Ayanamsa
Encyclopedia
Sanskrit
Sanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...
term in Indian astronomy for the amount of precession
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...
. In astrology, this is the longitudinal difference between the Tropical (Sāyana) and Sidereal
Sidereal astrology
Sidereal and tropical are astronomical terms used to describe two different definitions of a "year". They are also used as terms for two systems of ecliptic coordinates used in astrology....
(Nirayana) zodiacs.
The above is a modern definition of ayanamsha, based on arguments of Colebrooke, Burgess, etc. But ancient definition of ayanamsha had no relation with precession of equinoxes. Suryasiddhanta (iii, 9-10) defines ayanamsha as the to and fro motion of the circle of asterisms (Nakshatra-chakra or Bhachakra) within a maximum range of + and - 27 degrees at an annual rate of 54". Burgess could not digest the idea of trepidating Nakshatra-chakra, and assumed that some error had creeped in the text. On the basis of this assumption, he advocated the use of precession of equinoxes to define ayanamsha, following the arguments of his predecessors like Colebrooke. They assumed that ancient Indians did not know how to measure precession accurately and therefore invented a wrong concept of trepidating precession. But Bhaskar-ii in Siddhanta Shiromani gives equationjs for measurement of precession of equinoxes, and says his equations are based on some lost equations of Suryasiddhanta plus the equation of Munjaala.
Overview
Ayanamsa is now defined as the angle by which the sidereal ecliptic longitude of a celestial body is less than its tropical ecliptic longitude. Ayanamsa is mostly assumed to be close to be 24° today, according to N. C. Lahiri 23.85° as of 2000. This value would correspond to a coincidence of the sidereal with the tropical zodiac in or near the year 293 AD, roughly compatible with the assumption that the tradition of the tropical zodiac as current in Western astrologyWestern astrology
Western astrology is the system of astrology most popular in Western countries. Western astrology is historically based on Ptolemy's Tetrabiblos , which in turn was a continuation of Hellenistic and ultimately Babylonian traditions....
was fixed by Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
in the 3rd century.
- The sidereal ecliptic longitude of a celestial body is its longitude on the eclipticEclipticThe ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...
defined with respect to the "fixed" starStarA star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
s. - The tropical ecliptic longitude of a celestial body is its longitude on the ecliptic defined with respect to the vernal equinox point.
Since the vernal equinox point precesses westwards at a rate of about 50".29 per year (the rate has been accelerating) with respect to the fixed stars, the longitude of a fixed body defined with respect to it will increase slowly. On the other hand, since the stars "do not move" (this ignores the effect of proper motion
Proper motion
The proper motion of a star is its angular change in position over time as seen from the center of mass of the solar system. It is measured in seconds of arc per year, arcsec/yr, where 3600 arcseconds equal one degree. This contrasts with radial velocity, which is the time rate of change in...
) the longitude of a fixed body defined with respect to them will never change.
Traditional Vedic astrology (Jyotisha
Jyotisha
Hindu astrology , also Jyotish or Jyotisha, from Sanskrit , from "light, heavenly body") is the ancient Indian system of astronomy and astrology...
) uses a system of sidereal longitude. When the practitioners of these schools of astrology use modern astronomical calculations to determine the position of celestial bodies, they need to take into account the difference caused by the different reference point used in specifying the longitude, and this they call the ayanamsa.
But all orthodox schools of Vedic astrology reject modern astronomy and still base their computations upon traditional texts and treatises, mostly following the Surya Siddhanta
Surya Siddhanta
The Surya Siddhanta is one of the earliest siddhanta in archeo-astronomy of the Hindus by an unknown author. It describes the archeo-astronomy theories, principles and methods of the ancient Hindus. This siddhanta is supposed to be the knowledge that the Sun god gave to an Asura called Maya. Asuras...
or treatises based on it. They use ayanāmsa according to Surya Siddhānta, in which ayanāmsa rises from 0° to +27° during 1800 years, then decreases to 0° and further to -27°, thereafter rising again, thus oscillating within a rage of ±27° instead of cyclically moving in a circle as modern concept of ayanāmsa suggests.
