Surya Siddhanta

[ This project aims at providing a thorough commentary of Surya Siddhanta and its comparison with modern astronomy, together with its use in astrology.]

In ancient India 18 original theoreticians were frequently mentioned in the field of astronomy, but Varah Mihir could get tangible proofs of only five, which he mentioned in his Panch-siddhantika ('Of Five Theories'), among which Surya Siddhanta was the only theory which was complete in itself and therefore highly regarded as the most reliable among all theories about heavens.

In India, the actual formulae of Surya Siddhanta are orally preserved by brahmachari brahmanas (lifelong celibates) and are regarded as sacrosanct by traditional scholars of this field, and are never published, because it is believed that the practical method of using this text ought to be given only to worthy persons, who does not make a living out of it(-Manusmriti). No commentator has ever published the practical methods of making computations from Surya Siddhantic formulae. These commentators themselves did not know these formulae. The Makaranda-Tables are Surya Siddhantic, made from some approximate formulae of Surya Siddhanta (there is error in mean Mars of Makaranda because Makarandacharya forgot to undertake beej-samskara in Mars), which implies that Makarandacharya possessed at least the approximate formulae and publicised the tables made from those formulae, but did not made public those formulae. Recently, many governmental and non-governmental organisations in India have started publishing annual almanacs based upon a freely distributed Surya Siddhantic software, whose developer refuses to publish the formulae, saying publicising it is prohibited in Surya Siddhanta itself. It is still claimed by many astrologers of India that predictions based upon Surya Siddhanta are perfect, but professors of astrology in Indian universities neither refute nor accept such claims.Currently a high court in India(Patna High Court) is sitting over a public interest litigation which charges that Surya Siddhantic formulae are not known to university professors and therefore wrong knowledge and wrong degrees are being awarded to students of Surya Siddhanta !

In 2006, a book was published in Hindi in which all major constants of modern astronomy were mathematically deduced, by means of theorems, from Surya Siddhanta ! But the author stated that Surya Siddhantic planets occupy different positions in heaven than material planets (Vinay Jha,2006). If the claims made in this Hindi book is accepted, it will mean that constants of modern astronomy were known to many ancient scholars with a high degree of precision !

Surya Siddhantic 'Sun' is stated to be a deity, only 5.5 million kilometres from Earth. A deity cannot be seen by ordinary senses, argue the proponents of Surya Siddhanta. The only proof of Surya Siddhanta is its astrological predictions, which are held to be absolutely perfect. Since astrology based upon modern astrononomy has already proven to be a fake science, Surya Siddhantic astrology needs to be tested for its claims.

There was one prehistoric Aryabhata whose commentary upon Surya Siddhanta was extant till 16th century AD, but was subsequently lost (cf. reference in Grahalaghava of Ganesh,1519 AD). Author of Aryabhatiya was not a follower of Surya Siddhanta, and differs from the latter in all major practical aspects, e.g, number of revolutions per mahayuga, sizes of epicycles, sequence of corrections to be made in the mean planet to get true one, etc. Aryabhatiya was widely criticised by supporters of canonical astronomy in India. It is noteworthy that the philosophical and astronomical or astrological statements made by epic and puranic authors of India conform to Surya Siddhantic views. Hence, Surya Siddhanta is the sole book which can make a claim to constitute the bedrock of India's traditional astronomical/astrological mathematics. Other traditional text are are either incomplete or inconherent.

The problem with western commentators is that Surya Siddhantic system has many similarities with that of Almagest, on account of which Surya Siddhanta is declared to be influenced by Almagest. But detailed investigation of Surya Siddhantic system does not support this view. Almagest also does not seem to be directly influenced by Surya Siddhanta. There seems to be a long history of distortions through translations, which may place original Surya Siddhanta in distant prehistory. The idea of trepidation originated from Surya Siddhanta, in which 360° was multiplied with 30% to get 108°, which had four parts of 27° each, in both positive and negative phases. Some prehistoric translator multiplied this 27° with 30% again and deduced the maximum value of trepidation to be 8° only, which was current in Babylon and Europe till 15th century AD, when modern astronomy proved that material universe does not manifest any to and fro oscillation or trepidation of equinoxes at all. But Surya Siddhantic system cannot work without trepidation ( = ayanaamsha ), and Indian astrology will die if ayanaamsha is removed. If astrology has any merit at all, it must be based upon Surya Siddhantic system , because this system has a complete and coherent system as well as a complete parallel universe of gods who regulate the destinies of living creatures. Those commentators who confuse Surya Siddhantic planets to be same as material planets observed by astronomers declare this text to be imprecise, and such commentators do not even try to test the validity of Surya Siddhantic system for astrology based upon Parashara.

