Dulakara+Ayanamsa

Research Article

Dulakara Ayanamsha – A NEW CONCEPT ON AYANAMSA Buddhike Sri Harsha Indrasena * April 6, 2011 (revised May 22, 2011)

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 Abstract  Objective:

To find out correct ayanamsha.

  Principles:

1.” Beginning of Aries rises when star Spica sets” – Hipparchus 2. Jupiter – sun cycle of Persian astronomy/astrology

  Results:

Zero ayanamsha year AD 244  Ayanamsha for 29th March 2011 at 0.00 GMT based on true precession of equinox is 24° 35' 34"

Introduction Correct ayanamsha for a given year is the single most important component in sidereal astrology and is a hot topic of debate. A sidereal system is used in Hindu astrology. Among western astrologers tropical zodiac is  popular. Sidereal longitudes of planets are not calculated directly at present but by subtracting the ayanamsha from the tropical longitudes which are formulated precisely by modern astronomy. In Sidereal astrology zodiac is defined based on the fixed stars in sky round the earth (Fig 1).

Fig 1: Sidereal Zodiac

*

Dr. B S H Indrasena (MBBS, MS) is a consultant surgeon from Sri Lanka.

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Research Article In Tropical astrology the zodiac is defined based on the position of vernal equinox, i.e. the equinox that the Sun  passes from south to north (Fig 2). As the rotational axis of the Earth is not perpendicular to its orbital plane, † the equatorial plane is not parallel to the ecliptic plane , but makes an angle of about 23°26'. The celestial equator and the ecliptic are the imaginarily projected terrestrial equatorial and ecliptic planes respectively out ‡ into the celestial dome . The intersection line of the two planes results in two diametrically opposite intersection points, known as the equinoxes. The equinox that the Sun passes from south to north is known as the vernal equinox or first point of Aries and the opposite point is known as autumnal equinox or first point of  Libra. Sign Aries starts at vernal equinox or first point of Aries and other signs are named every 30 degrees around the ecliptic in the celestial dome irrespective of the arrangement of the fixed stars (Fig 2).

Fig 2: Tropical Zodiac

Therefore the starting point of tropical zodiac is definitive and can be calculated with high degree of precision (Fig 2). But the sidereal zodiac is only a circle of stars in the ecliptic and there is no intersection point as in tropical zodiac the location of starting point of sidereal zodiac/Aries has to be defined by other means (Fig 1). The Earth wobbles in space like an out-of-balance top. The reason for the slow wobble is that the Earth is not a   perfect sphere. The equatorial diameter of the Earth is larger than the polar diameter. Each full wobble takes about 25,765 years. Because of the slow change in earth’s orientation to the stars, the position of the Sun on the first day of spring (the vernal equinox) slowly shifts westward around the sky at a rate of 50.29” arc seconds  per year with respect to the fixed stars (Fig 3). This phenomenon is called precession of equinox.

†

Ecliptic plane is the geometric plane containing the mean orbit of the Earth around the Sun. Celestial sphere is an imaginary sphere of arbitrarily large radius, concentric with the Earth and rotating upon the same axis. All objects in the sky can be thought of as projected upon the celestial sphere. ‡

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Fig 3: Precession of equinox

As a result of moving vernal equinox, longitude of a fixed body, such as fixed stars of sidereal zodiac, defined with respect to vernal equinox will change (increase) slowly (Fig 4). On the other hand, since the stars "hardly ever move with respect to the other stars” (ignoring the effect of proper motion) the longitude of a fixed  body/point (or the point of beginning of sidereal Aries) defined with respect to stars will never change.

