial equator is the vernal equinox , the point at which the sun crosses the celestial equator in March. To designate the position of a star, the astronomer considers an imaginary great circle passing through the celestial poles and through the star in question. This is the star's hour circle , analogous to a meridian of longitude on earth. The astronomer then measures the angle between the vernal equinox and the point where the hour circle intersects the celestial equator. This angle is called the star's right ascension and is measured in hours, minutes, and seconds rather than in the more familiar degrees, minutes, and seconds. (There are 360 degrees or 24 hours in a full circle.) The right ascension is always measured eastward from the vernal equinox. Next the observer measures along the star's hour circle the angle between the celestial equator and the position of the star. This angle is called the declination of the star and is measured in degrees, minutes, and seconds north or south of the celestial equator, analogous to latitude on the earth. Right ascension and declination together determine the location of a star on the celestial sphere. The right ascensions and declinations of many stars are listed in various reference tables published for astronomers and navigators. Because a star's position may change slightly (see proper motion and precession of the equinoxes ), such tables must be revised at regular intervals. By definition, the vernal equinox is located at right ascension 0 h and declination 0°.
Another useful reference point is the sigma point, the point where the observer's celestial meridian intersects the celestial equator. The right ascension of the sigma point is equal to the observer's local sidereal time . The angular distance from the sigma point to a star's hour circle is called its hour angle ; it is equal to the star's right ascension minus the local sidereal time. Because the vernal equinox is not always visible in the night sky (especially in the spring), whereas the sigma point is always visible, the hour angle is used in actually locating a body in the sky.