Manjula
Manjula
- The arts :* Manjula , a Kannada film actress* Manjula Ghattamaneni, an Indian film producer and actress* Manjula Padmanabhan an Indian playwright, artist and author* Manjula Vijayakumar, a Tamil film actress...
advocated a cyclical concept of ayanāmsa, but it could not gain currency among almanac makers. In West Theon (ca. 4th century AD) was the earliest known advocate of Surya Siddhāntic type of ayanāmsa (although Theon said trepidation varied within a rage of ±8° only : Surya Siddhāntic trepidation was deduced by multiplying 90° with 0.3, Theon multiplied 27° again with 0.3 to get 8° ). This oscillating type of ayanāmsa, known as trepidation, was a favourite of Indian, Arab and European astrologers and astronomers till the time of Copernicus. Modern science does not support the idea of trepidation or oscillating ayanāmsa. 499 AD is regarded as the zero date of this type of ayanāmsa according to Surya Siddhānta, Aryabhatiya
Aryabhatiya
Āryabhaṭīya or Āryabhaṭīyaṃ, a Sanskrit astronomical treatise, is the magnum opus and only extant work of the 5th century Indian mathematician, Āryabhaṭa.- Structure and style:...
and other ancient treatises. Thus the present value of traditional ayanāmsa is nearly +22.64°, which is less than modern the value of about +24°.
After 2299 AD, the traditional ayanāmsa will start decreasing from the maximum value of +27°, while modern value will keep on increasing. Equations of sunrise and ascendant (lagna) need accurate value of ayanāmsa, upon which all important components of religious almanac and horoscopes are based in India.
The ayanamsha describes the increasing gap between the tropical and sidereal zodiacs. The ayanamsa, changes continually through the Precession of the Equinoxes
Precession of the equinoxes
In astronomy, axial precession is a gravity-induced, slow and continuous change in the orientation of an astronomical body's rotational axis. In particular, it refers to the gradual shift in the orientation of Earth's axis of rotation, which, like a wobbling top, traces out a pair of cones joined...
at the rate of approximately 50" a year, is currently about 24°.
Western Astrologers Fagan
Cyril Fagan
Cyril Fagan was an astrologer, who claimed historical use of sidereal astrology in the west and established it as a separate field from tropical astrology....
and Bradley computed it at 24 degrees in 1950; however, there are various values in use in India. While the general consensus is that the star Alcyon represents the first point of Aries, differences arise because of the indefinite ancient boundaries of the constellation of Aries.
Ancient concepts
In the chapter "Direction, Place and Time" (Suryasiddhānta, Ch.iii), E. Burgess writes:This is the interpretation of existing version of Surya Siddhānta (त्रिंशत्कृत्यो युगे भानां चक्रे प्राक् परिलम्बते ..., SS,iii.9) in the words of E. Burgess, "as it is actually intended to put forth" by all traditional commentators.
The moot point is this: Burgess knew the traditional interpretation (भानां चक्रे.., i.e. pendulum-like motion of nakshatra orbit itself) , but gave his own meaning based upon modern concept of precession of equinoxes, and tried to create doubts about the authenticity of these verses (iii, 9-12) by putting forth deliberately false arguments. Let us examine Burgess.
In verse-9 (Suryasiddhānta, Ch.iii), he translates pari-lambate as "falls back", although he says lambate means "lag, hang back, fall behind" and pari means "about, round about". Therefore, pari-lambate should have been translated as "fall back roundabout" and not merely as "fall back" according to own logic of Burgess. If the circle of asterisms lags roundabout any fixed point (whether Revati or Chitrā), it is a to and fro motion as all traditional commentators accepted. Modern concept of precession is something different from the original concept of ayanāmsha. Theon in West had mentioned this oscillating motion, Arab astronomers also accepted it, and almost all Europeans accepted it up to Renaissance, after which Hipparchus was rediscovered and modern concept of precession became a well established fact in astronomy. But this concept of equinoctial precession (as well as anomalistic precession) was also known to ancient Indians and Greeks, a fact deliberately ignored by modern commentators.
Burgess misquotes Bhāskara II, because he relied upon a wrong translation of Bhāskara by Colebrooke (As. Res., xii 209; Essays, ii,374, etc.) and did not try to examine Siddhānta Shiromani which was wrongly translated by Lancelot Wilkinson due to Colebrooke's influence. Bhāskara II did not give his own opinion at all, and merely quoted Surya Siddhānta and Mujjāl (elsewhere Munjāla and Manjula), saying Suryasiddhānta gives -30000 revolutions of sampāt or equinoctial point per Kalpa while ayana has a motion of +199669 revolutions per Kalpa (of 4320 million years). Bhāskara's own opinion was that these should be followed, which means both Surya Siddhānta and Mujjāla were correct in Bhāskara's opinion. Colebrooke, Burgess, Wilkinson, etc. have misquoted Siddhānta Shiromani and created an impression that ancient Indians were inept in astronomical observations, as Whitney shamelessly declared in his prologue to Burgess, but the Hindi translation by Satyadeva Sharmā is correct, although he could not get the real meaning.