Fig 4: Moving vernal equinox

At one point of time the starting point of Aries of movable tropical zodiac and the same of the fixed sidereal zodiac overlapped, and started drifting apart relative to each other at a rate of about 1.4 arc degrees per century. 3

Research Article Earlier Greek astronomers like Eudoxus spoke of vernal equinox i.e. starting point of tropical zodiac, at 15° in Aries of sidereal zodiac, while later Greeks spoke of vernal equinox at 8° and then 0° in Aries. The latter is the  point of time when tropical zodiac coincided exactly with the sidereal zodiac. The sidereal zodiac was used in Greece before Ptolemy and Hipparchus. The precession of equinox was discovered by Hipparchus, and later  tropical system was introduced by Ptolemy in the 2nd century and remains prevalent in western astrology to date. Since the point of vernal equinox (the starting point of tropical Aries) is precise and unambiguous and can be calculated with certainty, astronomers use this point to calculate planetary longitudes. Vedic astrologers who use sidereal position of planets for predictions subtract the range of separation of two zodiacs, which is called ayanamsha, to obtain the sidereal longitudes of planets rather than making their own calculations. The correct ayanamsha is debatable because no ancient text has exactly defined the zero ayanamsha year, i.e. the year of coincidence of two zodiacs. The official ayanamsha approved by the Government of India since 1952 is that of Lahiri who believed that zero ayanamsha year was 285AD, and this is also the official ayanamsha in Sri Lanka. Whereas Fagan - Bradley ayanamsha is popular among sidereal astrologers who   practise astrology in west and they believe that the zero ayanamsha year was 221 AD. These are just two examples of controversy and there are more than 25 different ayanamshas proposed by different scholars as given below in Table 1 (4). Table 1 Overbeck's comparison of 23 Ayanamsa Values at 27 October 2006§

The table includes the source of the ayanamsa, the reference (SE = Swiss Ephemeris, PC = Personal Communications), the Year of  Coincidence and the values for the ayanamsas and the moon calculated for 6:46:04 PM on 27 October 2006 at 32±N 150, 97±W 460, TZ +5

SOURCE Fagan/Bradley Lahiri De Luce Raman Sassanian Ushashashi Hipparchos Djwhal Khool Yukteshwar JN Bhasin Babylonian, Huber Babylonian, Kugler 1 Babylonian, Kugler 2 Babylonian, Kugler 3 Babylonian, Mercier Galactic Center Krishnamurti Aldebaran at 15 Taurus Chandra-Hiri Tarun Chopra Dhira Krushna Wilhelm Ardra

§

REF. SE SE SE SE SE SE SE SE SE SE SE SE SE SE SE SE SE SE PC PC PC PC PC

AYANAMSA -24 d 50 m 10 s -23 d 57 m 10 s -27 d 54 m 19 s -22 d 30 m 24 s -20 d 05 m 20 s -20 d 09 m 11 s -20 d 20 m 34 s -28 d 27 m 19 s -22 d 34 m 28 s -22 d 51 m 28 s -24 d 43 m 43 s -25 d 55 m 43 s -24 d 31 m 43 s -23 d 40 m 43 s -24 d 37 m 03 s -26 d 56 m 55 s -23 d 51 m 22 s -24 d 51 m 16 s -24 d 40 m 43 s -11 d 53 m 43 s -23 d 09 m 48 s -23 d 02 m 54 s -23 d 30 m 16 s

Y.O.C. 221 AD 285 AD 1 BC 389 AD 564 AD 559 AD 545 AD 41 BC 292 AD 364 AD 229 AD 143 AD 243 AD 305 AD 237 AD 69 AD 292 AD 220 AD 233 AD 1153 AD 342 AD 350 AD 317 AD

MOON 16d Sag 0 m 16d Sag 14 m 12d Sag 56 m 18d Sag 20 m 20d Sag 45 m 20d Sag 41 m 20d Sag 30 m 12d Sag 23 m 18d Sag 16 m 17d Sag 59 m 16d Sag 07 m 14d Sag 55 m 16d Sag 19 m 17d Sag 10 m 16d Sag 13 m 13d Sag 53 m 16d Sag 59 m 15d Sag 59 m 16d Sag 10 m 28d Sag 57 m 17d Sag 41 m 17d Sag 47 m 17d Sag 20 m

Table taken from the Ayanamsa Statistical Study, Buz Overbeck, 2007 (4)