Surya Siddhanta gives the locations of several stars other than the lunar nakshatras, which are not the stars of material universe according to proponents of Surya Siddhanta.

Later Indian mathematicians and astronomers such as Aryabhata and Varah Mihir made references to this text, while later Arabic and Latin translations were very influential in the Middle East and Europe.

Dating the Surya Siddhanta : Different Views

The Surya Siddhanta is one of the earliest astronomical treatises of India, but the form in which it has come to us is believed to date after circa 400. It has rules laid down to determine the true motions of the luminaries, which do not exactly conform to the positions of material objects in the sky. It is not known who wrote the Surya Siddhanta or when it was first compiled. It is stated in Surya Siddhanta that it was given by the Sun-God to an Asura named Maya in 2163101 BCE. Such a date cannot be accepted by modern scholars,but we do not have definite alternatives. The most common dates of the extant versions are usually around the 4th century,which are based upon concurrence of Surya Siddhantic tropical True Sun with that of modern astronomy. 782 AD is the date for such a concurrence in mean sun, and 908 AD is for true sun. Since Varah Mihir had stated around 500 or 550 AD that Surya Siddhanta was the most accurate and prominent of all theories, 800 or 900 AD cannot be the date of composition of original Surya Siddhanta.It is,therefore, proposed that 1 degree of error in Surya Siddhantic True Sun may place it around 400 AD. But there is no period in history when the descrepancy between Surya Siddhantic and scientific values of true positions of all planets fall within tolerable margins. Around 400 to 900 AD,all five planets show differences widely fluctuating bewteen ±12 degrees,which is too much to enable any dating based on this method.

It is inconceivable that errors of 12° went unnoticed by all ancient astronomers ! The reason is different,which is deliberately neglected by all modern commentators. Surya Siddhanta explicitly states that its planets are incarnations of God and are therefore deities. The whole material universe vanishes during the night of Brahma when Surya Siddhantic Sun continues moving, otherwise Brahma will not know that His night has elapsed. Hence,Surya Siddhantic planets were believed to be different from the material planets.The main purpose of astronomy was predictive astrology, hence actual position of material bodies in the sky did not matter at all to most of the ancient Indians. Modern commentators assume Sutya Siddhantic planets to be same as material objects of the sky, and therefore deduce that Surya Siddhanta is an inaccurate text as far as astronomy is concerned. No detailed examination of the original scheme of Surya Siddhanta is deemed necesasary. Dating the Surya Siddhanta needs a reevaluation in the light of many new facets of this mysterious text, unearthed in a Hindi book (Vinay Jha,2006).

Old and New Versions of Surya Siddhantas

In his famous treatise Panchsiddhaantika (Five Theories),Varah Mihira concluded that Surya Siddhanta was the most clear and valuable of all theories. But in his version of Surya Siddhanta the revolutions of planets during a mahayuga of 4320000 years (known as Yugabhagan) does not tally with the extant version of Surya Siddhanta. This descrepancy induced European scholars to call the Panchsiddhaantic version of Surya Siddhanta as the old one, and the extant version as the modern one. This nomenclature was used by G.Thibaut,the commentator of Panchsiddhaantika. But this decision was made without any scientific investigation into the causes of this descrepancy.

The Mahayuga-bhaganmaana (revolutions per 43200000 years) of five planets in old and modern versions of Surya Siddhanta are as follows:

                 Old SS     Modern SS           Differences
                                        Old SS    Actual SS   Aryabhatiya
      Mercury   17937000     17937060      +60     +12.58       -40
      Venus      7022388      7022376      -12     - 9.43       +12
      Mars       2296824      2296832      + 8     + 2.6        - 8
      Jupiter     364220       364220        0     - 6.29       + 4
      Saturn      146564       146568      + 4     + 9.43       - 4

There were three methods of making almanacs (panchangas) : Siddhanta, Tantra,and Karana. In the siddhaantic method, computations were made from the beginning of Creation. 499 AD was 1955883600 years after Creation according to Surya Siddhaanta, which was equal to 452.7508 Mahayugas. A difference of 60 revolutions during one mahayuga means a difference of 452.75 * 60 = 27165.05 revolutions since Creation ! Such a difference makes a mockery of everything. Hence Varah Mihir's figure cannot be related to Siddhaantic methodology in any case.

