Jyotish_Muddle of Ayanamsa

MUDDLE OF AYANAMSA

DrS. Madhavan M.Sc.; Ph.D. Prq(essor of MathemaHcs, L-ILiuerslly College, Trluandrum

Preface The aim of this booklet is to introduce the concept of the Precession of Equinoxes to the general reader. As I started writing. I found that I had to steer between Scylla and Charybdis: If the booklet bristles with technicalities and turns out to be suffocatingly intellectual the general reader may reject it; on the other hand, in the total absence of technicalities this may degenerate blto 'mere trash' , the most unwelcome form for a scientific work. So technicalities are Introduced, but reduced to a minimum and sufficient care is taken to make the lntroductton a bit informal. A bird's eye view of some astronomical and kindred concepts is made in the first four sections to prepare the reader for the later sections. To know what Ayanamsa is, one should know what the first point of Aries is and, in turn, to know that one needs to have some knowledge of Astronomy and this is what the first four sections deal with. : Around 1962. a series of articles under the caption ' 'the vexed question of Ayanamsa' was published in the Astrological Magazine. At that time I found these articles quite exciting and informative. I had often planned a general book on the subject, but because of hectic mathematical activities and many other con-

straints, I could hardly get the leisure required for the execution of my plan. The idea of writing such a book grew out of a conversation with Prof. N.E.Muthuswamy and I wishto express my sincere thanks for his encouragement and valuable suggestions. It is not out of place to point out some salient features of the booklet. As regards the dates of Aryabhata and Varahamlhira. the view generally accepted by the scholars is followed. The author has consulted many books in Sanskrit and English since the sources are referred to in important places, no bibliography is separately given. In the transliteration of Sanskrit words the standard scheme is avoided as the book is being addressed to the general reader. I wish to express my sincere thanks to Dr. B.V. Raman, the Editor, Astrological Magazine, for permitting me to incorporate the material on Ayanmsa from his Astrological Magazine of August 1991. I also express my sincere thanks to Shrl.V. Lakshmana Iyer, Chief Engineer (Retd), Kerala State for his valuable suggestions, particularly regarding the incorporation of various ayanamsa figures. I was initiated into Jyotisha by my revered father and Guru Shri. A.N. Srinivasaraghava Iyengar. when I was quite a boy. With respectful memories, the booklet is dedicated to him. I wish to thank Sri. M. Easwaran, Editor and Smt. M.Girija, Proprietor. CBH Publications, for undertaking to publish this book. S.Madhavan

Contents Preface l.Candles of the Heavens 2.Castle in the Air 3.Spln and Merry Go-roL·nds 4.From the Time's Abysmal Chasm S.Wlther Equinox? Westward Ho! 6.S\ving or Reel? 7. Ayanamsas in the Arena 8. Astrology sans Mythology 9.East is East and West is West 10. Sayan a versus Nirayana ll.Epllogue Appendices

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Candles of the Heavens Who is not enchanted by the myriads of twinkling stars that adorn the dark blue velvet of the night sky? The advancing night which sprinkles stars all over the sky excites the poet's imagination who lets his fancy roam everywhere. The average man, however Is forced to be indifferent to the celestial phenomenon. He finds pleasure in slumber after toiling and moiling during the day. Vociferous drunken brawls break the silence of night. Robbers stealthily move in darkness to achieve their ends. But there is one man who is really serious, trying to learn about the stars. He is the star-gazer. He searches for his celestial companions with the guidance of his telescope. At times there are signs of ardent pleasure on his face. His jubilant face turns pale when things are not up to his expectations. He makes some measurements on the graduated circles ofhis telescope and silently engages in computation. But, What is he actually doing? What does he measure and what does he compute? What is the framework in which he does his operations? One needs to know these before taking to a serious study of Astronomy.

Muddle ofAyanamsa/ The first task is to identify the stars. The primitive man to whom the stars were pieces of wonder imagined fanciful stories about them. An old Malayan story asserts that the stars were the children of the Moon mother who brought her children out only during the night, when jealous Sun who had no children, was not present. The milky way used to be identified with the celestial Ganges. Despite these descriptions of excited imagination, the early man took great efforts to stud\' the stars. The method ofidentification of stars is much like identifying a house in a city; give the name of the street and the number of the house. Since it is difficult to identify the stars unless they are sufficiently bright, stars are arranged in groups called constellations first and then with the constellations, the stars are identified. The constellations are given names after the anfmals or objects which they are supposed to resemble. Sometimes they are named after characters in mythology. 'Sapta-rishi-mandalam' for instance is named after the seven sages, Marie hi, Vasistha, An giras, Atri, Pulastya. Pulaha. and Kratu. The faint companion ofVasishta is named after Arundhati. The general method followed in the West is to give a Latin name to a constellation and name the individual star as Alpha, Beta, Gamma etc. of the constellation in descending order of brightness. Thus Canis major is a group of stars supposed to represent the figure in the form of a dog. The brightest star in the group is called Alpha Canis Majoris. This star is also known as Sirius (Lubdhaka in Sanskrit) and is the brightest star in the sky. Bright stars have generally individual names. There is an important group of constellations called the

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Zodiacal constellations viz., Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces. The constellation Aries is so called because ofits supposed resemblance to a ram. The brightest star in the constellation is Alpha Arietls. the second is Beta Arietis and so on. Indian astronomy refers to twelve rasis or signs as Mesha, Vrishaba, Mithuna, Karkataka, Simha, Kanya, Tula, Vrischika, Dhanus, Makara, Kumbha and Miua, which are supposed to be same as above. But Mesha represents a portion of Zodiac of length so• Vrishabha represents the region oflength 30° that follows, and finally Miua represents the last 30° of the Zodiac. One striking feature of Indian astronomy is that though Mesha represents a Zodiacal Rasi, no constellation or group of stars is identified as Mesha. Similarly none of the 12 Zodiacal rasis is represented by an actual group of stars. On the other hand, Mesha is identified with Asvtni, Bharani and the first quarter of Krittika. Vrishabha is identified with 2nd, 3rd, and 4th quarters of Krittika, Rohini and first two quarters ofMrigasirsa and so on. Thus all the 27 nakshatras are distributed among the 12 zodiacal rasis, each sign receiving 2 nakshatras and a quarter. These nakshatras are actu ally represented by groups of stars. For example, Asvini is a constellation of three stars resembling the face of a horse. Each nakshatra has a principal star or yogatara, which is generally a bright star of the group. However the two classifications do not completely coincide. Sravana or Altair. the principal star of the nakshatra sravana is in Makara rasi. One may expect it to be in the constellation Capricornus. But it is actually a star

Muddle ofAyanamsa I in the constelation Aquila. It is true that there are com-

mon stars in the two classifications. But they are not completely identical. But it is not important as the Mesha rasi, and the stars Asvini, Bharani and the first quarter of Krittika represent the same region of the Zodiac, and similarly for the other Zodiacal rasis and the corresponding nakshatras. We have given lllustra. tions of the constellation Leo, whl$ consists of the prlnclp~l stars of Magna (Regulus), Purvaphalguni [Delta Leonis) and Uttaraphall!uni (Denebola) and Leonis and Dipper, the constellation. (see figures i and U).

LEO and (2) here'

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figure (1) THE

DIPPER ( Snptnrshimnndalnm)

jlgure (2)

I Muddle of Ayanamsa We shall give below principal stars (yogatara) of the 27 nakshatras, and the corresponding names in the West. Nakshatra Western name Asvini Beta Arietis Bharani 41 Arietls Krlttilta Eta Tauri (Aicyon) Alpha Tauri (Aidebarren) Rohini Mrigasirsa Lambda Orionis Ardra Alpha Orlonis (Betalguese) Punarvasu Beta Geminiorum (Pollux) Delta Cancri Pushya Aslesha Alpha Cancri Magha Alpha Leonis (Regulus) Purvaphalguni Delta Leonis Uttaraphalguni Beta Leonis (Denebola) Hasta Delta Corvi Chitra Alpha Virginis (Spica) Svati Alpha Bootis (Arcturus) Visakha Iota Lobrae Anuradha Delta ScorpU Jyeshta Alpha Scorpii (Antares) Mula Lambda Scorpii Purvaashadha Delta Sagittarii U ttaraashadha Delta Sagittarii Sravana Alpha Aquilae (Altair) Sravishta Alpha Delphini Satabhishak Lambda Aquarii

Muddle of Ayanamsa / Nakshatra Western Name Poorvabhadrapada Alpha Pegasl Uttarabhadrapada Alpha Andromedae Revati Zeta Piscium In the boqk 'Popular Hindu Astronomy by Kalinath Mukherji an attempt has been made to identify Mesha, Vrishabha etc., i.e., Zodiacal rasis as constellations. The identification is done with the help of scriptures and Sanskrit Literature. However there is no conclusive proof to show that such a system of describing the rasis as constellations was actually in force in ancient India. It is likely that such a system was prevalent in ancient India and the knowledge of this system was lost with the passage of time.

