YOGATAARAS, THEIR MISIDENTIFICATIONS AND CORRECTIVE MEASURES
M. A. Venkatachar* ______
Abstract
Indian Astronomy is geocentric observational Astronomy. The stationary terrestrial observer is supposed to be at the centre of the star studded celestial sphere. The non varying great circle on the surface of the celestial sphere, representing the apparent annual path of the sun is the Ecliptic. The belt like region on the celestial sphere with the ecliptic as the central line and extending on either side of it by an angular width about 8 degrees is the Zodiac. In the all India Nirayana Luni-solar system of astronomy, starting from a special fixed initial point (origin) on the ecliptic, the ecliptic is divided into twenty seven (27) equal parts. Passing through the poles of the ecliptic, great semi-circles are drawn on the surface of the celestial sphere through these 27 points of section of the ecliptic. These great semi circles not only divide the entire surface of the celestial sphere into 27 equally spaced “Nakshatra Zones” but also divide the zodiac into 27 equally spaced regions called “Nakshatra Mansions” or Lunar Mansions. These mansions have been given Sanskrit names by ancient Indian astronomers. In each nakshatra zone, a visibly bright, conspicuous well known star (Nakshtra) is specially chosen and designated “Yogataara” (principal presiding star) of the nakshatra mansion. Thus, there are 27 yogataaras assigned to the corresponding 27 nakshatra mansions. The present paper analyses all aspects of the yogataaras, their definition, position, names, misidentification and proposed corrective measures in detail.
Key words : Ecliptic, Zodiac, Nakshatra, Nakshatra Zone, Nakshatra mansion, Yogataara, Vernal equinox, Celestial Coordinates, Sayana and Nirayana systems. ______
*Retired Professor of Physics and Principal, Vijaya College, Bangalore – 560 004. Res.: #9, Mahantha Layout, Kempegowdanagar, Bangalore – 560 019. Tel.: 080-26620593.
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1. General Introduction
The celestial sphere with its fixed stars, is found to rotate about its axis in space. For the
geocentric stationary observer situated at the centre of the celestial sphere, independent of
their distances from the terrestrial observer, the stars, planets (Grahaas) and similar bright
objects appear to be on the inner surface of the celestial sphere along their line of sight.
The Sun, Moon and other visible grahaas also appear to be moving with respect to the
fixed star background of the rotating celestial sphere.
Two important great circles can be imagined on the surface of the celestial sphere.
They are (i) The Celestial Equator and ii ) The Ecliptic.1
The Celestial equator is the great circle on the celestial sphere whose plane is normal
to the axis of rotation of the celestial sphere.
The ecliptic is the unvarying fixed great circle representing the apparent annual path
traced by the centre of the Sun on the celestial sphere.
As these two circles are inclined at an angle called obliquity of the ecliptic, they
intersect at two points called Equinoxes. The particular equinox through which the Sun
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crosses the equator from south to north is called the Vernal Equinox or spring Equinox and
is given the symbol ‘ γ ’ (Gamma).
To study the motion and position of the Sun and other planets (grahaas), two systems
in use are popular. In the Sayana equatorial system ‘γ’ is chosen as the origin of the frame
of reference. In the Indian Nirayana Luni-solar Ecliptic system the origin chosen by the
earlier nirayana astronomers is a fixed point on the ecliptic diametrically opposite to the
position of the very bright star spica (chitta nakshatra), the only bright star that is almost
on the ecliptic. As per M.N. Saha’s Calendar Reforms Committees report2 of 1955 AD,
this fixed nirayana origin of its frame of reference was also the position of the Vernal
Equinoctial point during the year 285 AD. The members of the Committee, by back
calculation have also found that at 21 hour, 27 minute (IST) on Sunday, the 22nd March of
285 AD, the Sun, in its journey on the ecliptic just crossed the Vernal equinox ( γ ). They,
thus confirmed that it was the same point on the ecliptic fixed with reference to the star,
‘Spica’.
This fixed initial point of the nirayana system is also called “The Nirayana Mesha Raasi
Arambha Bindu” as also “The Ashwini Nakshtra Mansion’s Arambha Bindu” (starting
point). While this point remains fixed with respect to the fixed star background on the
celestial sphere, the position of the vernal equinox γ goes on sliding backwards on the
ecliptic (Retrograde motion relative to the direction of the motion of the Sun) slowly as
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time progresses, due to the natural phenomenon called ‘Precession of equinoxes”. The
angular distance of separation between the Sayana origin, γ and the fixed nirayana origin
is called “Ayanamsa”. In fact, Ayanamsa which was zero in the year 285 AD has now
increased to about 24 degrees in the year 2000 AD.
It is this Luni-solar Nirayana System3 which is followed strictly in almost
all regions of India. The speciality of this system is its concept of Nakshatra, nirayana
raasi, tithi, yoga, karana, lagna, etc., which are not conceived in the Sayana system, though
it has the varying tropical “Sun Sign” (raasi) concept. ‘Sayana System” is popular in
many western countries.
2. Nakshatra, Nakshtra Zone, Nakshatra Mansion
Nakshatra, Star, Taara, are synonyms representing self luminous celestial objects
which appear as bright points on the celestial sphere independent of their size and historic.
Many of them appear to be fixed over several thousands of years. Some of the them
appear to be very bright and some others appear faint. Their apparent brightness is usually
expressed in terms of numbers called “apparent visual magnitude”(M). Only nakshatras,
whose apparent visual magnitudes are less than four (+4) are visible to the normal unaided
eyes of human beings. There are about 600 nakshatras that are visible. Many of them
have been assigned Greek, Latin, English etc names4 by astronomers. Indian, Sanskrit
names are available only for a small number of visible bright starts. For example, the
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visibly brightest nakshtra “Sirius” (M=-1.47) is called “Lubtaka”; next bright nakshatra
“Canopus” (M=-0.72) is called “Agastya”, Spica, M=+0.98 is called “Chitta” etc., Though
more than 50,000 stars have been detected using powerful telescopes (with M ≤+8) and
listed , Indian catalogues contain about 600 nakshatras (with M<+4), many of them
without equivalent Indian names.
Just as celestial equator and ecliptic are important great circles on the
celestial sphere, there is another region enveloping the celestial sphere called the
“Zodiac”1. This is a belt like region on the surface of the celestial sphere, with the
ecliptic as its central line and extending on both sides of it at angular distance of about
8 degrees. This 16 degree wide Zodiac has special significance. While the Sun is
moving on the ecliptic within the Zodiac all other visible grahaas (planets) known to
ancient Indian astronomers are found to have their entire journey confined to this region
only.