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Research Article

Background  It is my personal opinion that Lahiri ayanamsha (the only ayanamsha used by almanac makers of Sri Lanka at  present) is not capable of giving precise sidereal longitudes of heavenly bodies. Horoscope readings and Dasha   predictions done based on Lahiri ayanamsha goes wrong at many times. Further Lahiri ayanamsha fails significantly in divisional chart analysis and birth time rectification. The results seem to be better than Lahiri if Fagan-Bradley ayanamsha is used in combination with 360 day Savana year. Even better is Chandrahari ayanamsha plus 360 day Savana year, which gives much better results in divisional chart analyses and birth time rectifications but still with a few exceptions once in a while. The Babylonian-Huber and Babylonian-Mercier ayanamshas are closer to Chandrahari. I believed that the correct ayanamsha should be found somewhere in this range. When doing an internet search recently to find out the basis of Babylonian astronomy and the work of Huber  and Mercier, I came across the teachings of great Greek astronomer Hipparchus.

Hipparchus Hipparchus was born in Nicaea in Bithynia, but spent much of his life in Rhodes of Greece. His recorded observations span the years 147 to 127 BC. Virtually all his writings are lost to date. The Almagest, written by Ptolemy (second century A.D.) is the source of most of our knowledge about Hipparchus. Ptolemy made extensive use of the work of Hipparchus, building on the foundation laid by him. Almost all of the work of  Hipparchus is therefore derived today from this book of Ptolemy. One of the greatest discoveries of Hipparchus was precession of equinox. He vaguely concluded that the rate of   precession was not less than 1° in a century. However it was Isaac Newton, in the 17th century, who produced the first full theoretical explanation of precession, and accurately calculated its annual rate. The star Spica is  believed to be the star that provided Hipparchus with the data which enabled him to discover precession of the equinoxes. Spica (Alpha Virginis, Citra Nakshatra in Vedic astrology) is the brightest star in the constellation of Virgo, and the 15th brightest star in the nighttime sky (Fig 5).

Fig 5: Location of Spica

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Research Article Hipparchus made extensive observations of star positions, and is credited with the production of the first known catalogue of stars. Based on the observation made by Hipparchus on star Spica he concluded that “beginning of  Aries rises when Spica sets” (1). This sentence was the sole basis of the title of this paper. It is quite interesting that Hipparchus does not give an exact value to the position of Spica or any other star. Rather he recorded the observations he made about the relative position of stars. In his star catalogue he recorded the position of a quite large number of stars by comparing the placement of a particular star with another point or another star of the sky. He plainly recorded his observations rather than recording the speculations on it. Therefore we can take his work as unaltered virgin data which can be safely used for  experiments. These observations actually inspired the later astronomers like Ptolemy, Isaac Newton and others in their experiments.

Materials and Method  1. Observations of Hipparchus The observation of Hipparchus of interest of this article relates the location of zero point of Aries to star Spica. Hipparchus meekly and plainly said that Aries rose when Spica set. Therefore it is needless to say that if the location of Spica is known, 0° Aries can easily be speculated. Since Aries has been defined in relation to a star, this is the sidereal 0° of Aries. At zero ayanamsha year both sidereal and tropical longitudes coincide. Therefore in zero ayanamsha year the tropical longitude of Spica must be as same as sidereal longitude of Spica that Hipparchus observed. Tropical longitudes of stars are accessible today through astronomical calculations. Therefore the year when tropical longitude of Spica is as same as the sidereal longitude of Spica that Hipparchus observed would be the zero ayanamsha year.

2. Sun-Jupiter Cycle and Zero ayanamsha year  To verify the zero ayanamsha year obtained from the observations of Hipparchus I considered Sun-Jupiter  conjunction cycle and its relationship with zero ayanamsha year proposed by ancient Persian astrologers. According to an article circulating in internet “like the Sun and Moon opposition and conjunctions form the natural cycle for a month, Jupiter and Sun conjunction/opposition create a natural cycle defining not only a year   but also the entire precessional cycle of 25800 years”(2). Accordingly at the time of coincidence of two zodiacs Sun and Jupiter must be either in conjunction or opposition. Since at vernal equinox Sun is at the beginning of  Aries, Jupiter should be either in beginning of Aries or Libra.