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A Castle in the Air Any reader may have at least a dim recollection of the geography he learnt in the secondary school. However, no knowledge is presupposed. The ideas are introduced without much technicalities. One understands what is meant by a sphere. -Any section of a sphere by a plane is a circle. When the plane passes through the centre of the sphere, the section is called a great circle, otherwise a small circle. In the strict sense of the term the earth is not spherical in shape., but spheroidal. But as an approximation we shall treat the earth as a sphere and build our concepts. Any observer of the sky notes that the celestial bodies rise, move upwards, and set. Dynamical considerations force us to conclude that the earth rotates about an axis. We observe that the rotation is from west to east. This axis meets the earth in two points on earth called the North and South Poles. The terms Meru and Badavamukha are used to designate these in Indian astronomical literature. All the points equidistant from the two poles lie on a great circle called the equator, known as Niraksharekha in the Indian system. All

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circles that are passing through the North and the South poles are called meridians or circles of longitudes and small circles along planes parallel to that of the equator are called parallels of latitude. The meridian which passes through Greenwich is called the Universal Meridian. For any place on earth, the terrestrial longitude is determined thus. Draw the circle oflongitude through the place A. Let the Greenwich meridian and meridian through A meet the eQuator at G 1 and A1 respectively. Then the length G 1A1 which is the same as the angle subtended by G 1A1 at the centre of the earth is the longitude. Longitude varies form 0 to lso• and can be east or west of Greenwich. The parallels of latitude determine the position of a place north or south of the equator. For the place described above, terrestrial latitude is North or South according as the place is north or south of the equator. The terrestrial latitude is measured by the arc of the meridian through A intercepted between A and the equator. It varies form 0 to 90°. For an observer in the North Pole there will be no north, east or west. There is only South. Similarly for an observer in the South Pole, there is only North. For any observer the sky appears in the form of a hemispherical dome with the stars as points of light spread on its surface. Naturally an astronomer imagines a celestial sphere around him. He, treated as a point, is at the centre ofthe sphere. He finds the positions of the stars and other celestial bodies as seen on the sphere. The star Sirius, for example is at a distance of 8.7 light years from the earth, and the star Alpha Centauri is at a distance of 4.3 light years. But he uses the projections of these on the celestial sphere for his

Muddle ofAyanamsa immediate study. though the actual positiOns are required in some other contexts. Now the properties of the sphere and methods of spherical geometry and trigonometry can be effectively applied to study the movement of celestial bodies. Given any two points. we can always draw a great circle joining them. The distance between any two points on a sphere is measured by the arc of great circle joining them. This is taken to be the angle subtended at the observers position by the two points. The term 'horizon' is used in common life, and one is intuitively aware of what it Is. Varahamlhira. the celebrated astronomer of Ujjaln. defines it as a circle along which thesky and the earth appear to meet. More formally we can define horizon as the great circle of the celestial !phere intercepted by the tangent plane to ~ eallth's ' 1rface at the observers position. The point of celestial sphere that is vertically Overhead is called the Zenith (Z) and its antipodal point., the point diametrically opposite to it, is called the Nadir (N). The earth's polar axis when extended in either direction meets the celestial sphere in the North and south celestial poles. The North pole is conveniently located with the help of the pole star. The point on the horizon below the North pole Is called the North Point. From this the South/the East and the West points can be fixed. One important principle is that the height of the pole above the horizon is equal to the latitude of the place. For any circle on a sphere. the diameter of the sphere perpendicular to the plane of the circle is called its axis and the points of intersection of the axis with the sphere are called poles. For any circle, a great circle through its poles is called

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a secondary. The great circle with the north celestial pole and south celestial pole for poles is called the celestial equator. The celestial equator divides the celestial sphere into two hemispheres, the northern and southern hemispheres containing respectively the north and south celestial poles. The meridian of a place is the great circle passing through the Zenith, the Nadir and the poles. Verticals are secondaries to the horizon and the vertical through the East and West points are called the prime vertical. Any careful observer can see that the Sun is having an eastward motion in the sky with respect to the fixed stars. Observe the eastern horizon before sunrise. Certain stars will be visible near the horizon which gradually pale into insignificance with the arrival of the Sun at the eastern horizon. Repeat the process continuously for a few days. One can notice the group of stars visible near the horizon changes continuously suggesting thereby an apparent motion of the Sun eastwards with respect to the stars. The Sun completes the revolution with respect to the stars in the course of a period called a sidereal year. The apparent path of the Sun is called the ecliptic. This apparent motion is actually due to the earth's revolution, in the orbit around the Sun. The Zodiac or Zodiacal belt consisting of the constellations Aries, Taurus, Pisces. .........covers the ecliptic. The ecliptic is defined as a great circle of the celestial sphere and it is inclined at about 23• -2 T to the equator. The points of intersection of the celestial equator and the ecliptic are called the first point of Aries ( )' l and the first point of Libra (a). The point at which the Sun leaves the southern hemisphere to the northern hemisphere in the west to

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east motion along

II

is called the First point

N

E- the East point. W- the Westpoint. S - the South point. N- the North Point. P • the North cele sttal pole and P' the south celesllal pole. nS · • the celestial horizon, QR • the celestial equator. HL-the ecliptic. 1 - the First point of Aries. -~ - the First point of Libra. K and K' the poles of til•' ··rliplic.

Flg(lli) HL- the ecliptic K and K' • the poles qf the ecliptic • S · a celestial body D · the fool of the secondary through S ··t D • the (celesttal) longtlude of S S D - the (celestial) latitude of S Fig (iv) .l.'l};ttV}

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It is necessary to acquaint oneself with the system co-ordinates used for fixing the positions of stars and planets. Since we are not using all of them in the book, we shall discuss some of them which are relevant to the understanding of the remaining part of the book. The height of any body above the horizon is measured by its angular distance above the horizon along the secondary to the horizon through the body, and is called the altitude. If S is a body and SD is a secondary to the horizon D being the foot of the secondary then SD is the altitude. The angular distance measured from the North point (or the South) eastwards upto D is called the azimuth of the body. In this system the coordinates are;:._~tp. reference to the horizon. We can choose equator and a suitable origin for defining another system. Let S be a body. Draw SD secondary to the equator. D being the foot of the secondary. Then rD measured eastwards is called the right Ascension and SD is called the declination. The declination is measured positive or negative depending on the hemisphere which S (North or South) belongs. This system is generally used to give the positions of stars. We now start with the ecliptic and define another system. Let S be a body and SD, secondary to the ecliptic. rD measured eastwards is called the celestial longitude and SD ls called celestial latitude. SD is measured north or positive and south or negative as the case may be. See figure (lv) for a representation. We recall that tpe first point of Aries is one of the points of intersection

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,of the celestial equator and the ecliptic. It is found that :~'4Ji:e first point of Aries has a backward motion of abut '.50" .2 per annum in relation to the stars and this phe no me no n is called the precession of the equinoxes. In Indian Astronomy it is conventional to refer to longitudes in relation to a fixed star in the Zodiac which we shall call 'Meshadr and the longitude so measured is called the Nirayana longitude of the body. If it is measured from the first point of Aries, it is called Sayana longitude. The Meshadi is not the First point of Aries though at some point of time., it coincided with the F'ratpoint of Aries. In Indian Astronomy terrestrial latitude is called Akshamsa, the horlron is called Kl!ihlttja. the celestial equator is called Vishuvavritta, the ecliptic is called apamandala and longitude is called Jhuta. and the celestial latitude is called vikshepa; To quite specific, the celestial longitude is called Nirayana sphuta or Sayana sphuta depending on· whether it is measured with reference to Meshadi or the first point of Aries. The celestial latitude or Vikshepa is unaffected by precession. The precession of the equinoxes is called Ayanachalana in Indian Astronomy. Indian Astronomy employs a term Dhruva for giving the positions of stars. This is generally called the polar longitude, which is measured by the distance of the star from Meshadi along the ecliptic up to the foot of the circle through the celestial poles and the body. If S is the body and P Is the nearer pole and D is the point of inter section of PS with the ecliptic then the angular distance of D measured eastwards from Meshadi is the dhruva. Hence SD is the vikshepa or what may be translated as polar latitude.