In the Indian Luni-solar nirayana system, starting from its fixed origin of the ecliptic
and proceeding in the direction of apparent motion of the Sun, Indian astronomers have
divided the ecliptic into twenty seven (27) equal parts. Each part has an angular width of
3600 / 27 = 130-20’. The distance of any point on the ecliptic from the fixed origin is
called the nirayana Celestial longitude (λN) of the point. As such, first part of the
ecliptic has the nirayana longitude limit 00 to 130-20’. The nirayana longitude of the
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second part extends from 130-20’ to 260-40’ and similarly the 27th last part has the
0 0 corresponding limits of λN from 346 -40’ to 360 -00’.
The normal to the plane of the ecliptic, through its centre cuts the celestial sphere
at two diametrically opposite points called “Poles of the ecliptic”. Passing through
these poles of the ecliptic, 27 great semi-circles can be imagined to be drawn through
the 27 points of section of ecliptic. The region between any two such consecutive
(adjacent) semicircles is called “Nakshatra Zone”. Thus, these 27 nakshatra zones
completely cover the surface of the celestial sphere and accommodate all the
nakshatras and their constellations. These zones have a maximum width of 130-20’ at
the ecliptic region.
Further, these 27 semi circles will have divided the entire zodiac into 27 equal
regions. Each one of these regions is called “Nakshatra Mansion,” also named as “Lunar
Mansion” and forms the central part of the nakshatra zone. Starting from the fixed initial
point on the ecliptic, and moving in the direction of Sun’s motion, the 27
nakshatra mansions have been named as (1) Ashwini (2) Bharani (3) Krithika (4)
Rohini (5) Mrigashira (6) Ardra (7) Punarvasu (8) Pushya (9) Ashlesha (10)
Makha (11) Poorvaphalguna or Pubba (12) Uttara Phalguna or Uttara (13) Hasta
(14) Chitta (15) Swaati (16) Vishaka (17) Anuradha (18) Jyeshta (19) Moola (20)
Poorvashada (21) Uttarashada (22) Sravana (23) Dhanista (24) Shatabhisha (25)
Poorvabhadra (26) Uttarabhadra and (27) Revathi in this order. All the above points are
more clearly illustrated in Figure-I.
26/06/2014 Ashwini Zone Bharani Zone
---w E---
St
Figure-I: Nakshatras (Yogataaras), Nakshatra Zones, Nakshatra Mansions.
P and P' - Poles of equator. K and K' - Poles of ecliptic Y - Vernal Equinox 0 - The fixed initial point - Nirayana Origin. YO - Ayanamsa ACDB- Ashwini nakshatra mansion; Sa-Ashwini Yogataara CEFD - Bharani nakshatra mansion; Sb- Bharani Yogataara co- obliquity of the ecliptic figure- not to scale
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3. Yogataaras
Within each nakshatra zone there are large number of stars (nakshatras). Some of
them are visible to the unaided eye of the observer and others can be detected only by
using powerful telescopes. In each nakshatra zone, a particular conspicuous, prominent,
visibly bright, star (nakshatra) is identified by Indian nirayana astronomers as the
principal, presiding star of the nakshtra mansion within that zone. Such a star is
designated and named as the “Yogataara” of the nakshatra mansion. Even though such a
star has its own name (English or Indian), after selecting it as the Yogataara it gets the
same name as that of the nakshatra mansion to which it is considered as it presiding deity,
like Ashwini Yogataara, Bharani Yogataara etc., Thus 27 yogataaras were fixed to
govern the 27 nakshatra mansions.
In general, any star (nakshatra) could be chosen and designated as Yogataara of a
nakshatra mansion, provided it satisfies the following conditions:
(i) It should be a prominent, conspicuous, visibly very bright, easily recognizable the
unaided normal eye of the observer. In other words it should be a star whose apparent
visual magnitude is less than (+4).
(ii) It should be well within the nakshatra zone in which it represents the corresponding
nakshthra mansion. In astronomical language this means that the nirayana celestial
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longitude of the chosen star must have a value lying within the longitude limits of the
nakshatra mansion which it has to represent.
(iii) It should not be far away from the nakshatra mansion which it governs and casts its
aspects. In other words, its nirayana celestial latitude must be less than about 400 on either
side of the ecliptic. It may even be well within its mansion, if available.
These conditions were introduced and accepted as the “definition of the yogataara
by Indian astronomers, astrologers and Panchanga pandits.
Thus 27 yogataaraas were fixed to the 27 nakshatra mansions with the same name
of the mansion which they represent. During the days of ancient astronomers, due to lack
of measuring instruments, they were shown from expert gurus to their sishyas by pointing
their forefinger towards the yogataara. This method led to uncertainties and wrong
identifications and continued even during the time of Varaha Mihira (550 AD). The
situation now is different and clear5.
Just as x and y coordinates with rectangular axes are used in plane geometry to
know the exact position of any point on the plane, spherical coordinates are used to locate
and fix the position of any star on the celestial sphere. In the sayana equatorial system, the
vernal equinox is chosen as the origin and the coordinates right ascension (α) and
declination (δ) are evolved respectively along the equator and arcs drawn from the poles of
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equator. In the nirayana ecliptic coordinate system, the fixed point on the ecliptic is
chosen as the origin and nirayana celestial longitudes (λN) and celestial latitudes (β) along
the elliptic and semicircular arcs drawn from the poles of the elliptic are chosen to fix the
position of any star on the celestial sphere. These ideas are clearly illustrated in figure II.
Thus, if the values of spherical coordinates (α,δ) or (λN,β) of any particular star is known
(determined accurately by using sophisticated measuring instruments), the position of the
star will be known without any uncertainty.
By about the beginning of the 19th Century AD, astronomers in different parts of
the world including India have made detailed study of bright visible stars. While
Westerners gave Greek, Latin, English etc. names, Indians have given Sanskrit names to
most of the stars. These stars with their names and celestial coordinates (α,δ) and (λN,β)
have been listed and star catalogues have been prepared4.
It was only after 1950 AD, in India, the calendar reforms committee2 with N.C.
Lahiri6 examined all the star tables and agreed to adopt a traditional Yogataara table giving
details of names and coordinates of the 27 stars fixed by the ancient Indian astronomers as
the 27 yogataaras. The replica of this table available in the present day Indian astronomy
books, journals, articles etc are shown in table I below. Later attempts have been made
to identify stars having Indian names with the corresponding foreign names available.
The values of coordinates of the stars are helpful for correct matching.
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With the perfect definition of yogataara in mind, this traditional yogataara table can be
examined carefully. On critical examination of this table one cannot fail to notice the
following observations.
4. Misidentification of some Yogataaras
Of the 27 yogataaras, the critical examination of table I shows that 20 of them
satisfy almost all the conditions required to retain their yogataara names. Discrepancies
will be noticed in the case of the remaining 7 yogataaras. For example, 1) the 6th
Yogataara Ardra.
Table – I
List of 27 Yogataaras in their natural order, with their Nirayana Celestial longitudes, together with the 27 Nakshatra mansions with their angular range.