The Indian calendrical system is based on sidereal measurements. In order to understand the system we need to review some definitions of the year, month and the day.
The Year
A solar year and a sidereal year both refer to the amount of time it takes Earth to revolve about the Sun. The difference between the two measures is in the reference point for one revolution. The Latin root of sidereal is sidereus, “starry,” which itself comes from sides, “star, instellation.” The Latin root of solar is solis, “sun.” Thus, the difference between a solar year and a sidereal year is the difference in time between one complete revolution of Earth relative to the Sun, and one complete revolution of earth relative to the constellations respectively.
A tropical year (also known as a solar year) is the length of time the Sun, as seen from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere) relative to the equinoxes and solstices, or the time interval needed for the mean tropical longitude of the Sun to increase by 2π (360 sexagesimal degrees, a complete turn).
The length of time depends on the starting point on the ecliptic. Starting from the (northern) vernal equinox, one of the four cardinal points along the ecliptic, yields the vernal equinox year; averaging over all starting points on the ecliptic yields the mean
tropical year.
On the Earth, the tropical year is shorter than a sidereal year. This diference was, in AD 1900,
20.400 min, and in AD 2000, 20.409 minutes, and seems to slow the Sun from
south to north and back. The word "tropical" comes from the Greek tropos meaning
"turn". The tropics of Cancer and Capricorn mark the extreme north and south latitudes
where the Sun can appear directly overhead.
The position of the Sun can be measured by the variation from day to day of the length
of the shadow at noon of a gnomon (a vertical pillar or stick). This is the most "natural"way to measure the year in the sense that the variations of insolation drive the seasons.
The sidereal year is the time taken for the Sun to return to the same position with respect to the stars of the celestial sphere. It is the orbital period of Earth, equal to365.25636042 mean solar days (31,558,149.540 seconds), that is 366.25636042 earth rotations or sidereal days. (A true cycle will always compare two objects that differ mathematically by exactly 1). The sidereal year is 20 minutes and 24 seconds longer than the tropical year.
The Sun and the stars cannot be seen at the same time; if one looks every dawn at the eastern sky, the last stars seen appearing are not always the same. In a week or two an upward shift can be noted. As an example, in July in the Northern Hemisphere, Orion cannot be seen in the dawn sky, but in August it becomes visible. In a year, all the constellations rotate through the entire sky.
If one looks regularly at the sky before dawn, this motion is much more noticeable and easier to measure than the north/south shift of the sunrise point in the horizon, which defines the tropical year on which the Gregorian calendar is based. This is the reason many cultures started their year on the first day a particular special star, (Sirius, for instance), could be seen in the East at dawn. In Hesiod's Works and Days, the times of the year for sowing, harvest, and so on are given by reference to the first visibility of stars.
Up to the time of Hipparchus, at least in Europe, the years measured by the stars were thought to be exactly as long as the tropical years. Even then, in fact until the16th century they had no accurate sidereal measurements. In fact, sidereal years are very slightly longer than tropical years. The difference is caused by the precession of the equinoxes. One sidereal year is roughly equal to 1 + 1/26000 or 1.000039 tropical years,
But until 1540 CE, when the Society of Jesus sent a whole slew of Jesuits trained to absorb such knowledge, in order that they may learn the science of the calendar and of navigation from the Namboodri Brahmanas of Kerala, there was a lack of knowledge of subjects like navigation. Prior to this date the Portuguese who were the most advanced in these matters, only sailed during the night, when they had the visible stars to guide them. An average voyage to India took them 2 years from Lisbon. With the knowledge so gained they fixed the Gregorian calendar which was always error prone.
Julian Year - In astronomy, a Julian year (symbol: a) is a unit of measurement of time defined as exactly 365.25 days of 86,400 SI seconds each, totaling 31,557,600 seconds. That is the average length of the year in the Julian calendar used in Western societies in previous centuries, and for which the unit is named. Nevertheless, because a Julian year measures duration rather than designates date, the Julian year does not correspond to years in the Julian calendar or any other calendar. Nor does it correspond to the many other ways of defining a year .
Like most Asian calendars Indian calendars do not employ solely the solar year and day (i. e. tropical year and solar day) but the sidereal year, and the Synodic month (29.5306 days). Thus, the calendrical year based on the sidereal year is defined as the time between two successive passes of the sun through a certain star’s circle of declination. Lunar days and sidereal months are also used, and in certain lunisolar calendars lunar year and lunar month are taken into account, too.
The Astronomical knowledge of Ancient India was written down in scientific treatises, called Siddhantas. In them, values for the lengths of months and years were given representing the latest knowledge at the time the Siddhanta was written. The values range from 365.258681 days in the Âryabhatiya to 365.258756 days in the Surya Siddhanta and are all too long compared with the modern sidereal year length of 365.25636 days. Nevertheless they are still in use in Indian calendars today.
The Month
Lunar or Synodic Month - The month is a unit of time, used with calendars, which is approximately as long as some natural period related to the motion of the Moon. The traditional concept arose with the cycle of moon phases; such months (lunations) are synodic months and last approximately 29.53 days. From excavated tally sticks,researchers have deduced that people counted days in relation to the Moon's phases as early as the Paleolithic age. Synodic months are still the basis of many calendars today.
This longer period is called the synodic month from the Greek syn hodô (σὺν ὁδῴ), meaning "with the way [of the sun]". Because of the perturbations of the orbits of the earth and Moon, the actual time between lunations may range from about 29.27 to about 29.83 days. The long-term average duration is 29.530588 days (29 d 12 h 44 min 2.8 s). The synodic month is used in the Metonic cycle.
Sidereal Month - The period of the Moon's orbit as defined with respect to the celestial sphere is known as a sidereal month because it is the time it takes the Moon to return to a given position among the stars (Latin: sidus): 27.321661 days (27 d 7 h 43 min 11.5 s). This type of month has been observed among cultures in the Middle East, India, and China in the following way: they divided the sky into 27 or 28 lunar mansions, defined by asterisms (apparent groups of stars), one for each day of the sidereal month. The sidereal month is thus, about two day shorter (27.3217) than the Synodic month.
Like most Asian calendars Indian calendars do not employ the solar year and day (i. e. tropical year and solar day) but the sidereal year, and the Synodic month(29.5306 days). Thus, the calendric year based on the sidereal year is defined as the time between two successive passes of the sun through a certain star's circle of declination. Lunar days and sidereal months are also used, and in certain lunisolar calendars lunar year and lunar month are taken into account, too.
Astronomical knowledge of Ancient India was written down in scientific treatises, called Siddhantas. In them, values for the lengths of months and years were given representing the latest knowledge at the time the Siddhanta was written. The values range from 365.258681 days in the Âryabhatiya to 365.258756 days in the Surya Siddhanta and are all too long compared with the modern sidereal year length of 365.25636 days. Nevertheless they are still in use for Indian calendars today.

