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Dulakara Ayanamsha – A NEW CONCEPT ON AYANAMSA

Buddhike Sri Harsha Indrasena* April 6, 2011 (revised May 22, 2011)

Warning: All copyrights are reserved with the author. The article cannot be reproduced in any form, in part or

in whole, without expressed permission from the author. 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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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.

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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 REF. AYANAMSA Y.O.C. MOON Fagan/Bradley SE -24 d 50 m 10 s 221 AD 16d Sag 0 m Lahiri SE -23 d 57 m 10 s 285 AD 16d Sag 14 mDe Luce SE -27 d 54 m 19 s 1 BC 12d Sag 56 mRaman SE -22 d 30 m 24 s 389 AD 18d Sag 20 mSassanian SE -20 d 05 m 20 s 564 AD 20d Sag 45 mUshashashi SE -20 d 09 m 11 s 559 AD 20d Sag 41 mHipparchos SE -20 d 20 m 34 s 545 AD 20d Sag 30 mDjwhal Khool SE -28 d 27 m 19 s 41 BC 12d Sag 23 mYukteshwar SE -22 d 34 m 28 s 292 AD 18d Sag 16 mJN Bhasin SE -22 d 51 m 28 s 364 AD 17d Sag 59 mBabylonian, Huber SE -24 d 43 m 43 s 229 AD 16d Sag 07 mBabylonian, Kugler 1 SE -25 d 55 m 43 s 143 AD 14d Sag 55 mBabylonian, Kugler 2 SE -24 d 31 m 43 s 243 AD 16d Sag 19 mBabylonian, Kugler 3 SE -23 d 40 m 43 s 305 AD 17d Sag 10 mBabylonian, Mercier SE -24 d 37 m 03 s 237 AD 16d Sag 13 mGalactic Center SE -26 d 56 m 55 s 69 AD 13d Sag 53 mKrishnamurti SE -23 d 51 m 22 s 292 AD 16d Sag 59 mAldebaran at 15 Taurus SE -24 d 51 m 16 s 220 AD 15d Sag 59 mChandra-Hiri PC -24 d 40 m 43 s 233 AD 16d Sag 10 mTarun Chopra PC -11 d 53 m 43 s 1153 AD 28d Sag 57 mDhira PC -23 d 09 m 48 s 342 AD 17d Sag 41 mKrushna PC -23 d 02 m 54 s 350 AD 17d Sag 47 mWilhelm Ardra PC -23 d 30 m 16 s 317 AD 17d Sag 20 m

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

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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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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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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

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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 Star Spica AYANAMSHA Y.O.C. Dulakara 29°26'22" Virgo -24 d 31 m 35s 244 AD Fagan/Bradley 29° 06' 05" Virgo -24 d 50 m 10 s 221 AD Lahiri 0° Libra -23 d 57 m 10 s 285 AD Babylonian, Huber 29° 14' Virgo -24 d 43 m 43 s 229 AD Babylonian, Kugler 1 -25 d 55 m 43 s 143 AD Babylonian, Kugler 2 29° 26' Virgo -24 d 31 m 43 s 243 AD Babylonian, Kugler 3 -23 d 40 m 43 s 305 AD Babylonian, Mercier 29° 21' Virgo -24 d 37 m 03 s 237 AD

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

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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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Appendix

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

00.00 Hours GMT)

Ayanamsa Year Deg Min Sec

1900 23 02 22 1901 23 03 10 1902 23 03 57 1903 23 04 42 1904 23 05 26 1905 23 06 11 1906 23 06 56 1907 23 07 42 1908 23 08 30 1909 23 09 20 1910 23 10 12 1911 23 11 05 1912 23 12 00 1913 23 12 56 1914 23 13 52 1915 23 14 47 1916 23 15 41 1917 23 16 35 1918 23 17 27 1919 23 18 16 1920 23 19 03 1921 23 19 50 1922 23 20 35 1923 23 21 19 1924 23 22 03 1925 23 22 49 1926 23 23 36 1927 23 24 24 1928 23 25 15 1929 23 26 08 1930 23 27 02 1931 23 27 57 1932 23 28 53 1933 23 29 49 1934 23 30 44 1935 23 31 38 1936 23 32 31 1937 23 33 22 1938 23 34 10 1939 23 34 57

Ayanamsa Year Deg Min Sec

1940 23 35 43 1941 23 36 28 1942 23 37 12 1943 23 37 56 1944 23 38 43 1945 23 39 30 1946 23 40 19 1947 23 41 11 1948 23 42 04 1949 23 42 59 1950 23 43 54 1951 23 44 50 1952 23 45 46 1953 23 46 41 1954 23 47 34 1955 23 48 26 1956 23 49 16 1957 23 50 04 1958 23 50 50 1959 23 51 36 1960 23 52 20 1961 23 53 05 1962 23 53 50 1963 23 54 37 1964 23 55 25 1965 23 56 15 1966 23 57 07 1967 23 58 01 1968 23 58 56 1969 23 59 52 1970 24 00 47 1971 24 01 43 1972 24 02 38 1973 24 03 30 1974 24 04 21 1975 24 05 11 1976 24 05 58 1977 24 06 44 1978 24 07 29 1979 24 08 13

Ayanamsa Year Deg Min Sec

1980 24 08 58 1981 24 09 43 1982 24 10 31 1983 24 11 20 1984 24 12 10 1985 24 13 03 1986 24 13 58 1987 24 14 53 1988 24 15 49 1989 24 16 45 1990 24 17 40 1991 24 18 34 1992 24 19 26 1993 24 20 17 1994 24 21 05 1995 24 21 52 1996 24 22 37 1997 24 23 22 1998 24 24 06 1999 24 24 51 2000 24 25 37 2001 24 26 25 2002 24 27 15 2003 24 28 07 2004 24 29 00 2005 24 29 55 2006 24 30 51 2007 24 31 46 2008 24 32 42 2009 24 33 37 2010 24 34 30 2011 24 35 22 2012 24 36 11 2013 24 36 59 2014 24 37 45 2015 24 38 30 2016 24 39 15 2017 24 39 59 2018 24 40 45 2019 24 41 31