Dulakara Ayanamsha – A NEW CONCEPT ON … · Babylonian, Huber 24° 47' 56" 229 AD 15° Sag 25'...
Transcript of Dulakara Ayanamsha – A NEW CONCEPT ON … · Babylonian, Huber 24° 47' 56" 229 AD 15° Sag 25'...
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I started reading on Vedic astrology when I
was 15 years old. I learnt by self study. In
addition to classic Vedic astrology I am also
interested in Western astrology, Magi
Astrology and a few modern variants of
Vedic astrology. I incorporate and blend all
branches of astrology known to me when
analysing charts which I do as a hobby at
leisure time and am a consultant surgeon by
profession. The best single word that I can
find as of today to describe astrology is
"Astrology is a Science", and as such we
should not stick ourselves only to ancient
texts.
Email id [email protected]
A New Concept On Ayanamsa
By
Buddhike Sri Harsha Indrasena,
Sri Lanka
Abstract
Objective: To find out correct ayanamsha.
Materials: “Beginning of Aries rises when
star Spica sets” – Hipparchus
Principles: Atmospheric refraction
Results: Zero ayanamsha year is 244 AD
Ayanamsha for 1st January 2011 at 00
00 GMT based on true precession of
equinox is 24° 35' 22"
Introduction
Sidereal and Tropical Zodiac sidereal system is used in
Vedic astrology. Among
western astrologers tropical
zodiac is popular.
In Sidereal astrology, zodiac is defined
by the fixed stars in sky round the earth.
The zodiac starts undisputedly with
Aries, a constellation of stars which is
visible in night sky. But in this „circle‟ of
stars of sidereal zodiac the exact starting
point or 0° of Aries is debatable.
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In Tropical astrology the zodiac is defined by the position of vernal equinox, i.e. the
equinox that the Sun passes from south to north. Sign Aries or 0º of Aries starts at vernal
equinox and the other signs are named every 30° around the ecliptic in the celestial dome
irrespective of the arrangement of the fixed stars.
The equinoxes are formed as follows: 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, in the celestial dome. The equinox
that 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.
The starting point of tropical zodiac is definite and can be calculated with high degree of
precision. The sidereal zodiac is only a circle of stars in the ecliptic and there is no
intersection point as in tropical zodiac. Therefore the location of starting point of sidereal
zodiac has to be defined by other means. The aim of this article is to define the starting
point of Aries with respect to star Spica.
Precession of Equinoxes nlike the starting point of sidereal zodiac, which is fixed, the starting point of
tropical zodiac, or vernal equinoctial point, is not fixed because of the slow
change in earth‟s orientation to the stars. The position of the Sun on the first
day of spring (vernal equinox) slowly shifts westward around the sky at a rate of 50" arc
seconds per year with respect to the fixed stars. This phenomenon is called precession of
equinoxes.
Aristarchus of Samos (280 BC) is the earliest known astronomer to recognize and assess
the precession of the equinoxes. About 150 years later Hipparchus proposed that the rate of
precession of equinoxes was 46" per year. Hipparchus’s value is a good one compared with
the modern value of 50".
It was Sir Isaac Newton in the 17th century who produced the first full theoretical
explanation of precession and accurately calculated its annual rate (50.29" arc seconds per
year). The Earth wobbles in space like an out-of-balance top. The reason for the slow
* 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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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 25,772 Julian years‡.
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. 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.
Ayanamsha
he range of separation of two zodiacs is commonly known as ayanamsha
(Sanskrit - ayanāṃśa: ayana "movement" + aṃśa "component"), or precession.
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°, then 0° in Aries. The latter is the point of time when tropical zodiac
coincided exactly with the sidereal zodiac. This year is known as Zero ayanamsha year
(Figure 1).
Fig 1: Diagram showing the westward shift of the vernal equinox among the stars over the past six millennia
‡ In astronomy, a Julian year is a unit of measurement of time defined as exactly 365.25 days of 86,400 SI seconds per
day, totaling 31,557,600 seconds. Julian year measures duration of time rather than designating a date.
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The two zodiacs drift apart relative to each other at a rate of about 1.4° per century. The
sidereal zodiac was used in Greece before Ptolemy and Hipparchus. Tropical system was
introduced by Ptolemy and remains prevalent in western astrology.
Since the point of vernal equinox (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, rather than making their own calculations, alternatively subtract ayanamsha
from tropical position of heavenly bodies to obtain the sidereal longitudes of planets.