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The methods given in this section are for northern latitudes. Corresponding changes, whenever required have to be made for southern latitudes in the description of the celestial sphere. The attribute 'celes~l' is generally omitted by convention tn using the terms. Thus we simply say equator, longitude, latitude etc. dropping the adjective 'celestial'. Corresponding to every point on the surface of the earth, one can visualize a celestial sphere and co-ordinates of celestial bodies can be given with reference to that. However one can choose the centre of the earth as the centre of celestial sphere. co-ordinates referred to this are called geocentric co- ordinates. It is the convention to give the geo-centric right ascension, declination, longitude, and latitude of celestial bodies. This matters little in the case of distant objects like stars. In the case of comparatively nearer bodies like the Moon, the Sun and the Planets, geo-centric co-ordinates differ from those with reference to any station on the surface of the earth, due to parallax.

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Spins and MerryGo-rounds Before taking up the study of precession it is necessary to know about the diurnal motion of the stars and planets and the annual motion of the Sun. When the earth rotates about its polar axis once, this duration of time is called a sidereal day - in the west to east direction, the celestial bodies appear to move in the east to west direction. This is called diurnal motion. In the course of a sidereal day, every celestial body rises transits above, sets, transits below and rises again. The body is saia to rise when it reaches the horizon on the east and is said to set when it reaches the horizon on the west. The body is said to have the upper transit when it crosses the meridian overhead,and the lower transit when it crosses the meridian below the observer. Before studying the Sun's diurnal motion everyday, it is necessary to have a general idea of the annual motion of the Sun. We recall that the Sun moves along the ecliptic inclined at an angle of about 23° 27' called obll-

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}I)

quity. (it is denoted hereafter by w) to the celstial equator. On March 21st the Sun is at ( ) and the position is. called the Vernal equinox. At this instant, the longitude, the latitude, the right ascension and the declination are all zero. The Sun moves eastwards along the ecliptic and comes to the position S 1 on the ecliptic on June 22nd when the longitude =90°, The right ascension = 90° and the declina tlon=w (north). We emphasize that the Sun is always on the ecllp tic and hence the latitude is alwys o•- After June 22nd the Sunmoves eastwards and reaches the position called the Autumnal equinox on September 23rd. At this time the longitude has become 180• the right ascension 180: and the declination decreases to 0°. Thereafter the Sun moves along the ecliptic·. longitude and the right ascension increase and the south declination increases, On December 22nd Sun comes to S2 called the winter soilStice, when the longitude is 210•: The right ascension is 270° and the south declination is w. Thereafter the Sun moves eastwards and reaches the first point of Aries once again on March 21st( see figure (v ). ...

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....... -·- ,-,..., ,

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S:a. Fig(v)

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It is necesary to acquaint oneselfwith the nature of diurnal motion of the Sun. When the latitude of a station lies between 0 and go•.w (North) the general nature of the diurnal motion can be described thus. On March 21st, the Sun rises at east point and sets at the west pqlnt. the equator being its diurnal path. The day and night are of the same duration. After this the rising and setting points are shifted northwards, the Sun's diurnal path every day being a small circle parallel to the equator. The day lengthens and the night shortens. This phenomenon continues till June 22nd when the day is longest and the rising and setting points are in the northernmost position. Thereafter the Sun retraces Its path, the rising and setting points move backwards and the whole phenomenon repeats in the reverse .. order. On September 23rd, the Sun once again rises at ··· the East and sets at the West. The day and night have the same duration. Afterwards. the rising and setting points are shifted southwards., the day shortens and the night lengthens until December 22nd when the rising and setting points are in southenmost positions and the day is shortest. This pheno-menon repeats in the reverse order till the next March 21st. when the latitude Is go•.w the general description given above works through and on the day when the Sun's dedma• tion is W-north on the summer solstice day, the Sun touches the north point at setting and there is no night, in any higher latitude ¢ the Sun touches the north point on the day when the declination is 90"--? north and thereafter the Sun continues to hover over the horizon without rising and setting for a few days till the declination once again becomes 90'!.) , This is called

Muddle of Ayanamsa I perpetual day. There is an equal duration of perpetiual night, and it comes when the Suns declination is go::.; south. At the north pole the day lasts 6 months and the night of an equal duration. However, we are primarily interested in the latitudes between oo and 90' -w (North) for which the essential details are 1. At the equator i.e., when the latitude is 0, the day and night have the same duration on all days. 2. On the equinoctial day, i.e., at the Vernal equinox and the Autumnal Equinox the duration of the day and night are the same. 3. At the summer solstice the day is longest ( the njght is shortest) and at winter solstice the day is shortest (the night is longest). For southern latitudes the detaUs can be got by changing the day into night and night into day. It is necessary to add a word of caution. In all these descriptions above, the change in the declination of Sun in a day is not taken into account. In the strictest sense of the term. the dirunal path of the Sun on any day is not parallel to the equator, but only approximately so. Moreover on March 21st. the Sun need not be at the first point of Aries, at Sunrise and statement about the Sun's rising at the East point is only nearly true. However these minute differences can be omitted while making a general study ofthe diurnal motion. At the Vernal equinox, spring commences. Summer at the summer solstice, Autumn at the Autumnal equinox, and winter at the Winter solstice. The period

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between two successive passages of the Sun through the first point of Aries which we shall call the tropical year reproduces the seasons in the same order. The Indians have 6 seasons (Vasanta, Grishma, Varsha. Sarat. Hemanta, Sisira) each of two months duration starting fom the S nn 's passage through Meshadi. Thns it is with reference to the sidereal year which doesnot reproduce the seasons in the same way according to the western concept. Let us now examine these details in the light of the description in the preceding section. We recall that the nirayana longitude is measured from the fixed point of the Zodiac called Meshadi and not from the First point of Aries. The entry of Sun in Mesha is called Mesha-sankrantl which occurs when the nirvana longitude of the Sun is zero. In fact Mahavishuvat corresponds to the day on which the day and the night are of equal duration, and hence it falls on March 21st. This is called the Meshayana in Indian Astronomy. Therefore vishuvat as observed by the Hindu society is not exactly on the day when the lengths of the day and night are equal but a few days later. Similarly Uttarayana. strictly in accordance with the term starts on the day when the Sun starts moving towrds the north. This happens when the day is shortest in the northern latitudes. But the Uttarayana-punyakala observed by the religious Hindu is at the time of Makarasankranti, when the nirvana longitude of the Sun is 270°. This occurs a few days after the Sun has started his northward course. All these discrepancies occur because, of the phenomenon called the precession ofthe equinoxes due to which the First point of Aries moves westwards at

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the rate of about 50" .2 per annum. In the Indian system the year used is sidereal. A sidereal year is defined as the interval between two successive passages of the Sun through Meshadi. Let at a time Meshadi coincide with the first point of Aries. This corresponds to the Vernal Equinox. When the Sun comes back to Meshadi after one sidereal year. the First polnt of Aries has already moved westwards by 50" .2 year the real 'Mahavlshuvaf or the Vernal equinox is already over. The vernal equinox thus receeds every year and the difference that has accumulated now since the Meshadi and First point of Aries coincided is over 23°. In fact the First point of Aries is now in the constel Iation Pisces. At any tlme the quantity to be subtracted to get the nirayana longitude from the Sayana is called Ayanamsa. The Interval between two successive passages of the Sun through the First Point of Aries is called a tropical year. The first point of Aries and the instant of the Sun's passage through the first point of Aries are both known by the term the Vernal equinox. Similarly for the First point of Libra and the solstices. In Indian Astronomy the term Vishuva or Vlshuvat ls used to denote equinoxes or equivalently the first point of Aries and Libra. However one can name the First points of Aries. Mah avls hu vat for clarity. It is also called Sayana Meshadi. The term First Point of Aries alone is used in this book. When the term first point of Aries ls used, the reader will remember the synonyms the Vernal equinox, pilrvavishuvat and sayana meshadi.