The names of the months are as follows

Rasi Approximate
nakshatra on purnima Lunar month name Solar month name Assamese version Tamil version Punjabi version [20] Mesha Chitra Chaitra Vaisakha Bahag Chittarai Vaisakh Vrshava Visakha Vaisakha Jyaistha Jeth Vaikasi Jeth Mithuna Jyestha Jaishta Aashaadha Ahar Aani Harh Karkata (Purva & Uttara) Aashaadha Aashaadha Sraavana Saon Aadi Sawan Simha Sravana Sraavana Bhaadrapada Bhad Aavani Bhadon Kanya (Purva & Uttara) Bhaadrapada Bhaadrapada Asvayuja (Aasvina) Ahin Purattaasi Asu Tula Asvini Asvayuja (Aasvina) Kaarthika Kati Arppisi Katik Vrischika Krittika Kaarthika Maarghasira Aghon Karthigai Maghar Dhanus Mrugasira Maarghasira Pausa (Pushyam) Puha Maargali Poh Makara Pushyami Pausa (Pushyam) Maagha Magh Thaai Magh Kumbha Maagha Maagha Phalguna Phagun Maasi Phagun Mina (Uttara and Purva) Phalguni Phalguna Chaitra Chait Panguni Chet

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Saur Maas
(solar months) Ritu
(season) Gregorian
months Zodiac
Devanagari
Mesh Vasant
(spring) March/April Aries
मेष
Vrushabh April/May Taurus
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Mithun Grishma
(summer) May/June Gemini

Kark June/July Cancer

Simha Varsha
(monsoon) July/Aug Leo

Kanya Aug/Sept Virgo

Tula Sharad
(autumn) Sept/Oct Libra

Vrushchik Oct/Nov Scorpius

Dhanu Hemant
(autumn-winter) Nov/Dec. Sagittarius

Makar Dec/Jan Capricornus

Kumbha Shishir
(Winter-Spring) Jan/Feb Aquarius

Meen Feb/Mar Pisces

MONTHS OF THE LUNISOLAR CALENDAR
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According to the Indian calendar or Panchanga, 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 (Panchanga – 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 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:
Chaitra Vaishakh Jeshta Ashadh Shrawan(Sawan) Bhadrapad(Bhado) Ashwin Kartik Margshirsh Paush Magha Falgoon (Fagan)
As mentioned earlier, to account for the difference between the solar and lunar year an extra lunar month occurs about every 2 ½ years as “Adhik Mas”.[1][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 “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 “War”. Just as the English calendar has seven days for a week, the Indian calendar has seven wars 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 Krushna) 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 Shrawan Wadya Ashtami (eighth lunar day of Wadya Paksha of the lunar month Shrawan).
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 sorteneded 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 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 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 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 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 (no