Range of Nirayana Name of the longitude of
Yogataara Nakshatra mansion (which is also Nirayana longitude of Yogataara of the same name the name of corresponding S Nakshthra Degrees Minutes Seconds Degrees From To 0)
shathra mansion shathra (1S=30
k Mansion) a Serial number of Yogathaara Yogathaara of number Serial N 1. Ashwini 0 10 06 46 100.1128 00-0’ 130-20’ 2. Bharani 0 24 20 48 240.3467 130-20’ 260-40’ 3. Krithika 1 06 08 07 360.1353 260-40’ 400-00’ 4. Rohini 1 15 55 56 450.9322 400-00’ 530-20’ 5. Mrigashira 1 29 50 59 590.8497 530-20’ 660-40’ 6. Ardra 2 04 53 51 640.8975 660-40’ 800-00’ 7. Punarvasu 2 29 21 34 890.3594 800-00’ 930-20’ 8. Pushya 3 14 51 54 1040.8650 930-20’ 1060-40’ 9. Ashlesha 3 18 29 18 1080.4883 1060-40’ 1200-00’ 10. Makha 4 05 58 21 1250.9725 1200-00’ 1330-20’ 11. Pubba 4 17 27 33 1370.4592 1330-20’ 1460-40’ 12. Uttara 4 27 45 39 1470.7608 1460-40’ 1600-00’ 13. Hastha 5 19 35 42 1690.5950 1600-00’ 1730-20’ 14. Chitta 5 29 59 03 1790.9842 1730-20’ 1860-40’ 15. Swathi 6 00 22 36 1800.3767 1860-40’ 2000-00’
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16. Vishaka 6 21 13 32 2010.2256 2000-00’ 2130-20’ 17. Anuradha 7 08 42 50 2180.7139 2130-20’ 2260-40’ 18. Jyeshta 7 15 54 19 2250.9053 2260-40’ 2400-00’ 19. Moola 8 00 43 43 2400.7286 2400-00’ 2530-20’ 20. Poorvashada 8 10 43 26 2500.7239 2530-20’ 2660-40’ 21. Uttarashada 8 18 31 41 2580.5281 2660-40’ 2800-00’ 22. Sravana 9 07 55 06 2770.9183 2800-00’ 2930-20’ 23. Dhanishta 9 22 29 04 2920.4844 2930-20’ 3060-40’ 24. Shathabhisha 10 17 43 08 3170.7189 3060-40’ 3200-20’ 25. Poorvabhadra 10 29 37 43 3290.6286 3200-00’ 3330-20’ 26. Uttarabhadra 11 15 17 57 3450.2992 3330-20’ 3460-40’ 27. Revathi 11 26 01 13 3560.0203 3460-40’ 3600-00’
(Note : The Values of Nirayana Longitudes of the 27 yogataaras are reproduced in the above table, from N. C. Lahiri’s Indian Ephemeris 1995 and his books.)
1) In the case of the 6th Yogataara, named Ardra, its actual nirayana celestial longitude is
640.8975. But the longitude range of Ardra mansion is from 660-40’ to 800. Thus the
selected star is not in Ardra mansion/zone but is in mrigasira nakshatra mansion/zone
similarly,
2) The 15th yogataara, Swathi is in Chitta mansion/zone.
3 The 18th yogataara, Jyeshta is in Anuradha mansion/zone. 4) The 20th yogataara, Poorvashada is in Moola mansion/zone.
5) The 21st yogataara, Uttarashada is in Poorvashada mansion /zone.
6) The 22nd yogataara, Sravana is in Uttarashada mansion/zone.
7) The 23rd Dhanishta yogataara, is in Uttarashada nakshthra mansion/zone.
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On account of this there is no yogataara allotted to Dhanista nakshtra mansion. We
can also notice that the yogataara Jyeshta is very close to the division between Anuradha
and Jyeshta. Similar is the case of 19th Moola yogataara which is just near the border
between Jyeshta and Moola nakshatra mansions.
So far as the other 20 yogataaras are concerned, they lie in their respective nakshatra
mansion/zone with their nirayana longitudes well within the longitude limits of their
corresponding mansions.
Thus there seems to be some misidentification or wrong selection of the star
designated as yogataara, the presiding deity of the nakshatra mansion.
5. Some earlier remedial approaches to the problem
The recognition of misidentification is not recent. Even before the use of measuring
instruments, by mere accurate visual estimations several Indian astronomers sensed the
wrong identification. They have also attempted to set right matters by their own
suggestions. The earlier Indian Jain astronomers7 suggested changing the well established
fixed nirayana origin 1800 from star Chitta, to a suitable point on the Revathi mansion so
as to accommodate the selected yogataaras into their respective nakshatra mansion/zone
to which they should belong. This Chitta Paksha and Revathi Paksha controversy no doubt
solved the misfittings but only partially. Many yogataaras which were in correct zones got
mismatched due to this shifting of the origin. Thus the attempt resulted in failure. A little
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later, another school of Indian astronomers3 retained the established nirayana origin, but
tried to alter the equal range of the nirayana mansions. Without respecting the 130-20 wide
equally spaced nakshatra mansions, they suggested to alter them and have 27 mansions of
unequal width varying from 110 to 14.50 just arbitrarily to accommodate the already fixed
yogataaras. Even this method resulted in failure. A third attempt was to set right matters
using the non-uniform motion of the moon through these 27 lunar (nakshtra) mansions.
They thought of a fictitious moon that was to move uniformly through the zodiac.
Accordingly they divided the zodiac to mansions/zones to accommodate the 27 yogataaras
to the zones to which they should belong. Even this trick of the trade and manipulation did
not yield the required result. Anyone who goes through the details of such attempts will
not fail to realize how the methods suggested were arbitrary, irrational, unscientific,
unconvincing and were against all the well established basic norms and definitions of
fixed origin equally spaced nirayana nakshatra mansion/zones and perfect definition of
yogataaras etc……..
6. The proposed solution
This pitiable state of misidentification remained unsolved. This has prompted the author of
this paper to suggest a remedy to the problem of misidentification of some yogataaras
without changing well established norms. The problem has been approached from a
different angle. Correct analysis reveals that the problem of stars as misidentification is
after all due to wrong selection and wrong naming of stars as yogataaras. This led to the
detailed study of recent authentic star tables and star catalogues.
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Of the several Indian and foreign star catalogues8,9, it is now well known that the star
catalogue (an encyclopedia of stars) containing all data of more than 50.000 stars (of M
from -1.5 to +8.5) published by Sky Publishing Corporation4, Cambridge, Massachusetts
is the most accurate and authentic one. It has international approval from astronomical
data centre, NASA, Space flight centre in Greenbelt, Maryland and Similar global
organizations from Britain, France, and Germany etc… It has supplied accurate values of
the equatorial coordinates (α.δ), apparent visual magnitudes, their internationally agreed
Greek or Latin or Roman names, Flamseed number, Bayer letter, constellation etc. of all
these stars pertaining to the epoch of Greenwich noon of 2000.00 AD. Though this table
gives data of all 600 and odd visibly bright stars, (M<4), table II below has been prepared
now by selecting 102 bright stars from the above list. It is further found that these are the
only 102 bright visible stars which satisfy the definition of yogataaras and hence they are
the most eligible stars to be given the status of yogataaras. Further this table II indicates
all the eligible stars individually for each one of the 27 nakshtra zones separately.