In the Tantric Method (which has nothing to do with Tantra of religion or philosophy), difference of 60 revolutions during 4320000 years implies a difference of 18° during 3600 years ,i.e., between the onset of Kali Age and AD 499 , when trepidation or ayanamsha was zero and therefore the author of Aryabhatiya chose this year for his reference point,which was near the time of composition of Aryabhatiya. Varah Mihira is believed to have written his texts nearlt five decades later. An error of 18° could not be accepted by anyone. Since the modern Surya Siddhanta is the basis of a large number of Indian almanacs,being not much removed from actual positions of material planets as well, it is the Old Surya Siddhaanta of Varah Mihir which must be faulty.

There is a third possibility of Karana Method, in which any neighbouring year is chosen as reference point and Yuga-bhagans are readjusted accordingly in order to facilitate the task of almanac-makers. If the Old Surya Siddhanta had a Karana reference point only a few centuries before Varah Mihira, the error in mean planets will vastly decrease. Hence, it may be argued that the Old Surya Siddhanta quoted by Varah Mihira was actually quoted from not a Sidhhanta but a Karana text. This last possibility is really significant,because it has some remote connections with actual Beej-samskaara for AD 499 as shown in the table above.Although Varah Mihira's figures show large errors in magnitude, the sign of differences are never reversed. Hence, we must conclude that Varah Mihira had access to some almanac making Karana text supposedly based upon Surya Siddhanta, which used wrong values of beej-samakaara. See the section 'Siddhantic Beej Samskaara' for further details on Beej-Samskaara, which are essential corrections in mean planets. The figures given by Varah Mihira are certainly related to some lost Surya Siddhantic Karana text, but the values are wrong, which will result in a very faulty almanac for any period. For instance, Mercury will show a beej-samskaara of 18°,while its actual beej-samskaara ought to be a little over 6° only during the age of Varah Mihira. An error of 12° could not have been accepted by anyone. Had Varah Mihira possessed any idea of beej samskaara, he must have elucidated it by differentiating the Siddhantic bhagans(e.g.17937060 for Mercury) from beej samskaara (+12.6 or roughly +13 for Mercury). When he tried to find out the values of mahayuga-bhagans from some almanac making karana text, he failed to notice that Karana texts contain not the Siddhantic bhagans but beej-sanskrit bhagans(i.e.,corrections already made in the tables for mean planets).Varah Mihir was not an almanac maker, and therefore could not discern this nuance of traditional Indian astronomy, which has always remained a trade secret of almanac-makers. It is intereasting to note in this respect that all modern Surya Siddhantic almanac makers of India are using tables made in AD 1478 (known as Makaranda Tables), because these almanac makers do not know how to update the tables, and refuse to accept the views of those who know the secret.Hence, it is not surprising that Varah Mihir did not know a closely guarded secret and therefore gave wrong values in his treatise. No almanac for any period can be made from the values given by Varah Mihira. Hence, it is wrong to label his version as Old Surya Siddhanta, because he did not possess any version of Surya Siddhanta at all and merely tried to get something out of karana text which he failed to understand properly. Thibaut was totally in the wrong in proposing Old and Modern versions, because Thibaut did not try to understand the actual practices of traditional almanac making. The socalled modern Surya Sidhhanta is the only version ever available, and whatever Varah Mihir quoted was not from Surya Siddhanta but from a wrong interpretation of some almanac making text based upon Surya Siddhanta.(These sentences are being written by a person who is the maker of six governmental and non-governmental Surya Siddhantic almanacs in different states of India at present. Cf. Vinay Jha,2006).

The table of Mahayuga-bhagans shown above also shows the figures of Aryabhatiya, which apparently seem to be even more spurious than those of Varah Mihir,because the figures of Aryabhatiya have signs inverted in the case of all planets. Aryabhata could not have made such a blunder. The only plausible explanation is that he substracted beej corrections instead of adding them to mean planets. Even if this view is accepted, the values viven in Aryabhatiya will lead to a faulty almanac, containing errors of 6° in the case of Mercury if comparison with Surya Siddhanta are made. Aryabhatiya does not show good results even if comparison with modern methods are made. Moreover,the sequence of corrections made in mean planet to get true planet is wrong in Aryabhatiya, which is discussed in the section 'Corrections in Mean Planet to Make True Planet'.In this connection, the section 'Lost Surya Siddhantic Commentary of Aryabhata : New Lights ' should be viewed as well.