Sl.No Krsna paksa (dark fortnight) Waning moon Gaura or shukla paksa (bright fortnight) Lightening moon Deity and properties
1 Pratipat Pratipat 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 Pancami Pancami The Moon rules this day, which is favourable for administering medicine, the purging of poisons, and surgery.
6 Sasti Sasti Karttikeya presides over this day and is favourable 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 Astami Astami 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 Dasami Dasami 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 favourable.
12 Dvadasi Dvadasi 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 Trayodasi Trayodasi The day is ruled by Cupid and is good for forming friendships, sensual pleasures, and festivities.
14 Caturdasi 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 basis of the Hindu calendar calculation is Vedic[2]. 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.
For untold ages or yugas, the Hindus have observed the motion of the moon, the sun and the seven planets along a definite path that circles our sky and is marked by fixed clusters of stars. The moon afforded the simplest example. These early astronomers observed that the moon, moving among these fixed star constellations which they called Nakshatras, returned to the same Nakshatra in 27.32166 days, the exact quantity determined by Aryabhatta, thus completing one Nakshatra month. They found it convenient to divide these groups of stars into 27 almost equal sections, or the 27 Nakshatras. By this method of reckoning, instead of giving the date of a month, as Western calendars do, the Hindus gave the name of the Nakshatra in which the moon was to be seen. (The moon is in each of these Nakshatras for approximately one day plus eighteen minutes.)
This scheme fitted nicely with the sun's cycle, for the Hindus noted that the sun traversed the same circle through the sky, but that it returned to its starting place only after 365.258756481 days, or what we call a Solar Sidereal Year. (Modern figures based on this Hindu figure quote 365.2596296 days -- a distinction without a difference, for ordinary purposes.) Now, having already divided the month into the 27 Nakshatras for the convenience of reckoning the moon's voyage through the heavens, what more natural than that these same Nakshatras should serve for the study of the Sun's course? Being in a circle of 360 degrees, each Nakshatra takes up 13 1/3 degrees of that circle. The Sun, moving about 1 degree in a day, is seen for 13 1/3 days in each Nakshatra. The system of reckoning according to the moon Nakshatras is current today that of the sun's being uncommon.
During the course of one day, the earth has moved a short distance along its orbit around the sun, and so must rotate a small extra angular distance before the sun reaches its highest point. The stars, however, are so far away that the earth's movement along its orbit makes a generally negligible difference to their apparent direction (see, however parallax), and so they return to their highest point in slightly less than 24 hours. A mean sidereal day is about 23h 56m in length. Due to variations in the rotation rate of the Earth, however, the rate of an ideal sidereal clock deviates from any simple multiple of a civil clock. The actual period of the Moon's orbit as measured in a fixed frame of reference is known as a Sidereal month, because it is the time it takes the Moon to return to the same position on the celestial sphere among the fixed stars (Latin: sidus): 27.321 661 days (27 d 7 h 43 min 11.5 s) or about 27 ⅓ days. This type of monthhas appeared among cultures in the Middle East, India, and China in the following way: they divided the sky in 27 or 28 lunar mansions or Nakshatras, characterized by asterisms (apparent groups of stars), one for each day that the Moon follows its track among the stars.