The startling fact is that Siddhānta Shiromani clearly says that "the point of intersection of equatorial plane and ecliptic" (which is the very definition of equinox) has a negative motion of 30000 revolutions per Kalpa according to Suryasiddhānta, while Mujjala's value of ayana's motion is +199669, and both (Suryasiddhānta and Mujjala ) must be added to get the final motion (of the equinox ). Hence, we get +169669 revolutions per Kalpa, which gives (4320000000 / 169669 =) 25461 years per revolution or 50.9″ per year, which is very near to modern value of about 50.3″ per year for precession of equinoxes.
We must not forget that Hipparchus had given a period of 36000 years for precession, which was not corrected by Europeans till the onset of modern age. It is unfortunate that Siddhānta Shiromani is still being misinterpreted by moderners. Bhāskara II excluded neither Suryasiddhānta nor Mujjāla, but said that both must be used, which is clear from verse 19, where he clearly asks to add Mujjāla's ayana-chalam to Suryasiddhāntic sampāt-chalanam (this sampāt-chalanam is anomalistic precession with a period of 144000 years per cycle, against modern value of 136000 years).
Another startling fact is that Bhāskara II differentiates sampāt-chalanam of Suryasiddhānta from ayana-chalanam of Mujjāla, and says both must be added before computing phenomena like declension, ascensional differences, etc. But modern commentators like Colebrooke misinterpret Bhāskara II deliberately, and imply that sampāt-chalanam of Suryasiddhānta quoted by Bhāskara II was an erroneous thing which must be forgotten, while ayana-chalanam of Mujjāla was a crude approximation of modern precession. But this interpretation is falsified by Bhāskara's original verses as shown above. The root of this problem lies in the fact that sampāt-chalanam of Suryasiddhānta is a distinct phenomenon from ayana-chalanam of Mujjāla according to Siddhānta Shiromani, but readers are not informed of the real meaning of Siddhānta Shiromani and false quotation from Siddhānta Shiromani was quoted by Colebrooke and Burgess (12th verse, chap.iii).
Siddhānta-tattva-viveka by Kamlākara Bhatt is a medieval text, which clearly states that Saurpaksha is distinct from Drikpaksha. Saurpaksha (astronomy of bhuvaloka) is Suryasiddhānta as it exists. Drikpaksha (astronomy of Bhooloka or physical/material/sensory world) is that version of Suryasiddhānta which was not preserved because it was useless in astrology. Siddhānta Shiromani uses many concepts of Drikpakshiya astronomy, as the instance cited above proves. Saurpakshiya Suryasiddhānta does not contain any reference to 30000 cylces per Kalpa mentioned by Bhāskara II. He was quoting from Drikpakshiya Suryasiddhānta which as a text had been lost; Bhāskara II said in his own Vāsanābhāshya commentary of Siddhānta-shiromani that Suryasiddhānta is not available (anupalabdha) and he was quoting it on the basis of āgama. Only its fragments are left, scattered here and there. Modern commentators confuse both variants of Suryasiddhānta. Siddhāntatattvaviveka is prescribed in post-graduate (Ganitāchārya) syllabus of Sanskrit universities, but no modern commentator has ever tried to translate it or comment on it.
According to Bhāskara II, negative sampāt-chalanam of Drikpakshiya Suryasiddhānta should be added to positive ayana-chalanam of Mujjāla to get final Drikpakshiya precession, which is very close to modern value. Ayana-chalanam of Mujjāla is also Drikpakshiya, because Saurpakshiya entities are not used in Drikpakshiya astronomy, and vice versa.
Mujjāla's ayana-chalanam, as mentioned in Siddhānta Shiromani, gives a period of (4320 million / 199669 = ) 21636 years per cycle. Siddhānta Shiromani says that it is ayanachalanam and not precession, precession is obtained after substracting (Saurpakshiya) Suryasiddhāntic sampātchalanam. If this 21636 year cycle is not precession, what is it?