Unfortunately the above star catalogue gives equatorial coordinates (α and δ) of all stars
for the year 2000.00AD. But, for the present paper we require the equivalent nirayana
longitude and latitude coordinates (λΝ, β). As indicated in Appendix, using well known
coordinates’ conversion equations, (λΝ, β) of all the 102 stars have been calculated and
entered in addition in table II. As these authentic values are readily available, the problem
of correct misidentification reduces to rejecting wrong stars and selecting the correct stars
as the true yogataaras and designating them with the corersponding names of the nakshatra
zones to which they are affiliated. For example, there are only 4 eligible stars in Ardra
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zone of which we have to choose one star and name it as Ardra yogataara. Similarly there
are 12 qualified stars is Mrigasira zone, 3 in Bharani zone, and only 2 in Ashwini zone etc.
Thus the corrective measure for misidentification involves judicial selection of the best
suited 27 stars, one for each nakshatra zone and rejecting the remaining 75 stars for
justifiable reasons. This is what is done now, especially in the case of 7 misidentified
yogataaras in the traditional table I as indicated below.
Table II
Full list of all 102 eligible, qualified characteristic stars which can be used
Flam Catalogue Sl. Bayer λ limits of the Seed Constellation Name of the M ∝ δ λ β N No. N 27 mansions No. Letter Star 1 43 β Andromeda Mirach 2.06 17.4329 +35.6206 6.5529 +25.9404 1.Ashwini 0° to 13° 1/3 2 6 β Aries Sheraton 2.64 28.660 +20.808 10.1175 +8.4824 --Do--
3 13 ∝ Aries Hamal 2.00 31.789 +23.463 13.8065 +9.9617 2.Bharani 13°1/3 to 26° 2/3 4 41 - Aries - 3.63 42.496 +27.261 24.3512 +10.4437 --Do--
5 92 ∝ Cetus Menkar 2.53 45.570 +4.090 20.4654 -12.5908 --Do--
6 25 η Taurus Alcyone 2.90 56.871 +24.105 36.1391 +4.0435 3.Krittika 26° 2/3 to 40° 7 34 γ Eradonus Zaurak 2.97 59.5075 -13.5086 30.0125 -33.2023 --Do--
8 87 ∝ Taurus Aldebaran 0.85 68.980 +16.509 45.9354 -5.4753 4.Rohini 40° to53°1/3 9 67 β Eradonus Cursa 76.9625 -5.0864 51.4219 -17.7386 --Do-- 2.79 10 19 β Orion Rigel 0.12 78.6345 -8.2017 53.008 -31.1235 --Do--
11 13 ∝ Auriga Capella 0.08 79.1725 +45.9981 58.0059 +22.8597 5.Mrigashira 53°1/3 to 66°2/3 12 24 γ Orion Bellatrix 1.64 81.283 +6.3497 57.0934 -16.8203 --Do--
13 112 β Taurus Elnath 1.65 81.5729 +28.6075 58.7228 +5.3798 --Do--
26/06/2014 14 9 β Lepus Nihal 2.84 82.0613 -20.7594 55.8242 -43.9132 --Do--
15 34 δ Orion Mintaka 2.24 83.0016 -0.2992 58..5095 -23.3702 --Do--
16 11 ∝ Lepus Areneb 2.58 83.1825 -17.8222 57.5273 -5.4655 --Do--
17 39 λ Orion Meissa 3.30 83.786 +9.934 59.855 -13.3776 --Do--
18 44 ί Orion -- 2.77 83.8583 -5.9100 59.1449 -29.2001 --Do--
19 46 ε Orion Alnilam 1.70 84.0533 -1.2019 59.6110 -24.5094 --Do--
20 50 ζ Orion Alnitak 1.70 85.1896 -1.9428 60.8289 -25.2945 --Do--
21 53 κ Orion Saiph 2.06 86.9392 -9.6697 62.5463 -33.0714 --Do--
22 58 α Orion Betelguese 0.50 88.793 +7.407 64.9018 -16.0350 --Do--
23 2 β Canis Major Mirzam 1.98 95.675 -17.9558 73.3368 -41.2533 6.Ardra 66°2/3 to 80° 24 13 μ Gemini - 2.88 95.7401 +20.5136 71.5306 -2.8209 --Do--
25 24 γ Gemini Alhena 1.90 99.428 +16.399 75.252 -6.7509 --Do--
26 27 ε Gemini Mebsuta 2.98 100.9829 +25.1311 76.0873 +2.0672 --Do--
27 - ∝ Carina Canopus - 95.9879 -52.6955 81.1121 -75.8113 7.Punarvasu 80° - 93°1/3 0.72
28 9 ∝ Canis Major Sirius - 101.287 -16.7161 80.2308 -39.6050 --Do--
1.47
29 21 ε Canis Major Adhara 1.50 104.6563 -28.9719 86.9132 -51.3578 --Do--
30 25 δ Canis Major - 1.80 107.0979 -26.3933 89.5482 -48.4530 --Do--
31 3 β Canis Minor Gomeisa 2.90 111.7875 +8.2894 88.3417 -13.4876 --Do--
32 66 ∝ Gemini Castor 1.94 113.6496 +31.8883 86.3902 +10.0921 --Do--
33 10 α Canis Minor Procyon 0.34 114.8254 +5.225 91.9353 -16.0207 --Do--
34 78 β Gemini Pollux 1.15 116.329 +28.026 89.3631 +6.6762 --Do--
35 17 β Cancer - 3.52 124.1288 +9.1856 100.4104 -10.2913 8.Pushya 93°1/3-106° 2/3
36 47 δ Cancer Asellus 3.94 131.184 +18.154 104.8817 +0.0735 --Do-- Astrialis
26/06/2014 37 15 ρ Puppis - 2.81 121.8858 -24.3042 107.5412 -43.2659 9.Aslesha 106°2/3 - 120°
38 11 ε Hydra - 3.38 131.694 -6.419 108.494 -11.1097 --Do--
39 17 ε Leo Asad 2.98 146.4629 +23.7741 116.8536 +9.7130 --Do-- Astralis 40 30 ∝ Hydra Alphard 1.98 141.897 -8.659 123.4303 -22.3866 10.Makha 120° -133° 1/3 41 32 ∝ Leo Regulus 1.35 152.093 +11.967 125.9770 +0.4605 --Do--
42 41 γ Leo Algieba 2.61 154.9933 +19.8417 125.7620 +8.8128 --Do--
43 68 δ Leo Zosma 2.56 168.527 +20.524 137.462 +14.3308 11.Pubba 133° 1/3- 146° 2/3 44 94 β Leo Denebola 2.14 177.265 +14.572 147.7633 +12.2653 12.Uttara 146° 2/3-160° 45 2 ε Corvus - 3.00 182.5313 -22.6197 167.8157 -19.6725 13.Hasta 160° -173° 1/3 46 4 γ Corvus Gienah 2.59 183.9517 -17.5419 166.8739 -14.4992 --Do--
47 7 δ Corvus Algorab 2.95 187.466 -16.516 169.6005 -12.1914 --Do--
48 47 ε Virgo VindMiatrix 2.83 195.5442 +10.9592 166.0858 +16.2045 --Do--