In brief, then, the earliest method, the Vedic, of counting, was to name the moon through the various Nakshatras -- the circle or cycle repeating itself each Sidereal-Star-Month. Later the sun's place in the same Nakshatras was noted, the year ending when the Sun returned to the same Nakshatra. Then came the noting of the Solar and Lunar eclipses, and the observance of the New and Full Moons divided the month into the two phases of waxing and waning Moon, the month beginning at the moment of New Moon. This is how the Hindus reckon today, the month taking its name from the Nakshatra in which the Full Moon is seen each month. The Full Moon being exactly opposite the Sun, the Solar nakshatra bears the same name as the Lunar month six months ahead, while each Lunar month bears the same name as the 14th Solar Nakshatra ahead.
The Western student faced with these unfamiliar calculations may echo the old Persian proverb, "Why count big numbers and small fractions, when they are all amassed in 1?" But the Hindu looks on these figures from another point of view -- he lives with them, and among them, and by them, much of the time. Consider a Sanskrit sloka (verse) about the Savati or pearl nakshatra, which marks the new season after the monsoon is over. The sloka says, "If in the Swati a rain drop falls into the sea, that drop becomes a pearl." This may sound foolish, for the peasant, though he live in the depth of the interior of India, knows that pearls come from the sea -- even if he does not necessarily understand that these pearls grow inside the oyster. He does know, however, that if it rains at this period of the year, his crops will yield great wealth. And the pearl is synonymous with wealth among people who, if they have any money, invest it in jewelry, especially gold and pearls, rather than in the banks. (Poetically, rice, their staple food).
To summarize, the earth revolves around the Sun once in 365 days 5 hours 48 minutes and 46 seconds. Considered from the earth, the Sun appears to complete one round of the ecliptic during this period. This is the Tropical year. In the span of a tropical year, the earth regains its original angular position with the Sun. It is also called the Year of seasons since the occurrence, and timing, of seasons depends on the rotation of the earth around the sun. If, for example, we consider the revolution of the Sun around the earth from one vernal equinox (around 21st March, when the day and night all over the globe are equal) to the next vernal equinox, it takes one tropical year to do so.
However, if at the end of a tropical year from one vernal equinox to the next, we consider the position of the earth with reference to a fixed star of the zodiac, the earth appears to lie some
50.26 seconds of celestial longitude to the west of its original position. In order for the earth to attain the same position with respect to a fixed star after one revolution, it takes a time span of 365 days 6 hours 9 minutes and some 9.5 seconds. This duration of time is called a sidereal year .The sidereal year is just over 20 minutes longer than the tropical year; this time difference is equivalent to 50.26 seconds of celestial longitude.
Each year, the Vernal equinox will fall short by 50.26 seconds along the zodiac reckoned along the fixed stars. This continuous receding of the Vernal equinox along the zodiac is termed the Precession of the Equinoxes and it takes about 25776 years to make one complete revolution of the precessional motion of the earth’s axis. Hipparchus regarded as the discoverer of the precession of the equinoxes in the west gave us either 28,000 or 28,173 years for one revolution.. Another figure given is 25,920 years for the precession cycle, These figures indicate that the mean value of 27,000 years given in the Vedic scriptures is reasonable. The precession of the equinoxes has proved to be very useful for dating certain events in Vedic and Post Vedic times.
There are only a few methods, by which we can determine the age of an event in the absence of radiocarbon dating which is not as precise as the astronomical clocks,
Use the Precession of the equinoxes to determine the Nakshatra in which the Vernal equinox occurs in a particular Nakshatra. If, we recall there are 27 Nakshatras, it follows that the vernal equinox occurs in a different Nakshatra, once every 1000 years.
Use the statements made in the texts to check for internal consistency. If for example Aryabhatta uses a place value system, the zero must have been in fairly wide use by then. If further he uses classical sanskrit (codified by Panini then he must have lived after Panini.