Calculations What was the longitude of Star Spica that was observed by Hipparchus? Since Aries and Libra are opposing signs in the Zodiac one might place it on 0°of Libra which is exactly 180° opposite to 0° of Aries. But this is wrong. We must understand that what Hipparchus recorded was just what he perceived with the naked eye probably supplemented by simple instruments, such as dioptra and astrolabe, available at that time. It was his OBSERVATION or what he saw at night sky while sitting at Rhodos of Greece at latitude of 39°N. It is assumed here that Hipparchus made his observations at an altitude of zero i.e. at sea level. Due to atmospheric refraction what we see at horizon is not exactly located on a horizontal plane. Light rays bend due to the influence of atmosphere and what we see at the horizon is actually a few arc minutes beyond the exact horizontal plane (Fig 6). The refractive index depends on environmental temperature and elevation of the object from horizon.

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Research Article

Fig 6: Refraction of light by atmosphere

At 39° north of equator in Rhodes the average atmospheric temperature in March at present is 13.6°C. For these values the refractive index at sea level is 33.37 ' (3). When calculating the ascending degree or Lagna point for  astrological purposes the refraction is not considered. Further it is unlikely that Hipparchus was able to observe  both east and west horizons at the same time. He must have observed the setting of Spica in West but calculated the rising degree in East. Therefore at the time when beginning of Aries rises in East we cannot expect one to see the 0° of Libra to descend at the Zenith. It will be 33.37 ' arc minutes beyond the horizon. Therefore what Hipparchus saw on the western horizon when Spica was setting was actually NOT 0° Libra BUT 29° 26.23 ' Virgo. Therefore it can be concluded that during the time of Hipparchus the star Spica was at 29°26'13.8"Virgo.

Results Since this is an observation made in relation to the actual stars in night sky this can be considered as sidereal longitude of Aries and Spica. The zero ayanamsha year is defined as the time of coincidence of zero points of    both tropical and sidereal zodiacs. That is both sidereal and tropical longitudes will be the same and the ayanamsha on that day will be zero. Since the starting point of sidereal zodiac is not known precisely, and the  purpose of this study is to find out the starting point of sidereal zodiac, we cannot rely on any available sidereal longitudes of star Spica. Rather we must depend on the tropical longitudes devised by modern astronomers with a high degree of precision. At the time of zero ayanamsha year the sidereal longitude must be as same as tropical longitude. Since the starting point of tropical longitude is the vernal equinox, the exact time of  coincidence will be on the day of vernal equinox of a given year. To calculate the tropical longitude of star Spica I used ZET 9.1 software and the proper motion of star Spica was disregarded. Vernal equinox was calculated using the same software. I found that on the day of vernal equinox of AD 244, i.e. March 20, 244 AD at 18.46.54 hours GMT, the tropical longitude of Spica was 29° 26'22". This is almost as same as sidereal longitude of Spica at the time of Hipparchus i.e. at 29°26 '13.8" Virgo. You can notice that there is a discrepancy of just 12 " arc seconds between the tropical longitude of Spica in AD 244 and the sidereal longitude of Spica that was observed by Hipparchus. Since the evidence of Hipparchus comes from an observation made more than 2000 years ago, and if this were a rough approximation, it is also 7

Research Article  possible that the Zero ayanamsha year is either 243AD or 245AD or any other year around 244AD.According to the work of ancient Persians (as described earlier), at the time of coincidence of the two zodiacs, there should  be a close Sun – Jupiter conjunction. Sun-Jupiter conjunction cycles occur every 12 years. At vernal equinox of  244AD, when the tropical Sun was at 0°00'00" of Aries, the Jupiter was at 5° 4 ' in Aries, just 5° apart. The next Sun-Jupiter conjunction in Aries would be either in 232AD or 256AD which are far more distant from 244AD year. Neither in 243AD nor 245AD vernal equinox there is Sun – Jupiter conjunction or opposition. Even if we consider the proper motion of star Spica, which is only a few arc seconds per 1000 years, 244AD satisfy best as the zero ayanamsha year.