49 9 β Corvus - 2.65 188.5967 -23.3967 173.5448 -18.0427 14.Chitta 173° 1//3- 186° 2/3 50 46 γ Hydra - 3.00 199.7304 -23.1716 183.1653 -46.6091 --Do--
51 67 ∝ Virgo Spica 0.98 201.298 -11.161 179.9881 -2.0508 --Do--
52 8 η Bootes Muphrid 2.68 208.6713 +18.3978 175.4819 +28.0760 --Do--
53 16 α Bootes Arcturus -.04 213.915 +19.1825 180.377 +30.7322 --Do--
54 36 ε Bootes Izar 2.70 221.247 +27.074 184.2470 +40.6274 --Do--
55 - ∝ Crux Acrux 1.33 186.6496 -63.099 198.0188 -52.8719 15. Swati 186° 2/3-200° 56 - β Crux Mimasa 1.20 191.930 -59.6886 197.7943 -48.6324 --Do--
57 27 γ Bootes Seginus 3.00 218.0196 +38.308 191.797 +49.5491 --Do--
58 5 α Corona Alphecca 2.21 233.672 +26.715 198.4361 +44.3279 --Do-- Borealis 59 - β Centaurius Hadar 0.60 210.9558 -60.3731 209.9237 -44.1318 16.Vishakha 200°-213° 1/3 60 9 ∝ Libra Zuben 2.75 222.720 -16.042 201.2295 +0.3389 --Do-- Genubi
26/06/2014 61 27 β Libra Zuben 2.61 229.2517 -9.3831 205.5174 +8.4972 --Do-- Eschamali 62 24 ∝ Serpens Unukalhai 2.65 236.0671 +6.4256 208.2206 +25.5088 --Do--
63 - ∝ Centaurius Rigil -.01 219.9021 -60.8342 215.627 -42.5884 17.Anuradha Kentaurus 213° 1/3- 226° 2/3 64 6 Π Scorpius - 2.89 239.7129 -26.1142 219.0844 -5.4720 --Do--
65 7 δ Scorpius Deschubba 2.30 241.333 -22.622 219.850 -1.7542 --Do--
66 8 β Scorpius Graffias 2.62 241.3592 -19.8053 219.3362 -1.0120 --Do--
67 20 σ Scorpius - 2.88 245.2971 -25.5928 223.9448 -4.0342 --Do--
68 21 ∝ Scorpius Antares 0.96 247.521 -26.432 226.0593 -4.5388 --Do--
69 27 β Hercules Kornephoros 2.77 247.5554 +21.4897 217.2367 +42.7011 --Do--
70 13 ζ Ophiuchus - 2.60 249.2896 -10.5672 225.3760 +11.393 --Do--
71 23 τ Scorpius - 2.82 248.9708 -28.2661 227.6041 -6.1174 18.Jyeshta 226° 2/3-240° 72 35 η Ophiuchus Sabik 2.43 257.5946 -15.7250 234.1168 -7.2001 --Do--
73 26 ε Scorpius Wei 2.29 252.541 -34.293 231.4825 -11.7299 --Do--
74 55 ∝ Ophiuchus Rasalhague 2.10 263.7338 +12.560 238.5960 +35.9355 --Do--
75 35 λ Scorpius Shaula 1.60 263.402 -37.104 240.7322 -13.780 19.Moola 240° -253° 1/3 76 60 β Ophiuchus Cebalral 2.77 265.8683 +4.5672 241.4843 +27.9403 --Do--
77 19 δ Sagittarius Kaus Media 2.70 275.2488 -29.8281 250.724 -6.472 --Do--
78 3 ∝ Lyra Vega 0.03 279.2346 +38.7836 261.4681 +61.7287 20.Poorvashada 253°1/3-266° 2/3 79 34 σ Sagittarius Nunki 2.00 283.816 -26.297 258.5324 -3.4415 --Do--
80 38 ζ Sagittarius Ascella 2.60 285.6529 -29.8803 259.7871 -7.1772 --Do--
81 41 π Sagittarius - 2.89 287.4408 -21.0236 262.4008 +1.4372 --Do--
82 50 γ Aquila Tarazed 2.72 296.5650 +10.6133 277.0899 +31.2428 21. Uttarashada 266° 2/3-280° 83 53 ∝ Aquila Altair 0.77 297.696 +8.868 277.9269 +29.3093 --Do--
84 12 γ Saggitta - 3.47 299.6892 +19.4922 283.1932 +39.1894 22.Sravana 280-293 1/3 85 6 β Delphinus Rotanov 3.63 309.387 +14.595 292.4927 +31.9228 --Do--
26/06/2014 86 6 ∝2 Capricornus Algedi 3.57 304.5138 -12.5362 280.0133 +6.9407 --Do--
87 22 β Aquarius Sadal Suud 2.91 322.890 -5.571 299.5443 +8.6198 23.Dhanista 293°1/3-306° 2/3 88 49 δ Capricornus Deneb 2.87 326.7600 -16.1272 299.6923 -2.5996 --Do-- Algedi 89 50 α Cygnus Deneb 1.25 310.3646 +45.2803 311.4915 +59.8982 24.Satabhisha 306° 2/3-320° 90 8 ε Pegasus Enif 2.39 326.0467 +9.875 308.0377 +22.0997 --Do--
91 34 ∝ Aquarius SadalMelik 2.90 331.4458 -0.3197 309.5023 +10.6600 --Do--
92 73 λ Aquarius Markeb 3.84 343.1538 -7.5797 317.7254 -13.6082 --Do--
93 24 ∝ Piscis Fomalhaut 1.16 344.576 -29.622 310.144 -21.1895 --Do-- Austrinus 94 53 β Pegasus Scheat 2.42 345.9438 +28.0828 311.9923 +31.1354 --Do--
95 - ∝ Eridanus Acherner 0.50 24.4288 -57.2861 321.3867 -59.4045 25.Poorvabhadra 320°-333° 1/3 96 54 ∝ Pegasus Markab 2.49 346.190 +15.205 329.6356 +19.4063 --Do--
97 88 γ Pegasus Algenib 2.83 3.309 +15.184 345.3050 +12.5986 26.Uttarabhadra 333°1/3-346° 2/3 98 16 β Cetus Deneb 2.04 10.8975 -17.9867 338.7303 -20.7885 --Do-- Kaitos 99 21 ∝ Andromeda Alpheratz 2.06 2.0725 +29.0906 350.4356 +25.6875 27.Revati 346° 2/3-360° 100 31 δ Andromeda - 3.28 9.832 +30.861 357.9637 +24.3469 --Do--
101 86 ζ Pisces - 5.24 18.4329 +7.5753 356.0244 -0.2143 --Do--
102 55 ζ Cetus Baten Kaitos 3.73 27.865 -10.335 358.095 -20.33 --Do--
1) The 6th yogataara Ardra :
0 Earlier astronomers (as in Table I) had chosen the star with λN = 64 .89 as Ardra
yogataara. This star is after all the star 58- α- Orion (M = 0.6) called Betelgeuse. As this
star is in Mrigasira zone (and not in Ardra zone), it is replaced now by 24-γ- Gemini called
“Alhena” with M = 1.90. Thus the star Alhena gets its duly designated additional name
“Ardra yogataara” (see Tables II & III)
26/06/2014 20
2) The 15th yogataara Swati :
0 Traditionally the star with λN = 180 . 37 thought of as Swati yogataara was after all
the star with catalogue details, 16- α- Bootes - Arctures (M = -0.04). This had to be
discarded as it was not in Swati zone. Now it has been replaced by the star “Alphecca”
-5-α- Corona Borealis (M = 2.21) and made to adorn the Swati yogataara throne.