9 degrees to either side of the Ecliptic is a belt of the Heavens known as the Zodiac. (Dante called it the Oblique Line that beareth all planets).The first 30 degrees of the Zodiac constitute the sign of Aries.,the next 30 degrees Taurus and so on. The Zodiac counted from the first degree of Aries to the 360th degree of Pisces is called the Tropical Zodiac. These 12 signs are the limbs of the Cosmic Man or Time Eternal (Kalapurusha - The Almighty Self as Time). Aries is His head, Taurus His face, Gemini His neck, Cancer His heart, Leo the place beneath, Virgo His belly, Libra His generative organs, Scorpio the place beneath, Sagittarius His upper thigh, Capricorn his lower thigh, Aquarius His leg and Pisces His feet!

Western Zodiac name Indian Nakshatras Zodiac) (Sidereal Diety Sector in deg,min deg,min
1. Beta Arietis Aswini (Asvayjau) Asvinau 00 00 13 20
2. 41 Arietis ApaBharani Yama 13 20 26 40
3. Eta Tauri Karthika Agni 26 40 40 00
4. Alpha Tauri Rohini Prajapati 40 00 53 20
5. Lamda Orionis Mrigasira Soma 53 20 66 40
6. Alpha Orionis Aridra Rudra 66 40 80 00
7. Beta Geminorum Punarvasu Aditi 80 00 93 20
8. Delta Cancri Pushya Brihaspati 93 20 106 40
9. Alpha Cancri Aslesha Sarpah 106 40 120 00
10. Alpha Leonis Magha Pitarah 120 00 133 20
11. Delta Leonis Purva Phalguni Aryaman (Bhaga) 133 20 146 40
12. Beta Leonis Uttara Bhaga (Aryaman) 146 40 160 00
13. Gamma Virginis Hasta Savitar 160 00 173 20
14. Alpha Virginis(spica) Chitra Indra (Tvastr) 173 20 186 40
15. PI Hydrae Svati Vayu 186 40 200 00
16. Beta Librae Vishaka Indragni 200 00 213 20
17. Delta Scorpi Anuradha Mitra 213 20 226 40
18. Alpha Scorpi Jyeshta Indra (Varuna) 226 40 240 00
19. Lamda Scorpi Moola Pitarah 240 00 253 20
20. Delta Sagittari Poorvashad Aapah 253 20 266 40
21. Delta Sagittari Uthrashad Visvedevah 266 40 280 00
22. Beta Capricornus Sravana Visnu 280 00 293 20
23. Alpha DelphiniDelta capricornus Dhanishta (Sravistha) Vasavah 293 20 306 40
24. Lamda Aquar Satabhishaj Varuna 306 40 320 00
25. Alpha Pegasi Poorvabhadra (prosthapada) Aja Ekapad 320 00 333 20
26. Alpha Andromeda Uttrarabhadra (Uttara Ahirbudhya 333 20 346 40
27. Zeta Piscium Revathi Pusan 346 40 360 00

Each Nakshatra is associated with a deity, and that the deities associated with tha Nakshatra are mentioned in the Riv Veda Samhita is due to the research of Narahari Achar130. The antiquity of the naksatra system becomes clear when it is recognized that all the deity names occur in RV 5.51 (this insight is due to Narahari Achar21). This hymn by Svasty¯atreya ¯ Atreya lists the deity names as: A´svin, Bhaga, Aditi, P¯usan, V¯ayu, Soma, Brhaspati, SARVAGAN. AH.Vi´sve Devah. Agni, Rudra, Mitra, Varun.a, Indr¯agni. The sarvaganah are the ganah.
(groups) such as the Vasavah. Pitarah.Sarpah.ncluding Ahi and Aja), ¯ Apah. , and the ¯ Adityaganah Daks.a Praj¯apati,Aryaman, Vis.u, Yama, Indra) complete the list. There is no doubt that the ecliptic is meant because the last verse of the hymn refers explicitly to the
fidelity with which the sun and the moon move on their path, the ecliptic. The division of the circle into 360 parts or 720 parts was also viewed from the point of view the naks.atras by assigning 27 upanaks.atras to each naks.atra (´ Satapatha Br. 10.5.4.5). This
constituted an excellent approximation because 27 × 27 = 729. In other words, imagining each naks.atra to be further divided into 27 equal parts made it possible to conceptualize half a degree when examining the sky.
Values for the Lunar sidereal orbit and the Lunar Synodic orbit are given in Table 11 below

130 Achar, Narahari “In seach of Contemporary views on Indian civilization” , Proceedings of the Waves conference held in Hoboken, NJ, 2000, edited by Bhudev Sharma

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 29.530587946
1604 BCE 27.321668 29.530595


ASTRONOMIC AUTHORITY Àryabhata (from Clarke and Kay) Surya Siddanta
Years in Cycle 4,320,000 4,320,000
Rotations 1,582,237,500 1,582,237,828
Days 1,577,917,500 1,577,917,828
Lunar Orbits 57,753,336 (27.321668 days) 57,753,336
Kaye notes 57,753,339 lunar orbits rather than 57,753,336 per Clarke.
Synodic Months 53,433,336 (29.530582 days) 53,433,336
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