The correct ayanamsha for a given time is debatable. The official ayanamsha approved
by the Government of India since 1950s is that of N.C. Lahiri who believed that zero
ayanamsha year was 285 AD. Whereas Fagan - Bradley ayanamsha is popular among
astrologers who practise sidereal astrology in west and they believe that the zero
ayanamsha year is 221 AD. This is just an example of controversy and there are more
than 20 different ayanamshas proposed by different scholars. The sidereal longitudes of
planets are directly influenced by variable ayanamshas as shown below for Sun (Table 1).
Table 1: Comparison of longitude of Sun based on 20 different Ayanamsha Values on 1st
of January 2011 at 00 00 hours GMT
(Z.A.Y. – Zero Ayanamsha Year) (Sag - Sagittarius)
Source Ayanamsa Z.A.Y. Sun
Aldebaran at 15° Taurus 24° 54' 47" 220 AD 15° Sag 17'
Babylonian, Huber 24° 47' 56" 229 AD 15° Sag 25'
Babylonian, Kuglar 1 25° 59' 56" 143 AD 14° Sag 13'
Babylonian, Kuglar 2 24° 35' 56" 243 AD 15° Sag 37'
Babylonian, Kuglar 3 23° 44' 39" 305 AD 16° Sag 28'
Babylonian, Mercier 24° 40' 39" 237 AD 15° Sag 32'
Chandra-Hari 24° 44' 39" 233 AD 15° Sag 28'
De Luce 27° 57' 48" 1 BC 12° Sag 14'
Djwhal Khool 28° 30' 48" 41 BC 11° Sag 41'
Fagan/Bradley 24° 53' 39" 221 AD 15° Sag 19'
Galactic Center 27° 00' 24" 69 AD 13° Sag 12'
Hipparchos 20° 24' 05" 545 AD 19° Sag 48'
JN Bhasin 22° 54' 57" 364 AD 17° Sag 17'
Krishnamurti 23° 54' 51" 292 AD 16° Sag 17'
Lahiri 24° 00' 39" 285 AD 16° Sag 12'
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Raman 22° 33' 53" 389 AD 17° Sag 38'
Sassanian 20° 08' 48" 564 AD 20° Sag 03'
Sri Surya Siddhantha 22° 40' 32" 499 AD 17° Sag 32'
Ushashashi 20° 12' 40" 559 AD 20° Sag 00'
Yukteshwar 22° 37' 57" 292 AD 17° Sag 34'
Background
t is my personal opinion that Lahiri ayanamsha is not capable of giving precise
sidereal longitudes of heavenly bodies. Horoscope readings and Dasha predictions
done based on Lahiri ayanamsha go 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 Chandra Hari ayanamsha (version 238 AD zero
ayanamsha year), which gives much better results in divisional chart analyses and birth time
rectifications but still with a few exceptions once in a while. Babylonian-Huber and
Babylonian-Mercier ayanamshas are closer to Chandra Hari (Table 1). I believed that the
correct ayanamsha should be found somewhere in this range.
When doing an internet search to find out the basis of Babylonian astronomy and the
work of Huber and Mercier, I came across the findings of great Greek astronomer
Hipparchus.
Hipparchus
ipparchus was born in Nicaea in Bithynia, but spent much of his life in
Rhodes of Greece. His recorded observations span the years 147 BC to 127 BC.
Virtually all his writings are lost to date. The Almagest, written by Claudius
Ptolemy (90 AD –168 AD), is the source of most of our knowledge about Hipparchus.
Ptolemy made extensive use of the work of Hipparchus. Almost all the work of
Hipparchus is therefore derived today from Almagest of Ptolemy.
Apart from precession Hipparchus calculated the length of the year to within six and a
half minutes, developed a scale to rate the brightness of stars, was the first to record a
nova, theorized on the motions of the Sun and Moon, provided high quality planetary
observations and created a catalog of 850 stars.
His star catalog, believed to have been produced in 129 BC, is credited with the
production of the first known comprehensive catalog of stars in the western world.
Hipparchus made the star catalog in ecliptic coordinates. For the naked eye observations
of stars he used a self invented instrument called armillary sphere (Figure 2), a model of
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objects in the sky consisting of a spherical framework of rings centered on Earth, that
represent lines of celestial longitude and latitude and other astronomically important
features such as the ecliptic.
Fig 2: Armillary Sphere
The star Spica is the star that provided Hipparchus with the data which enabled him to
describe precession of the equinoxes. Spica (Alpha Virginis, Chitra Nakshatra in Vedic
astrology) is the brightest star in the constellation of Virgo, and the 15th brightest star in
the night time sky.