3) 18th Jyeshta :
As per old list, this was after all the star 21-α- Scorpus called Antares with M =
0 1.20 & λN =226 . This was not in Jyeshta zone hence it has now been replaced by26 - Є -
Scorpius with M = 2.29 called “Wei” and given the seat of Jyeshta yogataara.
4) 20th Poorvashada :-
As per old list, the star 19-δ- Sagittarius called Kausmedia M=2.84 was wrongly
thought of as Poorvashada yogataara. Hence it is replaced by 34-σ- Sagattarius called
Nunki (M=2.00) which is in Poorvashada zone.
5) 21st Uttarashada :-
0 The traditionally selected Uttarashada yogataara (λN=258 .6) was not at all in
Uttarashada zone. Hence the correct star 53-α- Aquila – Altair (M=0.77) has now been
0 identified as the Uttarashada yogataara (λN =277 .9) and replaces the old one.
26/06/2014 21
6) 22nd Sravana :-
0 Earlier the star with (λN=277 .9) was thought to be the Sravana yogataara. But it
was not in the Sravana zone. Hence by correct selection the star “Rotanov”-6-β- Delphinus
(M=3.63) which lies in the Sravana zone has been designated as the Sravana yogataara.
7) 23rd Dhanishta :-
0 Traditional list has selected the star with λN=292 .5. This was the star 6-β-
Delphinus M=3.63 which was not is Dhanishta zone. Hence using table II, the eligible star
“Sadal Saud” -22-β- Aquarius (M=2.91) lying in the Dhanishta zone is given the status of
Dhanishta yogataara.
Any person who has respect and regard to the wisdom of all ancient of Indian
astronomers and their followers would not attempt to radically change the entire list I of
traditional yogataaras. They would correct only the cases of misidentification and retain
the rest which were in order. With this in view table III has been constructed to replace
table I. Thus at this stage we get the feeling that the case of misidentification of yogataaras
has been solved perfectly well and this paper would have been closed.
26/06/2014 22
Table III List of traditional yogataaras together with the properly identified (suggested/proposed) yogataaras for serial nos 6,15,18,20,21,22, and 23 where misidentification was noticed and now corrected. Name of the Nirayana Yogataara Range of the Nirayana Astronomic Celestial which is also longitude of the Nakshatra Catalogue al proper longitude the name of the Mansion to which the name of the name of the of the star Nakshara zone Yogataara must belong star assigned star assigned and Mansion to as yogataara assigned as as Apparent which it is said yogataara yogataara on 2000AD-00’ VisualMagnitude as mansion akshatra to belong in degrees Serial number of (Lunar) (Lunar) of number Serial N From To 0 / 0 / 1 Ashwini 00 00 13 20 β-Aries Sheraton 100.113 2.64
2 Bharani 13 20 26 40 41-Aries - 24.347 3.63
3 Krithika 26 40 40 00 η-Taurus Alcyone 36.135 2.90
4 Rohini 40 00 53 20 ∝-Taurus Aldebaran 45.932 0.85
5 Mrigasira 53 20 66 40 λ-Orion Meissa 59.849 3.30
6 Ardra 66 40 80 00 24-γ- Gemini Alhena 75.252 1.90
7 Punarvasu 80 00 93 20 β-Gemini Pollux 89.359 1.15
Asellus 8 Pushya 93 20 106 40 δ-Cancer 104.865 3.94 Austrialis
9 Ashlesha 106 40 120 00 ε-Hydra - 108.488 3.38
10 Makha 120 00 133 20 ∝-Leo Regulus 125.973 1.35
Pubba / Poorva 11 133 20 146 40 δ-Leo Zosma 137.459 2.56 Phalguna
Uttara / Uttara 12 146 40 160 00 β-Leo Denebola 147.761 2.14 Phalguna
13 Hasta 160 00 173 20 δ-Corvus Algorab 169.595 2.95
14 Chitta 173 20 186 40 ∝-Virgo Spica 179.984 0.98
26/06/2014 23
∝-Carona 15 Swathi 186 40 200 00 Alphecca 198.4361 2.21 Borealis
Zuben 16 Vishaka 200 00 213 20 ∝-Libra 201.226 2.75 Genubi
17 Anuradha 213 20 226 40 δ-Scorpius Deschubba 218.714 2.30
18 Jyeshta 226 40 240 00 ε-Scorpius Wei 231.483 2.29
19 Moola 240 00 253 20 λ-Scorpius Shaula 240.729 1.60
20 Poovashada 253 20 266 40 σ-Sagittarius Nunki 258.5324 2.00
21 Uttrashada 266 40 280 00 ∝-Aquila Altair 277.9269 0.77
22 Sravana 280 00 293 20 β- Delphinus Rotanov 292.4927 3.63
23 Dhanishta 293 20 306 40 β-Aquarius Sadal Suud 299.5443 2.91
24 Shathabhisha 306 40 320 00 λ-Aquarius Markeb 317.719 3.84
25 Poovabhadra 320 00 333 20 ∝-Pegasius Markab 329.629 2.49
26 Uttarabhadra 333 20 346 40 γ-Pegasius Algenib 345.299 2.83
27 Revathi 346 40 360 00 ζ‐Pisces - 356.021 5.24
Note: This table III may be compared with table I to know how misidentification is
corrected in the case of serial numbers (6, 15, 18, 20, 21, 22 and 23.) = (7 Cases)
7. Special considerations for reviewing the Proposal
Had the list in Table- II been available to the ancient Indian astronomers, they
would probably not stop with Table III. They would have been tempted to review their
old list as better alternatives are now clearly visible in Table II. With this idea in mind,
26/06/2014 24
taking into account the special considerations, Table III is further reformed as indicated
below :-
1. Consider the 24th Shathabhisha Yogataraa. No doubt that the star “Markeb” 73-λ-
Aquarius-M = 3.84 named as Shathabhisha Yogataara earlier satisfies all the requisite
qualities and has been rightly selected.
