Mathomathis would like to present an article on Indic Cosmology and Time Keepers by Kosla Vepa – Indic Studies Foundation. The articles would be broken down into various sections. The following article would represent the basics of the Indic Cosmology and its background, followed by explanation of times and its divisions in subsequent articles


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 . As we have emphasized, there were exceptions such as Brennand, Playfair, Colebrooke, and Bailly.

TH RELUCTANCE OF INDOLOGISTS IN THE OCCIDENT TO ACKNOWLEDGE THE VEDIC EPISTEME:- 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, a period exceeding 1600 years. 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 . When it came to reconciling himself with the obvious depth of knowledge of the ancient indic ,the occidental had no hesitation in coming to the conclusion that the Indic had borrowed everything form Greece. But he is more than reluctant to accept that a massive transfer of knowledge took place from India to Europe, even though the evidence is far more compelling The conventional wisdom in the West was that the Jesuits were sent to convert the Indics to the Christian faith and as a byproduct teach them 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. While there is nothing here that can be considered to be morally reprehensible, one wonders why there was the extreme reluctance to admit that they learned from others too. In this one has to concede that the scholar during the heyday of Islam observed a higher degree of ethics than his brethren in the Occident, because he never exhibited the slightest hesitation in attributing to the Indic the episteme that he had learned from him.

Author view’s 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 and periodicities that they observed, in order to help them plan their activities, such as the planting of their crops 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, and the development of methods now known collectively as Archaeo-astronomy. 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 including the day, the week, the fortnight and the month are shown in Table 1.

60 ghatikas (or 30 muhurtas or 8 praharas) in a 24-hour period (ahoratra)
15 tithi in a paksha or a fortnight, 15th is Poornima or amavasya
The Lunar Month (2 pakshahs in a month), shukla waxing and krishna waning
The Sidereal Year(Nirayana) , the Tropical Year,the Anomalistic Year
The six seasons of a year (each season comprises 60 days)
60 year Jovian cycle/ 360 year ‘divine cycle
2700 year cycle of the Sapta Rishi or the Ursa Major
26000 yer cycle of the asterisms called the Great Year or the precession cycle
432,000 year cycle called a yuga (= duration of Kaliyuga)
4,320,000 year cycle known as the Maha Yuga
Kalpa, the cycle consisting of 4.32*10**9 years

INDIAN COSMOLOGY AND TIMELINES OF HISTORY:- There are some who feel that the reference to a Mahayuga going back to 4,320,000 years, is without foundation, since author do not have recorded history going back that far and the more appropriate measure to us is the divine year. There is a suspicion that somewhere along the historical past, there was confusion in the interpretation of the various definitions of the year, which has resulted in such long periods being assigned to the Yugas such as Kaliyuga. For example the duration of a Kaliyuga in Divine years is a more manageable 1200 years and the entire Mahayuga is 12000 years which is of the same time scale as the beginning of river valley civilizations, if we assume that there was a confusion regarding the interpretation of the year. We will discuss this later. It is the attempt of the ancient Indic to describe geologic time scales associated with the beginning of recorded history that causes confusion and has invited the ridicule of some in the occident such as Thomas Babingtin Macaulay and has prompted him to characterize the entire literature of India as being worthless

THE CELESTIAL SPHERE:- It is conceptually useful to visualize the sky as the interior of a vast celestial sphere, but before we do so , let us recap the essential features of the Terrestrial sphere. The earth is generally represented as a perfect sphere. Although in reality it is an oblate spheroid (ellipsoid), with a larger diameter at the equator equal to 7,926.41 miles (12,756.32 kilometres). The diameter of the great circle passing through the north and the south pole is slightly less and is equal to 7,901 miles (12,715.43 km) , the difference amounting to .32 %. To specify the location of a particular point on the surface of the earth, we use the measures of longitude and the latitude. The longitude is the angle subtended by the arc of a great circle from the equator to the point. The latitude is is the angle subtended by the arc of the equator from the point to the projection of Greenwich, UK on the great circle. Both these quantities are measured in degrees. The great circle passing tough Greewnich is known as the prime meridian.

Every day the celestial sphere, (the interior of a vast sphere centered in the earth) appears to turn in the opposite direction as the earth rotates, causing the daily rising and setting of the sun, stars and other celestial objects. We know now that the sky and the objects in the sky do not rotate (at least not with respect to the earth), but it is an extremely useful construct that serves our purpose of describing the sky and locate the planets and the stars. The Celestial sphere is a vast imaginary sphere with the earth as its center that appears to rotate from East to West.

The celestial sphere showing the ecliptic and its inclination to the celestial equator
The celestial sphere showing the ecliptic and its inclination to the celestial equator

ECLIPTIC (KRANTHIVRUTH):- 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 equatorial 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 (Rasi).

The Ptolemaic Armillary sphere
The Ptolemaic Armillary sphere

The Armillary sphere was also the model used by the Indics, even though Aryabhatta 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.