How old is the universe, Kalachakra and the Yuga concept, Hindu cosmological time frames
The Hindu Calendar or more appropriately Almanac(also known as the Panchanga ) currently in practice reckons time in terms of very large cycles called Kalpa (4.32 billion years) consisting of 14 Manavantaras(Manavantaras or age of Manu,~ 308 million years). A Manavantaras is made up of Mahayugas (Mahayuga= great yuga consists of 4 yugas: Krta, Treta, Dwapara and Kali). Kali yuga is equivalent to 432,000 years and 1 Mahayuga= 4.32 million years. This system appears to have been in use since the days of the Epics and Puranas, and attested in the Siddhantas. However, the earliest Vedic Calendar was based on a cycle also called yuga, but consisting of only five years. This ancient Vedic Calendar was a lunisolar calendar and used two intercalary months in a five year period and has often been criticized as being very crude.
First we have Kalpa, a day in Brahma’s ‘life’ or 4320 million earthly years, and a night of equal length. During the day he creates and during the night he absorbs to begin the cycle each Brahma day . Each kalpa is divided into 14 Manavantaras or
308.448 million years we are supposed to be in the seventh Manavantaras of Vaivasvata Manu. Each Manavantaras contains 71 Mahayugas, plus 1 Krtayuga ,and each Mahayuga is divided into 4 yugas — Krta, Treta, Dwapara and Kali of 4800, 3600, 2400 and 1200 divine years of the Gods, each of which = 360 human years. We are at present in the Kali yuga which began in 3102 BCE the traditional year of the Mahabharata war .

SO HOW OLD IS THE UNIVERSE
As of Vaisakhapratipada of 2009 CE, May 1 we are in the second quarter of Brahma’s day ( द्वितिय परार्थ ), called Shweta Varaha Kalpa, seventh Manavantaras named Vaivasvata and entered into the first quarter of the 28th Kaliyuga. Already 5110 years of this 28th KY have passed. so the time elapsed in this Kalpa is 6 Manus =1,850,688,000 Y = [6*(306,420,000+1,728,000)] = 6 Manus (includes 6 Jala pralayas or sandhis, periods between Manavantaras) And 27 MY = 116,640,000 Y (27 * 4,320,000)
=27/71.4M = 0.3781512605 M
Add 1 Jala Pralaya(depending on origin of cycle) = 1,728,000 Y
And 28th (Krta+Treta +Dwapara) = 3,888,000 Y (9*432,000) =0.9 MY =.9/71.4
= 0.012605042M
5110 Y of Kaliyuga) = 5110 Y = 5110/4,320,000 MY = 1.1828703704 (10*-3)
MY
So the current year 2009 CE = 1 ,972,949,110 Y or Solar years or 1.972949110 Billion years
= 426+27+(.4*7) + .9 +.001182703704
= 456.701182703704 MahaYugas
To put this in perspective, if we look at a galaxy 2 billion light years away ( a unit of distance) we would be looking at an object in time contemporaneous with the age of 1 Brahma day or the birthday of our solar system. It is incredible that the Indic ancients were able to fathom such cosmological time frames merely by the use of Observational Astronomy, using just his naked eye, especially when it is recalled that the Romans had no name for a number greater than a thousand, and the state of Tennessee passed a law saying that the value of PI should be legislated to be 3, as late as the 2nd half of the nineteenth century