According to Hipparchus‟s accounts of the rising and setting of the constellations
“beginning of Aries rises when Spica sets” (1). This finding is the sole basis of this paper.
Principles and Theory
ipparchus says beginning of Aries rises when Spica sets. Therefore it is
needless to say that if the location of Spica is known, 0° Aries can easily be
deduced, the two points being situated on either side of the horizon. 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 at zero
ayanamsha year the tropical longitude of Spica must be as same as (sidereal) longitude of
Spica that Hipparchus observed. Precise tropical longitudes of stars are accessible today
through astronomical calculations. Therefore the zero ayanamsha year will be the year
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when tropical longitude of Spica is as the same as the (sidereal) longitude of Spica that
Hipparchus observed.
Calculations
hat was the longitude of star Spica that was observed by Hipparchus? Spica
sets when beginning of Aries rises. Beginning of Aries and position of
Spica are related to two ends of the horizon. Since Aries and Libra are
opposing signs in the Zodiac one might place it at 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 supplemented by simple instruments available at that time. It was his
OBSERVATION or what he saw in night time 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
(Figure 3). The refractive index, which depends on environmental temperature and
degree of elevation of the object from horizon, is greatest at horizon.
Fig 3: Effect of atmospheric refraction on setting Sun
To a person at O watching sunset, Sun (S) appears to be above the horizon (S'), apparent
sun, even though it has actually already descended below the horizon, true Sun (S).
The blue line indicates horizon which if extended to the opposite direction will represent
the degree of Ascendant or Lagna.
Curved light black line represents light rays emanating from Sun influenced by
atmospheric refraction.
Dark black line represents the position of the image (S'), the apparent Sun which is
visible to O, of true Sun (S).
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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' (2). When
calculating the degree of ascendant or Lagna point for astrological purposes the refraction
is not considered (see notes in Figure 3). Therefore at the point of time when calculated
0° of Aries rises in East we cannot expect one to see with naked eye, a heavenly body
located at 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°26.63' Virgo or 29°26'37.8" Virgo.
Results
ince this is an observation made in relation to the actual position of stars in sky
this can be considered as sidereal longitudes of Aries and Spica. The zero
ayanamsha years 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 article 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 with a high degree of precision
by modern astronomers. 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 the author of this paper used ZET 9.1
software and opted for Swiss ephemeris. Vernal equinox was calculated using the same
software. It was found that at the time of vernal equinox in 244 AD, i.e. March 20, 244
AD at 18.46.54 hours GMT, the tropical longitude of Spica was 29°26'23.84" Virgo. This is
almost as same as the sidereal longitude of Spica obtained above from observations of
Hipparchus i.e. 29°26'37.8" Virgo, just a difference of 14" arc seconds.
In 245 AD the tropical longitude of Spica is 29°27'10" Virgo, a difference of 32" from the
Hipparchus‟s observed value. In 243 AD it is 29°25'35" Virgo, a difference of 63". It is only
in 244 AD that tropical longitude of Spica is closest to the observed longitude of Spica by
Hipparchus.
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Conclusion
Therefore it can be concluded that the zero ayanamsha year is 244 AD.
See the Appendix for ayanamsha figures for a period of 120 years based on 244 AD zero
ayanamsha year. The table has been prepared with the help of Zet 9.1 Lite software
(Please note that yearly rate of precession is not static because Nutation of zodiac has
been taken into account)§.
Discussion
Sun-Jupiter Conjunction Cycle
here is a discrepancy of 14" arc seconds between the tropical longitude of Spica
in 244 AD (29° 26'23.84" Virgo) and the sidereal longitude of Spica that was
observed by Hipparchus (29°26'37.8" Virgo). Since the evidence of Hipparchus
comes from an observation made more than 2000 years ago, and if his observations were
of rough approximations, it is possible that the Zero ayanamsha year is either 243 AD or
245 AD or any other year around 244 AD. This doubt can be sorted out considering Sun-
Jupiter cycle (3).
According to an article circulating on the internet (4) “like Sun and Moon opposition and
conjunction 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”. 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 at the beginning of Aries or Libra.
At the time of vernal equinox of 244 AD, when the tropical Sun was at 0°00'00" of Aries,
Jupiter was located at 5° 4' in Aries, just 5° apart. The next Sun-Jupiter conjunction in
Aries would be either in 232 AD or 256 AD which are far apart from 244 AD. Neither in
243 AD nor 245 AD at vernal or spring equinoxes is there any Sun – Jupiter close
conjunction or opposition.
Atmospheric Refraction
s explained earlier atmospheric refraction causes astronomical objects to appear
higher in the sky than they are in reality (Figure 3).