But Table II shows that the star 24-α-Pisces Austrinus called Fomalhaut with
(M=1.6) is a better contestant for the prestigious seat. Why not choose it in preference to
the earlier “Markeb”? “Fomalhaut” is more bright and satisfies all required conditions.
Further the name Fomal Haut in Parsi language means shata besa. Also this star was
earlier recommended by Jain astronomers for this post. Hence, this star has been proposed
now instead of “Markeb” of old selection.
2. Consider the 27th Yogataara Revati :As per the traditional list, the star 86-ζ-Pisces with
0 λN = 356 and M=+5.57 well within the Revathi Zone was rightly named Revathi
Yogataara. But the only defect in this selection is that this star (M=5.57) is not at all
visible to any normal human being (being M=5.57>4.0). It has to be traced only by using a
telescope to locate it. Hence in this article, as per table II the visible star 21-α-Andromeda
(M=2.06) called “Alpheratz” being a better contendent satisfying all requirements is
named Revathi Yogataara in the proposed final list (table-IV).
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Similarly, better choices have been preferred in the following cases which need special
considerations even though the traditional selection is equally correct. The intention is
only to improve the selection process and get a good final proposed accurate yogataara
table (See table-IV).
In fact, in the case of 1st Ashwini Zone we have only two alternatives of qualified
stars. In the traditional table,β-Aries-sheraton has been named Ashwini Yogataara. But
the other better alternative star 43-β-Andromeda “ Mirach” M=2.06 is preferred for the
final list.
0 Similarly, the star 41-Aries λN=24 .35 is chosen as Bharani Yogataara in the old
list. But table II presents 3 equally qualified stars in Bharani Zone. In this paper the
better star 13-∝-Aries- “Hamal” with M=+2.0 is preferred and included in the final table
IV as the 2nd Bharani Yogataara.
On similar arguments, for the 5th Mrigasira Yogataara 58-∝-Orion, Betelguese
(M=0.5) has be preferred to the earlier 37-λ-Orion-“Meissa” (M=3.30) and shown as
proposed Mrigasira Yogataara in the final list.
In the case of 8th Pushya Yogataara 17-β-Cancer (M=3.52) has been preferred to
δ-cancer-Asselus Austrialis (M=3.94) of the old list.
In the case of 13th Hasta Zone, 4-γ-Corvus-“Minkar” M=2.59 is preferred to the
earlier Hasta Yogataara, δ-corvus Algerab (M=2.95) as the proposed Hasta Yogataara. In
26/06/2014 26
the case 9th Ashlesha, the star ε-Hydra is replaced by ε-Leo as a better star distinguished
as its yogataara.
Thus after reconsideration and use of available Table II, better stars have been
recommended as yogataaras in the above (1, 2, 5, 8, 9, 13, 24 and 27th) cases of yogataaras
and the final table IV is presented as the best, accurate, proposed yogataara list.
8. Concluding Remarks
After realizing the cases of misidentification of Yogataaras in the old traditional
list, Table II containing all eligible stars has been prepared for the purpose of setting
matters right. The solution to the problem reduced to one of proper selection and naming
from this list. It will be noticed that in table II, each one of the 27 nakshatra zones
contains a number of eligible stars, all of them satisfying the basic definition of Yogataara.
After all we have to select only one qualified star for each one of the 27 nakshatra zones
and rename them as Yogataara and reject the remaining 75 equally good stars. Hence
before passing the final judgment we are forced to reveal and take note of special
considerations in addition to strict adherence to rules. Adopting this procedure, the best
suited 27 stars (One from each zone) has been judiciously selected and designated as the
yogataara to the nakshatra mansion to which it is to be attached. In fact, if sophisticated
accurate measuring instruments and above table II were available at the time of ancient
Indian astronomers, undoubtedly they would have done what has been described in this
paper, probably more effectively.
26/06/2014 27
Thus the properly selected 27 yogataaras finally assigned to their respective mansions are
shown in table IV. With this final proposed list, it is now felt that the problem is
scientifically, rationally, logically and effectively solved. It is hoped that this final list
(table IV) of proposed yogataaras gets unanimous approval and acceptance not only by
Indian Government, Indian astronomers and panchanga pandits but also by the global
International astronomical standardization union and it organizations. Further, as this
table IV has eliminated all uncertainties, ambiguities and misidentifications regarding
assignment of yogataaras, it is fervently hoped that there will be nothing like
“misidentification of yogataaras” in future.
Table IV
The Proposed corrected Yogataara Table (MAV′s) full revised list of stars which deserve to be the 27 Yogataaras.
Suggested names of the correct stars with their full details, which correspond to the 27 Yogataaras, thus correcting mismatch, misidentification, anomaly etc. in assigning, recognizing and designating the correct eligible star as Yogataara.