Many aspects of Surya Siddhanta have not been thoroughly researched. For instance, Surya Siddhantic equatorial diameter of Earth is stated to be 800 yojanas, one yojana equalling 7.97274625 kilometres. The distance from Girivajra (prehistoric capital of Magadha) to Mathura comes out to be 98.51 yojanas. In Mahabharata, it is stated that Mathura was 99 yojanas from Girivajra ! This story of Jarasandha of Girivajra is part of the basic story of Mahabharata and cannot be an interpolation. Moreover, only the Surya Siddhantic value of one yojana equalling 7.97274625 kilometres satisfies the statement in Mahabharata. During 500-600 AD, Earth's circumference was stated to be 3200 to 3300 yojanas by Aryabhata and Varah Mihira, 6600 yojana by Aryabhata II later, 4867 by Bhaskaracharya in 11th century and nearly 4000 by Ganesh of Grahalaghava in AD 1519. The implication is that the author of Mahabharata knew how to compute the diameter and other aspects of Earth !

The Moon's Risings and Settings

== Cosmogony and Geography ==Surya Siddhantic system is neither heliocentric nor geocentric. It clearly states that Mt Meru resides at the centre (equator) of globe in the region od Surya Siddhantic of Zamboodweep. In Africa, Mt Kenya is situated upon equatorin a region where place names are reminiscent of Surya Siddhanta : Meru town near Mt Kenya, another Mt Meru slightly southwards, a place named kinyan-giri which means Mr Kenya in sanskrit, river Zamboonadi > *zamboodi > *zambedi > *zambezi, Mu-zambique, Zambia, Zimb-abwe, Gabon (< *Zamboon), Congo (< *Gongo < *zambo),etc. Homo genus of mankind is known to have evolved in that region around 4 million years ago. Surya Siddhantic formulae of making true planets from mean ones require the use of distance from Earth's centre to a point in space 28.913 kilometres above the top of Mt Meru (Mt Kenya), which was believed to be centre of all universes by puranic authors.

Surya Siddhantic universe is much smaller in comparison to material universe, and Sun's distance from Earth is only 861.7 times of Earth's equatorial radius. Material Sun's distance is 23455 times of Earth's equatorial radius ! Ptolemy used a figure 1210, which is not much removed from Surya Siddhantic figure. Ptolemic system is well known, but Surya Siddhantic system is rather obscure, known to a few initiated brahmanas only. Due to lack of knowledge of orally transmitted and unpublished portions of original Surya Siddhanta, European commentators believe that Surya Siddhantic system was influenced by Ptolemy's Almagest. But those who know the secrets of Surya Siddhanta say that its framework is too complex and organically self-contrained to have been influenced by any other system. For instance, Surya Siddhantic daily motions of all planets are exactly equal to a constant, but this rule is not followed in Almagest. Surya Siddhantic system is based upon a cosmic centre at Meru,which is absent in Almagest. Surya Siddhantic solar epicycle is equal to 14 yojanas per degree, which is equal to 5040 yojanas for 360 degrees. Its diameter is 1604.3 yojanas, which is 4.3 yojanas more than Earth's equatorial diameter. 4.3 yojanas equals 5.199 kilometres ( height of Mt Meru or Mt Kenya)plus 28.913 kilometres. Solar epicycle equals to 14 yojanas, which gets reduced to 13:40 at perigee of this elliptical epicycle, which when divided by 2π gives 2:10:31 degrees, which is the maximum mandaphala (difference between mean and true Sun) for Sun. Surya Siddhantic theory, therefore relates yojana to degrees in an intrinsic manner, which makes it clear that it was not borrowed from Almagest. This value of yojana was not only prehistoric, manifest in the story of Jarasandha's 99 yojanas cited above, but was also intrinsically related to many native concepts of Surya Siddhanta.

Trigonometry of Surya Siddhanta

                             Trigonometry

The Surya Siddhanta contains the roots of modern trigonometry. It uses sine (jya), cosine (kojya or "perpendicular sine") and inverse sine (otkram jya) for the first time, and also contains the earliest use of the tangent and secant when discussing the shadow cast by a gnomon in verses 21–22 of Chapter 3:

Of [the sun's meridian zenith distance] find the jya ("base sine") and kojya (cosine or "perpendicular sine"). If then the jya and radius be multiplied respectively by the measure of the gnomon in digits, and divided by the kojya, the results are the shadow and hypotenuse at mid-day.