4 From the Time's Abysmal Chasm We shall introduce in this section the Indian concept of time. According to Suryasiddhanta the micro divisions of time are as follows. I 0 gurvaksharas 1 asu(prana) 6 as us 1 vinadi 60 vinadis 1 nadi 60 nadis 1 day We get a slightly different Version in the Sidhantaslromanl of Bhaskara. 100 trutis 1 tatpara 30 tatpara 1 nlmesha 18 nlmeshas 1 kastha 30 kasthas 1 kala 30 kalas 1 gatika · 2 ghatikas 1 kshana.muhurta 30 muhurtas 1 day The day referred to can be the sidereal day or the savana day. A sidereal day (nakshatra dina) 18 the time

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for one rotation of the circle of asterisms (bhachakra) or equivaleiJtly the time of one rotation of the earth about its axis. A savana day is defined as the interval between two successive risings of the Sun,. When the savana day is divided into smaller units the attribute savana' is also used to indicate that. Thus a savana day is equal to 60 savana nadis. Though the savana day is ofvariable length, it is what is used by the Indians for common purposes and what is called day in common parlance. With the sidereal year as the base, we have the rnacrodivisions of time. We emphasise that a sidereal year is the time taken by the Sun to move once round the earth in relation to the fixed stars. A rnahayuga or chaturyuga consists of four yugas occurring in the order Krita, Treta, Dvapara and Kali with the following durations: Duration ofKali4,32,000 years Duration ofDvapara2 x 4,32,000 years Duration ofTreta3 x 4,32,000 years Duration of Krita.4 x 4,32,000 years Thus the period of a Chaturyuga is 4,32,0000 years. A Kalpa consists of I OOOchaturyugas and it constitutes a day ofBrahma., the creator. There is an equal duration of night when the worlds cease to exist. The life span of the creator is I 00 years in his scale and it is but the twinkling ofan eye ofthe supreme Brahman. This kind of theoretical division of time looks apparently quixotic. A truti in fact is equal to 1 I 33750 of a second .. and it is defined as the time to break a leaf

I Muddle ofAyanamsa oflotus with a sharp blade. One wonders whether these things were actually used or the Hindus had any instrument to measure them. One important thing is that the Hindus had a great capacity for theorization. In fact, large divisions of time can be used to measure the lives of galaxies and small units for measuring the phenomenon in the microcosmic world. The period of 4,32,000 yeas is quite significant, because the planets come back to their mean positions in that time. The solar months can be defined in the following way. The Month Mesha starts at the entry of the Sun in Mesha and lasts till his entry in Vrishabha. The period of tracing a longitudinal distance 30° since the entry of Mesha is called the Month of Mesha. The month Vrishabha is the time to trace 30° since the entry in Vrishabha and so on. Thus the twelve months from Mesha to Mina can be defined. The term entry in Mesha is to be carefully defined. It is when the Sun's position is at Meshadi, a fixed star of the Zodiac we have defined, In other words it is the instant at which the nirayana longitude of the Sun is Zero. The duration of the years sidereal) according to the Suryasiddhanta is 365 days and 6 hrs, 12 mins. 38.56 seconds, and the modern figure is 365 days 6 hrs 9 mins, 8.6 seconds and there is a difference of about 3 minutes. These are in mean solar units defined later. Apart from the solar measure, or the sauramana, the lunar measure or the chandraniana is also in vogue. At the time when the longitudes of the Sun and the moon are equal, the New moon or amavasaya ends, This is called the conjunction of the Sun and the Moon. The period of tracing a longitudinal distance of 12° by the moon from this position is called

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21

prat ha rna and the period of separation of the Moon eastwards by 12° is called a thithi (lunar date). We give below the lunar days (thithis) of the bright half (sukla paksha) till the moon comes to opposition when the distance fom the Sun is 180°. The distance ofthe Moon Thithi from the Sun (eastward separation) 0- 12° (pratipat) Sukla prathama 12°- 24° Sukla dvitiya 24°- 36° Sukla tritiya 36°- 48° Sukla chaturthi 48°- 60° Sukla panchami 60°- no Sukla shasti no- 84° Sukla saptami 84·Sukla ashtami oo·- 108° Sukla navami 108·- 120° Sukla dasami 120°- 132°Sukla ekadasi 1320- 144° Sukla dwadasi 144·- 156° Sukla Trayodasi 156°- 168° Sukla Chaturdasi 168°- 180° Poornlma At the end of the Poornima or full moon Krishna Paksha or the dark half commences. The period to trace the first 12• after the full moon is called Krishna Prathama and the second 12° is called Krishna dvitiya and so 011. The fifteenth tithi of the Krishna Paksha is Altlavasya at the end of which the moon comes back to the next conjunction and the lunar month ends. Thus

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the lunar month consists of 30 tithis and is of duration of about 29 1/2 solar days. With these concepts the lunar months are intro duced., The lunar month Chaitra starts at the Sukla Prathama in the solar month Mina, Vaisakha starts at the sukla pratipat of the solar month Mesha and so on. Since the lunar montb is shorter than the solar the lunar year will be over IO or II days before the solar year. To adjust this adhimasa (intercalary month) is introduced once in three years. A lunar month without a solar ingress (sankramana) is called an intercalary month and it has the same name as the month that follows., but With the prefix adhi. Thus ifthere is an intercalary month before Sravana, it is called adhisravana. The Indian almanac normally gives the details according to the solar, lunar and other systems. But the sidereal solar year is the basis. One more important thing is that the time according to the Hindus is not universal. It is subjective. This is best illusrated by a puranic story. The King Revata desperately searched for a suit able bridegroom for his daugher Revati. He decided to meet the creator and get the informtion straight from him. He went to the creator·s place with his daughter, waited a bit to ask the creator about his problem being enchanted by the symphony of a Gandharva. The creator heard the problem of Revata, and replied. "Oh! Revata! you are in my world now and my time scale applies to you. When you go back to earth, none of the princes you have in mind will be alive. However at the time. there will be a prince named Balarama in Dvaraka, and you can choose him

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as your son-in-law". This Story illustrates that time as concieved by Indians was subjective. In the modern days mean solar units are used. Since the Sun's motion is not uniform and its path Is inclined to the equator, an astronomical mean Sun whose right ascension slightly differs from that of the Sun is defined and the time is measured with reference to that. The motion of the asrtronomical mean Sun being uniform makes time keeping convinlent. The interval between two successive mean midnights Is a mean solar day, which is divided ito 24 mean solar hours and so on. We shall close this account With a brief description of the Rashtriya Panchanga. As we have observed the Indian almanacs are based on the solar sidereal year. Consequently the equinoxes, the solistics, and the seasons do not repeat with the periodicity Of a solar year. The lunar calendar is adjusted against the solar calender wich is sidereal in character. On the other hand Western calender is based on the tropical year, the duration of which is 365.2422 mean solar days. In having a year of length 365 days an error od 0.2422 of a day , and this is offset by introducing a leap year once in four years, by introducing an additional day In February,. Ev.en with correction, an error crops up and this is removed by the Gregorian correction which rules that century years are not leap years unless divisible by 400. The Indian system as given in Rashtrtya Panchang is based on the tropical year and is aligned with the Gregorian Calendar in the following way.

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Month of the National calendar 1. Chaitra (30 days): 31 days in leap year

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Georgian date on the lst ojthe month

March 22 (March 2 1st in leap year) 2. Vaisakha(31 days) April 21st 3. Jyeshta(31 days) May 22nd 4. Asahada(31 days) June 23rd 5. Sravana(31 days) July 23rd 6. Bhadra(31 days) August 23rd 7. Asvina(30days) September 23rd 8. Kartlka(30days) October23rd 9. Agrahayana(30days) November 22 nd 10. Pausha(30days) December 22 nd 11. Magha(30days) January 21st 12. Phalguna(30days) February 20th Saka era which commenced in 78 A.D. is used for this purpose.