§ 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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The sole basis of this article is longitude of star Spica observed by Hipparchus with
naked eye. This longitude was refined against atmospheric refraction by the author.
Was Hipparchus aware of atmospheric refraction? The answer is No. By analyzing the
difference of 5 hours of predicted time of equinox by Hipparchus and the observation
made on Alexandria's large public equatorial ring on 24 March 146 BC it has been
concluded that Hipparchus was not aware of atmospheric refraction (5). Many scholars
have identified the errors caused by atmospheric refraction in the work of astronomical
observations made by Ptolemy (6).
In my humble opinion, not only Hipparchus and Ptolemy but also Varahamihira (505–587
AD), who lived about 700 years later than Hipparchus, and even other ancient
astrologers and astronomers were not aware of atmospheric refraction. The law of
“Refraction” was scientifically discovered only in early 1600s AD (6). Thus the longitudes
of any planet or star measured and recorded by any ancient astronomer by observation is
bound to be erroneous slightly by a few arc minutes (in a range from 0' to 34' depending
on elevation above the horizon) (2) from the exact position of celestial objects in sky;
therefore all such ancient knowledge and figures must be interpreted and used with
caution.
Dulakara Ayanamsha
t is interesting to note that an ayanamsha by his name of Hipparchus is already in
use (Table 1). This had been devised by Raymond Mercier based on Ptolemy‟s
accounts in Almagest. Rather than taking Spica, he 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 545 AD. Therefore to differentiate from Mercier‟s Hipparchus ayanamsha, I would like
to coin the term “Dulakara Ayanamsha” for what I found. The literal meaning of
„Dulakara‟ in Sinhalese language (mothertongue of the author) is „Sun‟.
Given below (Table 2) is a comparison of Dulakara ayanamsha with other ayanamshas
proposed based on star Spica.
Table 2 Comparison of Dulakara ayanamsha with other ayanamshas
(Z.A.Y. – Zero Ayanamsha Year) Ayanamshas given are for 1st January 2011
Source Star spica Ayanamsa Z.A.Y.
Fagan/Bradley 29° 06' 05" Virgo 24° 53' 39" 221 AD
Babylonian, Huber 29° 14' Virgo 24° 47' 56" 229 AD
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Babylonian, Mercier 29° 21' Virgo 24° 40' 39" 237 AD
Babylonian, Kuglar 2 29° 26' Virgo 24° 35' 56" 243 AD
Dulakara 29° 26' 23.84" Virgo 24° 35' 22" 244 AD
Lahiri 0° Libra 24° 00' 39" 285 AD
It is interesting to note that Dulakara and Kuglar 2 ayanamshas are almost the same. The year of
coincidence of Dulakara ayanamsha is 244 AD, and according to Kuglar 2 ayanamsha it is
243 AD. The raw data for the former comes from the work of Hipparchus whereas for the
latter it is from Babylonian planetary tablets. Babylonian astronomy is older than Greek
astronomy. 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's work provides a link between Babylonian
and Greek astronomy. Therefore it is not a surprise that Babylonian - Kuglar 2 and
Dulakara ayanamshas are almost the same because the sources for the calculations are
probably having a similar origin.
When compared with Lahiri ayanamsha, which is commonly in use among Vedic
astrologers, Dulakara ayanamsha is 0°34'29" more than Lahiri ayanamsha. Thus Dulakara
ayanamsha for a given date can be easily obtained by adding 0°34'29" to Lahiri ayanamsha.
It is my sincere and humble 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 here but should continue to research on this important
topic either to refute or confirm Dulakara Ayanamsha, or to come out with a better one.
References
1. http://www.astro.com/swisseph/swisseph.htm
2. http://wise-obs.tau.ac.il/~eran/Wise/Util/Refraction.html
3. http://www.ancientcartography.net/JupiterCalendar3.pdf
4. http://groups.yahoo.com/group/ancient_indian_astrology/message/1166
5. http://en.wikipedia.org/wiki/Hipparchus
6. http://mintaka.sdsu.edu/GF/explain/optics/discovery.html
7. Extra readings were done through Wikipedia. All diagrams, except related notes, in this article were
copied from the same, the free encyclopedia.
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Acknowledgments
Hipparchos (Greek: Ἵππαρχος, Hipparkhos; c. 190 BC – c. 120 BC)
A great astrologer, astronomer, geographer, and mathematician
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Appendix
Table of Dulakara Ayanamsha
(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)
Year
Ayanamsha
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
Year
Ayanamsha
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
Year
Ayanamsha
Deg Min
Sec
1980 24 08 58
14
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