The 12 signs of the Zodiac with Sanskrit names are mentioned In Brihat Samhita and Laghu Bhaskariyam. The former is the work of Varahamihira 505 CE. He is supposed to have borrowed it from a Greek of the 4th century BCE (Could it be Hipparchus). The whole theory of India borrowing from the Greeks needs to be re-examined in greater detail, since it is now clear that the methods used by the Indics were quite unique and distinct from those used by the Greeks. Further Yajnavalkya is credited with discovering that it takes 95 years to synchronize the motions of the sun and the moon The Indic tradition moreover is a living tradition which is practiced by Jyotish even till today. Surely such an observation would have been preceded by extensive data collection and the ability to manipulate large numbers mathematically and the ability to use a written script. There is ample evidence that the Shatapatha Brahmana and the Brhadaranyaka Upanishad both of which are credited to Yajnavalkya, and which contain significant amount of Astronomical observations predate the advent of the Greeks and possibly even the Babylonians
Quote from Koenraad Elst “To conclude this brief acquaintance with Vedic astronomy, we want to draw attention to the possible presence in the Rg-Veda of a momentous cultural artifact, the origin of which is usually situated in Babylonia in about 600 BC: the twelve-sign Zodiac. In RV 1:164:11, the sun wheel in heaven is said to have 12 spokes, and to be subdivided into 360 pairs of “sons”: the days (consisting of day and night), rounded off to an arithmetically manageable number, also the basis of the “Babylonian” division of the circle in 3600. The division in 12 already suggests the Zodiac, and we also find, in the footsteps of N.R. Waradpande, that a number of the Zodiacal constellations/ rAshis (classically conceived as combinations of 2 or 3 successive Lunar mansions or Nakshatras of 13 ˚ and 20’ each) are mentioned. Obviously the Rg should be dated prior to the beginning of Kaliyuga, as we have already demonstrated and hence the Babylonian origin of the twelve sign Zodiac is suspect.”

Figure 4 The shift of the vernal equinox through different Nakshatras over 6 millennia

The Zodiac is also tenanted by 27 constellations each of them spread over an arc of 13 degrees 20 minutes. The Zodiac counted from the first degree of Beta Arietis ( Aswini) to the 360th degree of Zeta Piscium ( Revathi) is known as the Sidereal[3] Zodiac.
[2] The following is based on an original account by Dr. Dwarakanath a physicist. He teaches sanskrit during his free time and is interested in vedic learning and vedanta.
[3] Sidereal month the actual period of the Moon's orbit as measured in a fixed frame of reference is known as a sidereal month, because it is the time it takes the Moon to return to the same position on the celestial sphere among the fixed stars (Latin: sidus): 27.321 661 days (27 d 7 h 43 min 11.5 s) or about 27 ⅓days. This type of month has appeared among cultures in the Middle East, India, and China in the following way: they divided the sky in 27 or 28
lunar mansions, characterized by asterisms (apparent groups of stars), one for each day that the Moon follows its track among the stars.


Next _ some of the referecnes to astronomy in the Samhitas

[ramana]

<!--QuoteBegin-Kaushal+May 26 2006, 07:50 AM-->QUOTE(Kaushal @ May 26 2006, 07:50 AM)<!--QuoteEBegin-->This isan important paper from the Tata Institute of Fundamental research on the observations in astronomy in ancient India ,in particular the conjunction called Rohini Shaketa Bheda

http://www.tifr.res.in/~vahia/rsb.pdf

Note the changes in sea level that are reported here.

<img src='http://kosal.us/Astronomy/sealevel.jpg' border='0' alt='user posted image' />


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So in effect the memory of a terrestial event was preserved as an astronomical conjunction and the original event was forgotten.

I dont think it was faraway event but more close to their observation area.

I have a question. When did Sage Kashyapa create Kashmir? The mythology was that he drained the Kashmir valley which was full of water. So its really a flood and earthquake story. Maybe the RSB conjunction refers to the double quake and flood that created Kashmir.

[Guest]

[quote=Kaushal,Feb 22 2009, 09:07 PM]
My ideas on the development of astronomy in India through the millennia are slowly taking shape. ' Clearly the words of William Brennand (Hindu astronomy are apropos here.

The revisions of this document are available at my site
http://www.indianethos.org/Astronomy/Ind...mology.pdf