5 •

Whither Equinox ? Westward Ho! Before discussing the evolution of the concept of precession, it is necessary to clarify what the term implies. We have defined the term"First Point ofA.r;ies" as one of the points of intersection of the celestial equator and the ecliptic. By the 'Precession of the Equinoxes' ·we mean a backward or westward motion of the First Point of Aries. In other words, it is not a fixed point, but has a westward motion relative to the stars. The longitudes of stars, thus, are not constant. but change according to the rate of precession. We shall describe a simple experiment. For any place on earth you find that the duration of day is same as that of night on two days in a year. This happens on the equinoctial days. Exactly after a few sidereal years are over, measure the durations of day and night. They will be different. If it is a millennium. the difference will be clearly perceptible. On the other hand, ifthe experiment is performed after an exact number of tropical years are over, the phenomenon of having the durations of day and night

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to be equal repeats. We shall describe a simpler experiment. Plant a staff of considerable height at a place. On an equinoctial day, note the position of the shadow at noon, and measure its length. Exactly after a few sidereal years are over repeat the experiment. The length of the shadow will be different. If the experiment is performed after the completion of an exact number of tropical years, the shadow will have the same length. From the experiment we can infer that the equinoxes recede. The idea is quite simple. But it took several centuries for mankind to arrive at a defmite conclusion on the phenomenon of precession. One does not know where human clvtllzatlon began. Historians tell us that it was in Babylonia, on the banks of Euphrates and Tigris. The Babylonian clay tablets with their cuneiform writing reveal some facts about the astronomical knowledge they possessed. Astrology was the main goal of Babylonians and as it depended on Astronomy, they devised methods of computation of planetary position. They had a luni-solar calendar and they measured planetary longitudes from a fixed point of the zodiac. it is doubtful whether they had any idea of precession of the equinoxes. There are clay tablets which give different positions of the sidereal Equinox. possibly for different times. This does suggest the idea of precession, but they had not penetrated deep into the problem. The Egyptians also devised a calendar. The solar year of 365 days was adopted, by them by about 3000 B.C. They understood later the inaccuracy of their methods and introduced some correction. Accordingly, the heliacal rising of Sirius was chosen as the beginning

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of the Egyptian year because it was the brightest star in the sky. Being enchanted by the bright ness of the star, they deified it by identifying with the Goddess Is is, However, they did not have any idea of precession. In Greek civilization we find really an attempt to explain the phenomenon of precession. Even this occurred only after the civilization reached a fairly high level of advancement. The systematic study of precession started with Hipparchus. He lived in Rhodes and had spent some time in Alexandria, the intellectual metropolis of the West during his days. An anecdote is narrated to show how he took interest in the precession of the equinoxes. The appearance of a new star in Scorpio in 134 B.C.created great interest in him and he prepared a catalogue of stars and classi fled them into six magnitudes, those of the sixth being just visible to the naked eye. When he compared the positions given by Timocharis and Aristyllus one hundred and fifty years before, he found that there was some difference. There was a general increase in the longitudes of stars and a natural conclusion was that the equinoctial points had changed. Hipparchus also noted that the obliquity and the latitudes of stars did not show any change. So he concluded that the equator might have shifted from east to west, retaining the inclination to the ecliptic unaltered. Thus he arrived at the important discovery ofthe precession of the equinoxes. He therefore defined two kinds of years, tropical and sidereal, The sidereal year is the time required by the sun to return to the same star after one revolution and the tropical year is the interval between two successive passages of sun through the first point of Aries. Hipparchus also computed the

Muddle of Ayanamsa I lengths of these two kinds of years with considerable amount of accuracy. The next important astronomer in the line was Ptolemy of Alexandria. Astronomers like Geminus, Kleomedes. Theon of Smyrna and Martinus Cappella do refer to the theory. But Proklus rejects the theory. Much similar to some Indian astronomers Proklus gives the theory of libration of the equinoctial points. The idea is that the longitude of a star increases for 640 years at the rate 1 • /SO years and then starts decreasing for 640 years and then again increases for 640 years again and so on. Ptolemy did not agree with this theory. To him, precession was due to the rota tion of the sphere of fixed stars from west to east around the poles in about 36,000 years. After Ptolemy there followed some Astront>m~rs in Alexandria and the last of them, Hypatia. was brutally murdered. This brought the intellectual activity in Alexandria to a standstill. The revival of astronomical studies starts from the Renaissance. How different facts individually helped to study the theory of precession of the equinoxes Is important. The Ptolemaic theory was deeply rooted in the academic circles of Europe until the Copernican challenge. The Ptolemaic theory was essentially geocentric. Copernicus replaced it by a heliocentric system. This had the specific advantage of explaining direct and retrograde motions. In his work De Revolutionibus, he explains that precession originates from a slow motion ofthe earths axis. such that it is inclined always at the same angle to the ecliptic. He gave the period for Its revolution as 26,000 years.

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Tycho Brahe, the celebrated Danish astronomer is another impor tant person in the list. With the help of King Frederick II, he established the Hveen Observatory or Uraniburg as he called it. He patiently made observations with the help of the instruments he had. He employed a system of Astronomy which was a hybrid of the Ptolemaic and Copernican systems. According to him the Sun and the moon revolved round the earth and the other planets revolved round the sun. To him, we owe a catalogue of 777 stars which furnishes an exact value of precession. Galileo, his contemporary was responsible for a breakthrough from the conventional methods. Though he did not directly influence the concept of precession. it was his invention of the telescope that paved the way for accurate observation. In the meanwhile, Kepler, an assistant of Tycho Brahe examined the planetary tables prepared by Tycho Brahe and arrived at his famous laws of Planetary motion. When this reached the hands of Newton, he discovered the inverse square law from which the theory of planetary motion could be inferred. This put science on sound foundations and heralded the era of classical physics. Newtonian theory of gravitation made possible a dynamical explanation for precession which we outline below: The earth is actually spheroidal in shape. The sun and the moon exert their attractive forces on the earth. Since they do not remain in the equatorial plane always, the resultant force does not pass through the centre of graqty of the earth. Therefore it does affect the axis of rotation of the earth by giving it a velocity of rotation round the axis of the ecliptic. A force acting

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through the centre of gravity of a body does not affect the rotation of the body about its centre of gravity. The resultant force of attraction of the sun and the moon on the earth acts in a direction inclined to the equatorial plane. If the earth were not rotating, this force will tend to make the earth's axis perpendicular to the direction of the resultant force. But because ofthe rotation of the earth the axis rotates about an axis perpendicular to the direction ofthe resultant. The rotation is very much like that of a top which is in rotation about the axis of symmetry. At each instant, the axis of the top moves at right angles to the direction of gravity without falling, since its rotational velocity is much more than the conical motion of the axis. in the case of the earth, the diurnal rotation is faster than rotation ofthe axis about the normal to the plane of the ecliptic. This motion of the terrestrial axis about the axis of the ecliptic is called the precession due to the sun. The moon also excerts a similar influence and the combined effect is called luni-solar precession. By solar precession the earth's axis takes about 26,000 years to make one revolution about the pole of the ecliptic. By Lunar precession it takes about 19 years. One of the important effects of precession is that the celestial pole revolves about the pole of the ecliptic completing one revolution in about 26000 years. As a result, the pole star has to be changed from time to time. The 'northern star' is not as constant as it was thought to be. The present pole star is not exactly at the North pole but slightly away from it. By A.D.7600 one may have to Alderminn (Alpha Cephei) as the pole star

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and by A.D.. l4,000 Vega( Alpha Lyrae) would have the claim. Flamstead, who was the first astronomer Royal has given the celestial history of the observations of fixed stars, planets, sunspots and Jupiter's satellites. His star catalogue is immensely useful in the study of precession. Bradley who was the third astronomer Royal is well known .for the study of aberration, observes thus: • when I considered these circumstances and the situation of the ascending node of the moon's orbit, at the time when I first began my observations, I suspected that the moon's action upon the equatorial parts ofthe earth might produce these effects, for if, the precession ofthe equinox be, according to Sir Isaac Newton's princlples,caused by the action of the Sun and the moon Qpon those parts, the plane of the moon's orbit being at one time above 10" more inclined to the plane ofthe equator, than another, it was reasonable to conclude that the part of the whole annual precession which arises from her action would in different years be varied in its quantity, whereas the plane of the ecliptic ,wherein the sun appears keeping always nearby the same inclination to the equator, that part of precession which is owing to the sun's action may be the same every year, and from hence, it would follow that although the Mean annual precession proceeding from the joint action of

the sun and moon were 50", the apparent annual precession might sometimes exceed and sometimes fall short of the mean quantity according to the various situations ofthe nodes of the moon's orblt."