As On 1.1/2000AD Nirayana Nirayana Name of Catalogue Name of star with Ayanamsa celestial celestial the 230.8528 at5.30AM longitude latitude Yogataara
Right Ascension α Astronomical belonging Flamseed to the Constellation Declination δ number/ proper name λ in deg β in deg nakshatra which the N Bayer mansion of stars belongs in Degrees Serial Number of Nakshatra Nakshatra of Number Serial letter of star the same . name
Apparent Visual Magnitude (∝) (δ)
1 43 β Andromeda Mirach 2.06 170.4329 +350.6206 60.5529 +250.9404 Ashwini
2 13 ∝ Aries Hamal 2.00 13.7890 +23.4630 13.8065 +9.9617 Bharani
26/06/2014 28
3 25 η Taurus Alcyone 2.90 56.871 +24.105 36.1391 +4.0435 Krithika
4 87 ∝ Taurus Aldebaran 0.85 68.980 +16.509 45.9354 -5.4753 Rohini
5 58 ∝ Orion Betelguese 0.50 88.793 +7.407 64.9018 -16.0350 Mrigasira
6 24 γ Gemini Alhena 1.90 99.428 +16.399 75.252 -6.7509 Ardra
7 78 β Gemini Pollux 1.15 116.329 +28.026 89.3631 +6.6762 Punarvasu
8 17 β Cancer - 3.52 124.1288 +9.1856 100.4104 -10.2913 Pushya
9 17 ε Leo Asad Astralis 2.98 146.4629 +23.7741 116.8536 +9.7130 Ashlesha
10 32 ∝ Leo Regulus 1.35 152.093 +11.967 125.9770 +0.4605 Makha
11 68 δ Leo Zosma 2.56 168.527 +20.524 137.462 +14.3308 Pubba
12 94 β Leo Denebola 2.14 177.265 +14.572 147.7633 +12.2653 Uttara
13 4 γ Corvus Minkar 2.59 183.9517 -17.5419 166.8739 -14.4992 Hasta
14 67 ∝ Virgo Spica 0.98 201.298 -11.161 177.9881 -2.0508 Chitta
Carona- 15 5 ∝ Alphecca 2.21 233.672 +26.715 198.4361 +44.3279 Swathi Borealis
Zuben- 16 9 ∝ Libra 2.75 222.720 -16.042 201.2295 +0.3389 Vishaka Genubi
17 7 δ Scorpius Deschubba 2.30 241.333 -22.622 219.850 -1.7542 Anuradha
18 26 ε Scorpius Wei 2.29 252.541 -34.293 231.4825 -11.7299 Jyesta
19 35 λ Scorpius Shaula 1.60 263.402 -37.104 240.7322 -13.780 Moola
20 34 σ Sagittarius Nunki 2.00 283.816 +26.297 258.5324 -3.4415 Poorvasad
21 53 ∝ Aquila Altair 0.77 297.696 +8.868 277.9269 +29.3093 Uttrasadha
22 6 β Delphinus Rotanov 3.63 309.387 +14.595 292.4927 +31.9228 Sravana
26/06/2014 29
23 22 β Aquarius Sadal Suud 2.91 322.890 -5.571 299.5443 +8.6198 Dhanista
Piscis 24 24 ∝ Fomalhaut 1.16 344.576 -219.622 310.144 -21.1895 Shathabhis Austrinus
25 54 ∝ Pegasus Markab 2.49 346.190 +15.205 329.635 +19.4063 Purvabadr
26 88 γ Pegasus Algenib 2.83 3.309 +15.184 345.3050 +12.5986 Uttrabadra
27 21 ∝ Andromeda Alpheratz 2.06 2.0725 +29.0906 350.4356 +25.6875 Revathi
26/06/2014 30
Appendix
Celestial Coordinates and their relations.
To locate the exact position of any star on the celestial sphere, a pair of spherical
coordinates are required. Most of the standard star catalogues quote equatorial co-
ordinates for the stars. They are, right ascension (α) and declination (δ) expressed in
degrees. But, for the purpose of the present paper we need a pair of ecliptic coordinates.
They are, tropical or sayana celestial longitude (λT) or (λS) and celestial latitude (β).
Spherical trigonometry gives equations for conversion of star coordinates from one system
to the other.
In fact if (α,δ) of a star is known, its (λT,β) can be calculated using the following
two equations.
tan λT = {(sin ω . tan δ) + (cos ω . sin α)}/ cos α - ( 1 )
sin β ={(cos ω. sin δ) - (sin ω. cos δ. sin ∝)} - (2)
Where ‘ω’ is the obliquity of the ecliptic, whose value is 230.4392 on 1.1.2000AD.
For the purpose of this paper, the nirayana celestial longitude, λN and latitude β are
required. As table II has supplied (∝.δ) of stars for 1.1.2000AD, the corresponding values
of (λN,β) referred to, which are time independent, are required. For this we have the
0 relation λN ={λT ─ (ayanamsa on 1.1.2000AD)}. This ayanamsa was (23 .8528) then.
26/06/2014 31
In the above case,
0 λN= (λT - 23 .8528) – (3)
Using the above 3 equations and using the catalogue values of (∝.δ) of the special 102
stars of table II, the values of (λN.β) are calculated for all of them and entered in table II.
Note: Figure II gives the correct idea of what (∝.δ), (λN.β) and (λT,β) for the stars are.
Notice that ‘β’ will be the same whether it is called Sayana tropical latitude or Nirayana
latitude.
26/06/2014
26/06/2014 32
Notes and References 1. Balachandra Rao, S. 2000 2. Saha M.N. and Lahiri N.C. 1954 3. Chatterjee S.K, IJHS, 2004, pp 519-534. 4. Hirschfeld, Sinnott and Ochsenbein, 1991 5. Pingree,D., and Morissey.P., 1989, pp 99-119. 6. Lahiri, N.C., 1995. 7. Abhyankar,K.D., IJHS, 2002, pp 31-36. 8. Henry Draper Sky Catalog, 1996. 9. Smithsonian Astrophysical Observatory Star Catalogue (SAS), 1966 / 1971.
Bibliography
∙ Abhyankar, K.D, ‘Probable rationale for unequal nakshatra divisions in Jain Astronomy,’ IJHS, vol 37.1, 2002. • Abhyankar, K.D., ‘Some comments on Kelkar committee’s proposed all India calendar’, IJHS, vol 40.2, 2005. • Balachandra Rao, S., ‘Indian Astronomy – An Introduction’, Universities Press, Hyderabad, 2000. • Basu, Biman, ‘Joy of Star Watching’, New Delhi 2004. • Chatterjee, S.K., ‘Uniform All India Nirayana Solar Calender, IJHS, vol 39.4, 2004. • Henry Draper Star Catalog, Willman – Bell Inc., 1996. • Hirschfeld, Alan, Roger Sinnott and Francois Ochsenbein (Ed), ‘Sky Catalogue 2000.0’ vol I & II, Sky publishing corporation, Cambridge, Mass, USA, 1991. • Kelkar,R.R., ‘Peer review committee report’ May 2002. • Lahiri, N.C., ‘Indian Ephemeris for 1995AD’, Astro-Research Bureau, Calcutta, 1995.
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• Norton, A.P and J.Gall Inglis, ‘Star Atlas and Reference Handbook’, Gall and Inglis, London, 1946. • Pandya S.P, ‘Review Committee Report’, March 1988. • Pingree, D and Morrissey, P, ‘On the Identification of the Yogataaras of the Indian Nakshatras,’ Journal of the History of Astronomy’, vol 20, No.2, June 1989. Also provided by NASA Astrophysics data system as science history publication. • Ramachandran, G.V, ‘A Text Book of Astronomy’, (3rd edition), Rukmini Ramachandran, Tiruchirapalli, 1960. • Rashtriya Panchang of Saka Era 1932, (2010-11), India Meteorological Department, Delhi, 2009. • Saha, M.N and Lahiri N.C, ‘Calendar Reforms Committee Report’, Sept.1954. • Smart, W.M, ‘Foundations of Astronomy’, Longmans, Green & Co, London, 1947. • Smithsonian Astrophysical Observatory Star Catalogue, Washington D.C., 1996 / 1971. • Swamikannupillai, L.D, ‘Indian Chronology’, Madras, 1911, Reprinted by Asian Educational Services, New Delhi, 1982.
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