Earth's axis completes one full cycle of precession approximately every 26,000 years (25771.4 precisely at present); see Milankovich cycles. At the same time, the elliptical orbit rotates, more slowly, leading to a 21,000-year cycle between the seasons and the orbit. This orbital precession is in the opposite sense to the gyroscopic motion of the axis of rotation (cf. anomalistic precession as distinct from equinoctial precession), shortening the period of the precession of the equinoxes with respect to the perihelion from 26,000 to 21,000 years. (Some NOAA websites give 22000 years instead of 21000.)
Ayana-chalanam of Mujjāla is not orbital precession, it is the most important of all components of Milankovitch cycles as this Wikipedian definition shown. If we take cue from Siddhānta Shiromani, the aforementioned statement can be rewritten thus: This orbital precession of equinoxes is in the opposite sense to the gyroscopic motion of the axis of rotation, shortening the period of the precession of the equinoxes with respect to the perihelion from 25771 to 21,636 years.
Siddhānta Shiromani also says that Mujjāla's ayana-chalanam (21,636 years per cycle) is opposite to sampāta-chalanam. Bhāskara II clearly defines sampāta-chalanam as "the point of intersection of equatorial plane and ecliptic" (which is the very definition of equinox). Hence, what Siddhānta Shiromani says is exactly what Milankovitch informs us, the only difference is that Siddhānta Shiromani is misinterpreted and declared to be obscurantist, and the great cycles mentioned in Siddhānta Shiromani is "discovered" by 20th century scientists. But we must remember Bhāskara II did not discover these things, he acknowledged Suryasiddhānta and Munjāla.
Bhāskara II knew Drikpakshiya Suryasiddhānta, which has not survived because it was not useful in astrology. In his formula of precession, Bhāskara II used a figure 30000 cycles per Kalpa. Bhāskara II got an approximate value of 50.9″ per year, which was the most precise value before modern astronomy developed in the West. Here is a Puranic verse (cited by Dr Ramchandra Pandey in his commentary on Suryasiddhanta) which proves knowledge of equinoctial precession in Puranic times :
- उत्तानपादपुत्रोऽसौ मेढीभूतो ध्रुवो दिवि ।
- स हि भ्रमन् भ्रामयते नित्यं चन्द्रादित्यौ ग्रहैः सह ।।
("Uttanpāda's son Dhruva is the fixed point in the Heavens, round which all planets including Sun and Moon, but Dhruva himself also moves round.") Round what ? Mt Meru, which is the only fixed point in Cosmos according to Purānic-epic stories. Hence, the Bhachakra also librates with respect to this fixed point Meru.
According to Bhāskara II, orbital precession is derived by substracting anomalistic precession (sampāt-chalanam) from the first component of Milankovitch cycles (Munjāla's ayana-chalanam). Bhāskara II acknowledged earlier authors. Hence, we must conclude that modern values and concepts of orbital precession, anomalistic precession, Milankovitch cycles, etc. were known to ancient Indians well before Bhāskara II.
But two things about confusing terminology must be borne in mind : this sampāt-chalanam he finally gets by combining the two quantities mentioned above. According to Bhāskara II, Suryasiddhāntic sampāt-chalanam is 30000 per Kalpa. He does not give a name for the term which is finally obtained by combining this sampāt-chalanam with Munjāla's ayana-chalanam, but the definition he provides for Suryasiddhāntic sampāt-chalanam is exactly the definition of the final quantity whose name he does not provide. Hence, there were many types of sampāt-chalanams !! This is not a case of confusion of terms. It is a result of Saurpakshiya term with Drikpakshiya terms bearing same names but having different magnitudes and sometimes even having difference in basic properties !
Second confusion is due to use of the term ayana-chalanam for Munjāla's precession. It is quite distinct from Saurpakshiya Suryasiddhāntic ayana-chalanam (trepidation) as mentioned in existing text. Burgess could not digest this theory of libration (oscillation or trepidation, i.e., ayanāamsha - motion) and tried to distort the meaning of terms to fit modern view of orbital precession with this Saurpakshiya precession. Bhāskara II knew and respected Suryasiddhānta which he cited and used in his computations as shown above, and gave exact value of Drikpakshiya precession. Therefore, it is foolish to impose Drikpakshiya precession (50.9″ per year according to Bhāskara II, 50.3″ really) upon Saurpakshiya ayanamsha (54″ per year, oscillating within a range of ± 27 degrees).