CELESTIAL SPHERE
CELESTIAL SPHERE

However, RA differs from longitude in essential ways. RA is measured always from the first point of Aries or Mesha as opposed to longitude which is measured from Greenwich, England, and the units are always measured in hours, minutes and seconds rather than degrees, minutes and seconds.

CELESTIAL SPHERE
CELESTIAL SPHERE

In astronomy, the hour angle of an object relative to a particular location is one of the coordinates used in the equatorial coordinate system for describing the position of an object on the celestial sphere. The hour angle of a point is the angle between the half plane determined by the Earth axis and the zenith (half of the meridian plane) and the half plane determined by the Earth axis and the given location. The angle is taken with minus sign if the location is eastward of the meridian plane and with the plus sign if it is westward of the meridian plane. The hour angle is usually expressed in time units, with 24 hours corresponding to 360 degrees. The hour angle must be paired with the declination in order to fully specify the position of an object on the celestial sphere as seen by the observer at a given time.

Relation with the right ascension:- The hour angle (HA) of an object is equal to the difference between the current local sidereal time (LST) and the right ascension (RA) of that object: HAobject = LST – RAobject

Thus, the object’s hour angle indicates how much sidereal time has passed since the object was on the local meridian. It is also the angular distance between the object and the meridian, measured in hours (1 hour = 15 degrees). For example, if an object has an hour angle of 2.5 hours, it transited across the local meridian 2.5 sidereal hours ago (i.e., hours measured using sidereal time), and is currently 37.5 degrees west of the meridian. Negative hour angles indicate the time until the next transit across the local meridian. Of course, an hour angle of zero means the object is currently on the local meridian. The Local Celestial Meridian is the great circle that passes through the North Celestial Pole and a particular location. Thus, the angular displacement of a star to the west of the celestial meridian (as measured along the celestial equator, analogous to longitude) is equal the HA, which is usually given in time units at a rate of 15° per hour. Apparent solar time is given by the hour angle of the Sun plus 12 hours (the 12 hours added so that the “day” starts at midnight).

Because of the eccentricity of the Earth’s orbit and the obliquity of the ecliptic, apparent solar time does not keep a constant pace. Corrections for their effects lead to constant mean solar time, which can differ from apparent solar time by up to 17 minutes. The hour angle of the Sun, and therefore the time of day, varies continuously with longitude, wherein longitude differences exactly equal time differences. Standard times are the mean solar times of the closest standard meridians, which are displaced in units if 15° from Greenwich. (Political boundaries cause variances.) Star time, properly called sidereal time, is the hour angle of the Vernal or Spring Equinox. Because the Sun moves to the east along the ecliptic, the Sun takes longer to make a circuit of the sky on its daily path than does a star or the equinox, so the solar day is 4 minutes longer than the sidereal day. As a result, the sidereal clock gains 4 minutes (actually 3 minutes 56 seconds) per day over the solar clock, starting from the time of solar passage across the autumnal equinox on September 23, when the two are the same. To repeat, the RA of a star or any other celestial body (given by the lower-case Greek letter alpha) is the angle the body makes with the vernal equinox as measured to the east, again along the celestial equator. It too is usually measured in time units. The right ascension and hour angle of a body always add to equal the sidereal time. Given the sidereal time and the right ascension of a body, you can compute its hour angle, which with the declination allows you to set a telescope and to find anything

EQUINOX वसंत संपत (VASANTH SAMPAT) VERNAL EQUINOX:- 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. Thus 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.

SOLSTICE:- SUMMER SOLSTICE: The first day of the Season of Summer. On this day (JUNE 21 in the northern hemisphere*) the Sun is farthest north and the length of time between Sunrise and Sunset is the longest of the year.

WINTER SOLSTICE:- The first day of the Season of Winter. On this day (DECEMBER 22 in the northern hemisphere*) the Sun is farthest south and the length of time between Sunrise and Sunset is the shortest of the year. In the southern hemisphere, winter and summer solstices are exchanged. Summer: December 22. Winter: June 21.

PRECESSION OF THE EQUINOXES:- 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 called a 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 seasons depend on this Earth-Sun cycle. If 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. 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 called the Precession of the equinoxes.

Table 2
Table 2

SOLSTICE:-  A solstice is an astronomical event that happens twice a year, when the tilt of the Earth’s axis is most oriented toward or away from the Sun, causing the Sun to reach its northernmost or southernmost extreme. The name is derived from the Latin sol (sun) and sistere (to stand still), because at the solstices, the Sun stands still in declination; that is, it’s apparent movement north or south comes to a standstill. The Summer Solstice falls between June 20 and 23 of every year in the northern hemisphere and has different significance for various religions. The term solstice can also be used in a wider sense, as the date (day) that such a passage happens. The solstices, together with the equinoxes, are connected with the seasons. In some languages they are considered to start or separate the seasons; in others they are considered to be center points.