Discussion It can be seen that this is a quite simple but logical method of defining the starting point of sidereal zodiac. The technique I used was as simple as the observations made by the Hipparchus. It is interesting to note that an ayanamsha value by his name of Hipparchus is already in use. This has been calculated by Raymond Mercier    based on Ptolemy’s accounts in Almagest. Rather than taking Spica, he has used star Zeta Piscium as the reference point. However this ayanamsha differs quite significantly from the ayanamsha that I propose. According to Mercier’s ‘Hipparchus ayanamsha’ the Zero ayanamsha year is 545AD. Therefore to differentiate from Mercier’s Hipparchus ayanamsha, I propose the name “Dulakara ayanamsha” for what I found. The literal meaning of ‘Dulakara’ in Sinhalese language is ‘Sun’, which compares quite well with precession of equinox, which is based on the apparent movement of Sun along the ecliptic. Foregoing (Table 2) is a comparison of different ayanamshas suggested by different authors using star Spica as reference point. The ayanamshas given are as at 27 October 2006(4). Table 2 Comparison of Dulakara ayanamsha with other ayanamshas based on star Spica (Y.O.C – Year of coincidence of two zodiacs)

SOURCE Dulakara

Star Spica 29°26'22" Virgo

AYANAMSHA -24 d 31 m 35s

Y.O.C. 244 AD

Fagan/Bradley

29° 06' 05" Virgo

-24 d 50 m 10 s

221 AD

Lahiri Babylonian, Huber  Babylonian, Kugler 1 Babylonian, Kugler 2 Babylonian, Kugler 3 Babylonian, Mercier 

0° Libra 29° 14' Virgo

-23 d 57 m 10 s -24 d 43 m 43 s -25 d 55 m 43 s -24 d 31 m 43 s -23 d 40 m 43 s -24 d 37 m 03 s

285 AD 229 AD 143 AD 243 AD 305 AD 237 AD

29° 26' Virgo 29° 21' Virgo

The Spica/Citra and Lahiri Ayanamsha Lahiri ayanamsha is based on the assumption that star Spica is located at 0 degrees of Libra as given in Surya Siddhantha. The year of coincidence of two zodiacs according to Lahiri is 285 AD. It is well known to the  present day astrologers that the calculations in Surya Siddhantha are only approximations and even the concept of precession of equinox was not correct. Further the author of Surya Siddhantha by himself advised to make corrections to longitudes of planets by observing the sky from time to time. Therefore, in my opinion, it is not  prudent to rely on Surya Siddhantha to calculate ayanamsha.

Fagan-Bradley Ayanamsha After going through old Babylonian astrology, Fagan and Bradley in 1950s defined their ayanamsha. They calculated the location of Spica as 29°06'05" in Virgo, without taking proper motion of the star into 8

Research Article consideration (For the year 100 BC, this ayanamsha places Spica at 29° 07 '32" Virgo). According to them the year of coincidence of two zodiacs is 221AD.

Babylonian Kugler, Huber and Mercier Ayanamshas In 1900 F. X. Kugler, according to planetary tablets recorded by ancient Babylonians, categorized Babylonian star positions into three sets. In set 2 he postulated the position of Spica as at 29° 26 ' of Virgo. Peter Huber in 1958, reviewed the same planetary tablets in the light of new materials found and concluded that the sidereal longitude of Spica was 29° 14 ' Virgo. Still later in 1977 Raymond Mercier after going through Babylonian star tablets and concepts, used the star  Zeta Piscium to find the location of star Spica and placed it at 29° 11 ' of Virgo.