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Jean Le Rond D"Alembert who is well known for his famous mechani cal principles contributed to Mathematical Physics extensively. He made investigations of the precession of the equinoxes and the rotation of the earth's axis, and demonstrated that his theory tallied with that of Bradley. Laplace well known for his equation that bears his name and a contemporary of Napoleon, has discussed precession in his work.Mecanlque Celeste. Frederick Wilhelm Bessel established an observatory in Konigsberg under the patronage of the King of Prussia. With the munificence of the King, he installed instruments to make precise observa tions. He undertook the great task of determining the positions of all stars upto the ninth magnitude between 15• south and 45•north declinations. In twelve years, he made about 75,000 observations and these are greatly useful in determining astronomical constants such as precession, aberration and refraction. The head of the astronomical family of the Strunas, Frederick Wilhelm was succeeded by his son Otto as the Director of the Palkovo observatory. He won the gold medal of the Royal Astronom ical society for his determination of the constant of precession in which included the proper motion of the solar system. The rate of precession is not actually a constant, but depends on time.

We have discussed only luni-solar precession. When the planets are also taken into account, it is called generalized precession. Science proceeds on the assumption that out knowledge is incom plete. So continues the research on precession. It goes on like that

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.,

The reader is referred to standard books on Astronomy for a detailed information on precession and the allied concept of nutation.

6

Swing or Reel? Before discussing the Indian concepts on precession we shall introduce a few terms for convenience. As we have seen, the first point of Aries is one of the points ofintersection ofthe equator and the ecliptic and it has a backward notion of about 50".2 per annum. The longitude measured from it is called Sayana longi tude. The longitudes measured from a fixed point of the ecliptic called Meshadi is called Nirayana longitude. Thus we get zodiacs of two kinds, the say ana zodiac and the nirayana zodiac. The sayana longitude of a planet exceeds the nirayana longitude by a quantity called Ayanamsa. In Indian astronomy precession is called ayanachalana. The cele brated astronomer Aryabhata I does not explicitly refer to ayanachalana in his treatise. Since the ayanamsa at this time was nearly equal to zero, it is likely that he bypassed it. At the same time the reference to Kali 3600 in his book has given rise to

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some conjectures. The commentator Suradevayajvan on Aryabhatiya observes that a correction has to be effected, posi tive or negative, as the case may be with reference to 3600 kali, thereby suggesting that 3600 is the year in which the two zodiacs coincided. There is no mention about precession in the works of Brahmagupta or Lalla. Bhaskara I did not even approve of the concept. We get a reference to precession ofthe equinoxes in Varahamihira s Brihatsamhita. Varahamihira observes: " there was a time when the suns southerly course commenced from the middle of the star Aslesha. and northerly course started from Dhanishta. This has been mentioned in ancient works". "At present the southerly course of the sun commences from the beginning of Karkataka, and the other from the beginning of Makara. The fact which is against the old statement can be verified by the observation. The sun's change of course can be ascertained by marking the position of a distant object either at sunrise or sunset or by marking the entry and the exit of the shadow by the gnomon installed at the centre of a big circle ( drawn on the surface of the earth)". This suggests that Varahamihira was aware of precession and the Sayana and Nirayana zodiacs nearly coincided during his lifetime. This is important since Varahamihira's period can be fixed by other methods. The Pane hasiddanthika is dated around 505 ADr from an internal evidence and a rough estimate ofthe period in which the coincidence of the two zodiacs took place would be 3rd, 4th, 5th or 6th century A.D.

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The Suryasiddhanta makes an explicit reference to precession, but purports a theory of libration instead of recession. According to the Suryasiddhanta, equinoxes swing on either side of the fixed point Meshadi amounting to 600 oscillations in 4,32,0000 years, a mahayuga. Thus the period of oscillation is 7200 years. According to the Suryasiddhanta, it moves uniformly forwards by 27° in the first 1800 years and retraces the path in the next 1800years .. By 3600 years it reaches the zero position. Then it moves backwards to 27° and then retraces its path back to Meshadi. By 7200 Kall, it is again in the zero position .. This theory of libration is now not generally accepted since a dynamical expla nation of recession is given. However, we have to wait till 5400 kali i.e.2229 A.D. to verify the statement ofthe Suryasiddhanta. lf atthat time, the first point of Aries, instead of receding, starts moving forward, the theory of oscillation gets justified. Who knows what may or may not be happening? The rate of precession here is 54" per annum. This theory ofayanadolana[trepidation) as it is called, instead of ayanachalana receives a crushing blow from the remarks in Satapathabrahmana. It is mentioned therin that krittikas were always in the east. Being a constellation close to the ecliptic this points out that they were in the equator at the time of Satapathabrahmana. The yogatara or the principal star of krittikas is at a distance of about 36° from the first point of As vim. One is forced to conclude that it was at the first point of Aries. The dolana theory allows a range of24° to 27° and the separation ofthe equinoctial point .bY 36° is not contemplated by the theory unless it is suitably amended.Thus for the time being one is better

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off with the theory of recession and there is no scope for the optimism of dolana-theorlsts. A remarkable exposition of precession is given by Munjala in the work Laghumanasa. He explains the precession ofthe equinoxes and gives the precessional rate as 59". 9 This figure is really significant. In a certain sense the estimate is startlingly accurate in the Indian context. Actually the Indian sidereal year is slightly greater than the actual value and this contributes about 9.76 in the backward direction. Adding this to the precessional constant of 50" .049 the figure works out to 59".8. Bhaskara II gives the theory of complete revolution of the equinoxes. According to him the number of revolutions in one Kalpa i.e. 437 x 107 years is 199,669. This leads to the rate of precession of 59" .9007 per annum. He follows Munjala clearly in this regard. It is surprising that some commentators of Bhaskara reject his theory and advocate the theory of oscillation of equinoxes instead. It is important to note that later writers have abandoned the theory of libration and developed the theory of recession of the equinoxes. Some Indian books on Astronomy give methods of computing the Ayanamsa. Here is a sample: The Saka year reduced by 278 and divided by 70 would give the total precession in degrees at any time. The rate of precession is 51". In this 278 saka is the zero period. This corresponds to 3457 kali or to 355 AD. There are other methods also. But a full discussion Is not attempted here.

7

Ayanamsas in the Arena The main problem is this. There is a fixed zodiac or the nirayana zodiac. The nirayana longitudes are measured from a fixed point called Meshadi. At the same time we have the sayana zodiac in which the true longitudes or say ana longitudes are measured from the first point of Aries which moves backwards at about 50".2. per annum. What is the correction required to get the nirayana longitude from the sayana longitude? The correction is called Ayanamsa and the determination of the value of Ayanamsa has given rise to many controversies mainly becS.:ul= of the divergent views on Ayanamsa. At preset$ the .-st point of Aries is at about 7th degree of Pisces: At some point of time these two zodiacs coincided and the coincidence takes place with an iriterval of about 28000 years. But when did they coincide last? From Varahamihira's Brihatsamhita (section 6 supra) one in-

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fers that the two zodiacs coincided at some point of his life or at least the difference between the two was quite insignificant during his lifetime. By reference to 427 Saka or 505 A.D. in his Panchasiddhantika for the computation, it is naturally inferred that he lived at that time. Normally it is reasonable to fix the time of coincidence of these two zodiacs in the 3rd, 4th, 5th or 6th century A.D .. From the commentary on Aryabhatiyam, we observe, that 3600 Kali which corresponds to 498/499 A.D. was the year of zero precession. This Is quite an acceptable suggestion, more so, because of the views in the Suryasiddhanta. Only when we probe further into it, new theories emerge. First of all, what is meant by Meshadi? It is a fixed point of the ecliptic or more informally a fixed, identifiable star of the zodiac. The starting point should be a bright star or at least a star which can be easily recognised. We normally expect lt In the segments of Revati or Asvlnl. It is also likely that a yogatara of these is used as the Meshadi. It is also possible that the star has now disappeared. Indian books on Astronomy give the polar longitudes of the prlnclpal stars of the various nakshatras and we can easily convert them into longi tudes. The longitudes we get here are fixed quantities, having been measured from a fixed point of the ecllptlc.A comparison of the figures with a modern star catalogue suggests the Ayanamsa. According to the Suryasiddhanta, the star Revati marks the end of Zodiac. (Paushnanthe bhagana: Smruta:)

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The Yogatara or principal star of Revati is identified with the star Zeta Piscium. The polar longitude of Revati according to Suryasiddhanta is 359o 50' and nirayana longitude is 0. Rev. Ebenezer Burgess who has made an intensive study of the Suryasiddhanta observes:'' In order to get an exact comparison of the positions of junction stars. as defined by the Hindus with those of stars contained in our catalogue, we reduced the polar longitudes and latitudes to the longitudes and latitudes by the following formula .... " • The true positions of stars compared we take from Flomsteed's catalogue Britanicus subtracting in each case 15° 42' from the longitudes there given in order to reduce them to distances from the vernal equinox of A.D. 560 assumed to coincide with the initial point ofthe Hindu sphere." According to this, Revati is the starting point and the zero precession corresponds to A.D.560. This system is known as the Raivata school( Raivatapsaksha Ayanamsa). As regards the date we should note that the Suryasiddhanta has been the basis for the longitudes of stars. If a different value for the longitude is used, the date will be different. There is another school known as Chaitrapaksha Ayanamsa. The yogatara of Chitra or Spica { Alpha Vlrginis ) has a nirayana longitude of nearly 180*. Since this is a bright star, it is likely that this was used as the point diametrically opposite to the Meshadi. From the current value of the say ana longitude of this star, we can estimate that the zodiacs coincided in 345 A.D. However. the longitudes given in various texts differ.

