1

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 harsha.indrasena@hotmail.com

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