Dulakara Ayanamsha It is interesting to note that Dulakara and Kuglar 2 ayanamshas are almost the same. The year of coincidence of  Dulakara ayanamsha is 244AD, and according to Kuglar 2 ayanamsha it is 243AD. The raw data for the former  comes from the work of Hipparchus whereas for the latter it is Babylonian astronomy. Babylonian astronomy is older than Greek astronomy. Various claims have been made that Babylonians and Egyptians had discovered  precession of equinoxes even before Hipparchus. It is possible that Hipparchus' used Babylonian astronomical material, including methods as well as observations, to some extent in his studies. Certain historians actually  believe that Hipparchus' work provides a link between Babylonian and Greek astronomy. Therefore it is not a surprise that Kuglar 2 and Dulakara ayanamshas are almost same because the basis of the calculations is  probably has a similar origin. Anyhow this is the first time that one can find two ayanamshas calculated using two different techniques giving almost the same results. In the presence of supporting evidence from Babylonian Kugler 2 ayanamsha, it is my sincere belief that Dulakara ayanamsha is the most precise ayanamsha that has ever been proposed. It is not just another ayanamsha but it is THE ayanamsha that everybody has been in search for for centuries. However  readers need not stop from here but should continue to research on this important topic either to refute/support the Dulakara ayanamsha or to come out with a better one. See the Appendix for a Table of Dulakara Ayanamsa for a period of 120 years, which has been prepared with the help of Zet 9.1 free software (yearly rate of precession is not static because Nutation of zodiac has been ** taken into account) .

References 1. http://www.astro.com/swisseph/swisseph.htm 2. http://groups.yahoo.com/group/ancient_indian_astrology/message/1166 3. http://wise-obs.tau.ac.il/~eran/Wise/Util/Refraction.html 4. http://home.windstream.net/overbeck/AyanStat.pdf  5. http://www.encyclopedia.com/topic/astrolabe.aspx 6. http://www.hps.cam.ac.uk/starry/hipparchus.html 7. All the diagrams were copied from Google image search

**

Nutation (in longitude) accounts for perturbations in the position of the Vernal Point which is brought about by gravitational impact of our Sun and Moon upon the Earth.

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Research Article Appendix

Table of Dulakara Ayanamsa (Computed with the help of Zet 9.1.31 software, using true precession of zodiac for 1 st of January each year, at 00.00 Hours GMT) Year

Ayanamsa Deg Min

Sec

Year

Ayanamsa Deg Min

Sec

Year

Ayanamsa Deg Min

Sec

1900 1901

23 23

02 03

22 10

1940 1941

23 23

35 36

43 28

1980 1981

24 24

08 09

58 43

1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914

23 23 23 23 23 23 23 23 23 23 23 23 23

03 04 05 06 06 07 08 09 10 11 12 12 13

57 42 26 11 56 42 30 20 12 05 00 56 52

1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954

23 23 23 23 23 23 23 23 23 23 23 23 23

37 37 38 39 40 41 42 42 43 44 45 46 47

12 56 43 30 19 11 04 59 54 50 46 41 34

1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994

24 24 24 24 24 24 24 24 24 24 24 24 24

10 11 12 13 13 14 15 16 17 18 19 20 21

31 20 10 03 58 53 49 45 40 34 26 17 05

1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927

23 23 23 23 23 23 23 23 23 23 23 23 23

14 15 16 17 18 19 19 20 21 22 22 23 24

47 41 35 27 16 03 50 35 19 03 49 36 24

1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967

23 23 23 23 23 23 23 23 23 23 23 23 23

48 49 50 50 51 52 53 53 54 55 56 57 58

26 16 04 50 36 20 05 50 37 25 15 07 01

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

24 24 24 24 24 24 24 24 24 24 24 24 24

21 22 23 24 24 25 26 27 28 29 29 30 31

52 37 22 06 51 37 25 15 07 00 55 51 46

1928 1929 1930

23 23 23

25 26 27

15 08 02

1968 1969 1970

23 23 24

58 59 00

56 52 47

2008 2009 2010

24 24 24

32 33 34

42 37 30

1931 1932 1933 1934 1935 1936 1937 1938 1939

23 23 23 23 23 23 23 23 23

27 28 29 30 31 32 33 34 34

57 53 49 44 38 31 22 10 57

1971 1972 1973 1974 1975 1976 1977 1978 1979

24 24 24 24 24 24 24 24 24

01 02 03 04 05 05 06 07 08

43 38 30 21 11 58 44 29 13

2011 2012 2013 2014 2015 2016 2017 2018 2019

24 24 24 24 24 24 24 24 24

35 36 36 37 38 39 39 40 41

22 11 59 45 30 15 59 45 31

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