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The Surya siddhanta gives the longitude as 180° 40*. According to Brahmagupta this is 183• and so according to Graha-laghava. Taking these different values, different values of Ayanamsa will be obtained. The Indian book Grahalaghava takes the year 444 saka ( 522 A.D.) as the year of zero precession and 60" as the rate of annual precession. This, now a days, is of purely his tor leal interest. B.V.Raman gives the following rule, subtract 398 from the Christian era and multiply by 50" 113. The constant for precession is thus obtained. The year of zero position corre sponds to the 398 A.D. Lahiri observes in his Ephemeris, "The initial point of nirayana zodiac coincided with the mean equinoctial point. ....of the mean arrival of equinox day of 285 A.D. which occurred on Sunday. At the moment both the sayana and nirayana longitudes of the star spica were 180° 0 °3", of the mean moon 353• 31' and ofthe mean sun 360° and it was a new moon day." The calendar reforms committee of the Government of India adopted an ayanamsa of 23° 15' for the saka year 1880 to bring about a uniformity among the different Ayanamsas. The year of coinci deuce in this case is 285 A.D. Some Indian astrologers use the Ayanamsa due to Newcomb. In this system the zero position corresponds to 291 A.D. Sepharial, a western exponent of Hindu Astrology observes in his book." A Manual of Astrology" thus: " By reference to Various Sanskrit and vernacular texts, we have decided in common with many competent Pandits that zodiacs exactly coincided in the year of

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Kaliyuga 3600. And this agrees with the observation of Mihira in his Samhlta. where commenting on the phenomenon of precession of the equinoxes, he states that in his day the summer solstice coincided with the first degree ofKatakam and the winter solstice with the first degree ofMakara." Kali 3600 corresponds to 498

A.D. While writing this booklet I came across an interesting account on ayanamsa in the Astrological Magazine of August 1991. I re pro duce below a portion of the article entitled ' As it strikes Me' by Agastya in the above issue of the Astrological Magazine. • Ayanamsa. " In the sixties a number of articles on this subject contributed by well known scholars in Astrology and Astronomy appeared in these columns. Today, the generality of Astrological students follow either Lahiri or Raman. Buell Huggins ln an exclusive article written a decade ago established on the basis of a study of a number of horoscopes, the accuracy of Raman Ayanamsa. Ifthe proofofthe pudding is in the eating, then the fulfillment of a large percentage forecasts bearing on world affairs made by the Editor in these columns lends credence to the correctness of the so-called Raman Ayanamsa." The well known British astrologer Vivian Robson's observation under the caption" The Kaleidoscope" published in the November 1933 issue ofthe " The British Journal of Astrology" on Ayanamsa reproduced below should be viewed by our readers objectively.

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" The term 'Ayanamsa· may heed some explanation for those who are not conversant with Hindu Astronomy. The Hindu astrologers count their Jon • gitudes along the Zodiac of constellations, while we use the Zodiac ofsigns. By the precession of the Equinoxes the signs slip backwards through the constellations, so that our o· Aries is gradually receding from the Hindu o· Aries at the rate of a little over 50- seconds a year. The number of degrees between these points at any given date is called the Ayanamsa for that date. At first sight, it would appear to be easy to calculate this value with proper accuracy, but unfortunately the problem is one which has never been satisfactorily settled, and many different estimates are current even among the Hindus. Part of the. difficulty lies in the fact that exact Hindu starting point is not very definitely known. while differences between the Hindu and western astronomical constants add further obstacles to solution. The reason I am bringing up this matter is that I have received a very interesting letter on the subject from Mr. Henry Sellqerg. who contends that the true value of the Ayanamsa should be obtainable from the ancient Hindu chronology and Astronomy, and supports his case by calculations based upon the Delambre"s Ancient Astronomy. As the matter is one of considerable importance and De-lambre"s method has not, I think, been put before astrological students. I make no apology for appending the fol lowing details. According to the Suryasiddhanta the whole period of Cosmic evolution known as a Kalpa or day of Brahma consists of 4,320.000,000 years. This is made up of 14 Manvantaras each of306,720,000 years, together with overlap-

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ping twilight periods, each Manvantara being again sub-divided into 71 Mahayugas of 4,320,000 years. A Maht:tyuga contains four Yugas, namely the Satyayuga covertng 1,728,000 years, the Tretayuga covering 1.296,000 years the Dwaparayuga covering 864,000 years, and the Kaliyuga covering 432,000 years. The world is now in the Kali yuga of the 28th Mahayuga of the 7th Manvantara. The actual number ofyears from the beginning of cosmic evolution to the present date Is as follows: Twilight at beginning ofKalpa 1.728.000 1 ,850,688,000 6 Manvantaras 116,640.000 27 Maha-Yugas Satyayuga 1,728,000 1 ,970, 784,000 Less duration of creation 17,064,000 Times since first movement of planets to the end ofsatyayuga 1.953,720,000 Treta Yuga 1,296.000 Dwapara Yuga 864,000 Preseent year ofKali Yuga 5,034 1.955,855,000 This represents the number of years from the beginning of Cosmic Evolution to 193~ A.D. Multiplying this figure by 12 gives us 23,470.620,408 as the number of solar months expired to date. Then as the number of solar months in one Mahayuga (51.840,000) is fe be the number of inter-calary months in the same period ( 1,593.336) so is the number of solar months expired to,date to 721,384,730 which being added to

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months since creation gives us 24,192,005,138 as the number of lunar months expired. Multiplying th1s by 30 gives the number of lunar days expired as 725,760,154,140. Then as the number of lunar days in one Mahayu ga( 1603.000.080) ls to the difference between the number oflunar and solar days ( 25,082,252) so is the number of lunar dates expired to 11,356,018,190 which being subtracted from the lunar days expired gives 714,404,136,050 as the number of solar days expired. It should perhaps be mentioned here that the Hindu solar days are longer than our own, and that their value of precession is also longer than ours, being about 54.525." Using Delambre's method of conversion to arc we multiply the number of lunar days expired by 600 and divide by the number of solar days in a Mahayuga( 1,577.917.828). The result is in seconds of arc. and is equal to 271,650 complete circles plus 8s. 11" 47' 43" .From this six signs must be subtracted as there is a half circle in excess, giving 71" 47* 43" and the Ayanamsa ls three tenths of this result, namely 21 • 32'18.9". This means that o· Aries in our zodiac now coincides with Pisces go 27'41M of the constellations and incidentally, like all estimates of the Ayanamsa, it confirms the fact that the Equinox does not enter the constellation Aquarius for another six hundred years, so that astrologers who are so found of telling us that we are now entering the Aquarian age are really rather premature." " It will be noted that the Raman Ayanamsa for 1933 viz. 21 o 28*31" is very near this figure". This suggests a different line of thinking in the study of Ayanamsa.

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The choice of the most appropriate candidate has to be made after going deeply into the merits and demerits of the systems. The different Ayanamsas used and their values are given in the Appendix II.

8

Astrology sans Mythology Hitherto we have been discussing Astronomy, unequivocally acclaimed as a science. We shall now digress a bit to discuss another branch of learning, namely, Astrology. The purpose is two-fold: tlrst. to discuss the rationale of astrology and then to analyse the need to prepare the astrological documents scientifically and how this process rests on the use ofthe correct Ayanamsa. The man who raises his skeptical eyebrows and denounces astrology often does so because some western scientists also do not accept it. The real pity Is that those who criticize astrology often do not know the A B C of it. But those who really charge-sheet astrology with reasons say that astrology is not a science in the sense that Physics or Chemistry is. Whereas these sciences rest on a well-established corpus of scientific theory, they contend. astrology is not. But one should understand that as a science astrology is not deterministic, but probabilistic. From my experience I have

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found that the probability of any event indicated astrologically by a single planet or a single combination ranges generally from one third to half. One has to search for other similar astrological indications which could increase the probability. before making any prediction. The quacks are also greatly responsible for the prevalence of erroneous notions about astrology. With half-baked knowledge one sets up practice tn astrology. By sheer luck he becomes the chief astrological. councellor to a ring ofV I Ps. Because of the publicity, the press interviews him. He does not realize that he is there because his stars are good and not because of his know-ledge. He goes on saying whatever he Ukes and gives more opportunity to opponents of astrology to attack it. In this section, the author has presented different theories of astrology, old and new. While fdling in the gaps. it seems necessary to formulate an astrological theory consistent with the current scientific thought. particularly when " rising out of social deeps, astrology knocks at the doors of the universities from which it was banished three hundred years ago/ Astrology·: Genesis and Growth: The origin of astrology is as obscure as that of many other ancient sciences. Planets were worshiped by the Harrannians ofMesapo~la. Canopus and Odin were symbols of-to borrow Carlyle's phrase-"transcendent wonder". which crystallized into worship. In this connection, the author wishes to emphasize that it was not merely the worship of celestial bodies that led to

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astrology at least in India. In fact, the Indian astrologers were aware of scientific theories of astrology. But, they could not be presented to the common man for obvious reasons. Moreover, any theory could get popular acceptance only ifpresented in a semi-mythical fashion. For instance, Varahamihira says in Brihatsamhita that a rainbow is caused when the 'colours' of the Sun's rays are separated. Then he gives the mythological account of a rainbow. Also man, by nature, is interested in fairy tales. Even now there is science fiction, the counterpart of the old mythology. If scientific theories can co-exist with science fiction, certainly astrological theories can co-exist with mythology. The rejection of astrology on the basis of mythology is similar to that of science on the basis of science fiction. One of the earliest accounts of astrology is the cuneiform text Enlmu Anu Enlll( 18th to 16th century B.C.) which belongs to the Babylonian civilization. It describes celestial omens classified into four categories ruled by the gods Sin.Shamsh, Adad and Ishtar. The influence of the Babylonian text is clearly discernible in the astrological analysis of the Egyptians around the 5th century B.C. Later, Hipparchus who belonged to the Greek School made substantial contribution to the subject. The works Syntaxis and Tetrabiblos attributed to Ptolemy sum up the knowledge of Astrology acquired by the Babylonains, the Egyptians and the Greeks. The Sassanian Iran produced Pahlavi expositions of as trology, stimulated by the Hellenistic and the Indian schools. After the decline of Sassanian empire, the Islamic world promoted astrology. The Arabic texts written during that time influenced the development of

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astrology in Europe. in western Europe, learning of astrology was promoted until the emergence of the Copernican theory of planetary motion. In India, astrology is as old as the Vedic Literature. According to tradition, there are eighteen pro pounders of astrological theory, Surya ,Pitatriaha, Vyasa Vasistha Atrt.Parasara. Kasyapa.Narada,Garga. Martchi,Manu .A nglras.Romasa. Poulisa, Chyavana,Yavana,Bhrigu and So unaka. Most of the works of the above authors are not available now. There is a mention of Yavana or the Greeks, whose school is one of the eighteen. The greatest of the later astrologers is undoubtedly Varahamihira, the celebrated astronomer of Ujjaln. who flourished in the fifth century AD. Varahamihira wrote treatises on all the three branches of Jyotlsha namely Siddhanta, Hora and Samhlta. These represent astronomy, predictive astrology and mundane astrology respectively. In his Panchaslddhanthika. he describes the five systems of astronomy. In Brihajjataka. he covers the astrological literature. His Brihatsamhita deals with a wide vartety of topics and Is encyclopedic in its range. In fact. Varahamihira has summarized the earlier literature in astrology, quite intensive in analysis and extensive in range. Starting from Prithuyasas, the son of Varahamihira, there is a galaxy of eminent astrologers who have written extensively on the subject. Though some of the books fall into the category of "tales retold"; the contribution of India to astrology is enormous. From the way in which the Indian astrological literature has developed, it is clear that it is of independent origin. Such an early author Parasara deals

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with dasas (periods ) and many other concepts. which are not even contemplated by the Hellenistic school. Any attempt to trace Indian astrology to other systems appear meaningless. In this context, one is reminded or a strange theory about the Indian drama. The term 'Yavanlka' tn Sanskrit means a curtain. Some scholars trace the word to 'Yavana' and suggest a Greek origin for the Indian drama. But there Is an equivalent to Yavanika. namely 'Javanlka', which means • fastmoving' and hence a curtain. While commenting on Indian astronomy Neugebauer remarks," In spite of the pioneering work done by H.T.Colebrooke, G.Thlbaut and others the study of Hindu astronomy is still in its beginning. The mass of uninvestigated material in Indian as well as Western collections is enormous. May lt suffice to remark that many hundreds of planetary tables are easily accessible in American libraries. So far. only a preliminary study of this material has been made revealing a great number of parameters for lunar and planetary tables. The planetary tables themselves are of great extent and based on methods., so far not encountered in Western material, the basic idea being that the planetary positions are computed for the whole year as a function of the initial condi tions at the entry. of the sun into Arles;" Very little is known even about the published literature. For instance, ln hls Siddhanta slromanl. Bhaskara ( c.llSO A.D.) refers to the gravita tiona) force of the earth. Books on the history of Astronomy generally do not refe'- to this. It seems that these books are based not on original Sanskrit texts, but on mistranslations and mischievous misinterpreta-

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tlons. To a great extent, all these remarks apply to astrology too.

Astrological Theories : Old and New Some people regard astrology as a branch of philo-sophy: some consider it as a pseudo-science; and some others, as an off-shoot of mythology or necromancy. These diverse notions prevail because ofthe several theories of astrology and the ways they are presented. According to Babylonians, astrology is not deterministic, but indicative. They believed that the evil influence of planets could be mitigated by ritualistic means. Bardasanes. a Christian Scholar opines that the motion of planets can affect only the elemental world and not the soul. Ptolemaic astrologers interpreted astrology in terms of Platonic or Aristotelian theory concerning the earth as the centre of the planetary system. Hindu Astrology is based on the theory of Karma. There are three kinds of karma or deed, namely Prarabdha, Sanchita and Agami. Prarabdha refers to the actions, the effects which have started. sanchita refers to the hidden, and agami to be acquired ln future. The horoscope is only the balance-sheet of one's karma at the time of birth. The soul ls eternal and it undergoes the cycle of births and deaths until the final emancipation. The real merit o£-the Hindu theory lies in the fact that it is not based on any astronomical theory. but on some philosophical concepts. In fact, such expressions

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as the baneful influence of Mars are inaccurate in Hindu Astrology. The planets do not influence any body direct, but indicate certain types of karma, which are really responsible for all that is encountered in one's life. The theory would be complete if the correspondence between planets and karma is defined. Hindu astrology does define a correspondence, but the discussion of details would take us far afield. But the question Is this: is it possible to formulate a theory that is not alien to the current scientific thought? Once time Is accepted as a dimension, the problem is quite simple. The time of birth is an important factor, man is an entity in space-time and the birth of an individual is an event. The time is recorded by the planetary position at the time of birth. as observed from the place of birth. In short, the planetary system serves as a clock. The question now is how to use the planetary configuration. We start with an astrological experiment. It is said in books on astrology that the Sun in the ascendant affects vision. The rule was tested by the author himself with a collection of 100 horoscopes. It was found that in 65 cases it was true. In the remaining there were counteracting influences, and experimental errors. The astrological analysis is not based on an isolated combination as the Sun in the ascendant, but the swn•total of all the important combinations. To analyse the effects of an isolated combination, one has to use the techniques of experimental designs. Once proves successful, a general rule can be formulated, by ind~tlve reasoning. Thus we conclude that the Sun in the ascendant affects \