In modern notation, this gives the shadow of the gnomon at mid-day as

$s={\frac {g\sin \theta }{\cos \theta }}=g\tan \theta$

and the hypotenuse of the gnomon at mid-day as

$h={\frac {gr}{\cos \theta }}=gr{\frac {1}{\cos \theta }}=gr\sec \theta$

where $\ g$ is the measure of the gnomon, $\ r$ is the radius of the gnomon, $\ s$ is the shadow of the gnomon, and $\ h$ is the hypotenuse of the gnomon.

Practical Method of Casting a Surya Siddhantic Horoscope

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Methods for accurately calculating the shadow cast by a gnomon are discussed in both Chapters 3 and 13.

The astronomical time cycles contained in the text were remarkably accurate at the time. The Hindu cosmological time cycles, copied from an earlier work, are described in verses 11–23 of Chapter 1:

11. That which begins with respirations (prana) is called real.... Six respirations make a vinadi, sixty of these a nadi;

12. And sixty nadis make a sidereal day and night. Of thirty of these sidereal days is composed a month; a civil (savana) month consists of as many sunrises;

13. A lunar month, of as many lunar days (tithi); a solar (saura) month is determined by the entrance of the sun into a sign of the zodiac; twelve months make a year. This is called a day of the gods.

14. The day and night of the gods and of the demons are mutually opposed to one another. Six times sixty of them are a year of the gods, and likewise of the demons.

15. Twelve thousand of these divine years are denominated a caturyuga; of ten thousand times four hundred and thirty-two solar years

16. Is composed that caturyuga, with its dawn and twilight. The difference of the krtayuga and the other yugas, as measured by the difference in the number of the feet of Virtue in each, is as follows:

17. The tenth part of a caturyuga, multiplied successively by four, three, two, and one, gives the length of the krta and the other yugas: the sixth part of each belongs to its dawn and twilight.

18. One and seventy caturyugas make a manu; at its end is a twilight which has the number of years of a krtayuga, and which is a deluge.

19. In a kalpa are reckoned fourteen manus with their respective twilights; at the commencement of the kalpa is a fifteenth dawn, having the length of a krtayuga.

20. The kalpa, thus composed of a thousand caturyugas, and which brings about the destruction of all that exists, is a day of Brahma; his night is of the same length.

21. His extreme age is a hundred, according to this valuation of a day and a night. The half of his life is past; of the remainder, this is the first kalpa.

22. And of this kalpa, six manus are past, with their respective twilights; and of the Manu son of Vivasvant, twenty-seven caturyugas are past;

23. Of the present, the twenty-eighth, caturyuga, this krtayuga is past....

When computed, this astronomical time cycle would give the following results:

• The average length of the tropical year as 365.2421756 days, which is only 1.4 seconds shorter than the modern value of 365.2421904 days (J2000). This estimate remained the most accurate approximation for the length of the tropical year anywhere in the world for at least another six centuries, until Muslim mathematician Omar Khayyam gave a better approximation, though it still remains more accurate than the value given by the modern Gregorian calendar currently in use around the world, which gives the average length of the year as 365.2425 days.

• The average length of the sidereal year, the actual length of the Earth's revolution around the Sun, as 365.2563627 days, which is virtually the same as the modern value of 365.25636305 days (J2000). This remained the most accurate estimate for the length of the sidereal year anywhere in the world for over a thousand years.

The actual astronomical value stated for the sidereal year however, is not as accurate. The length of the sidereal year is stated to be 365.2587565 days, which is longer than the modern value by 3 minutes 27 seconds. This is due to the text using a different method for actual astronomical computation, rather than the Hindu cosmological time cycles copied from an earlier text, probably because the author didn't understand how to compute the complex time cycles. The author instead employed a mean motion for the Sun and a constant of precession inferior to that used in the Hindu cosmological time cycles.

Calendrical uses of Surya Siddhanta

The Indian solar and lunisolar calendars are widely used, with their local variations, in different parts of India. They are important in predicting the dates for the celebration of various festivals, performance of various rites as well as on all astronomical matters. The modern Indian solar and lunisolar calendars are based on close approximations to the true times of the Sun’s entrance into the various rasis.

Conservative "panchang" (almanac) makers still use the tables based upon Surya Siddhanta to compile and compute their panchangs. The panchang is an annual publication published in all regions and languages in India containing all calendrical information on religious, cultural and astronomical events. It exerts great influence on the religious and social life of the people in India and is found in most Hindu households.

References

• Ebenezer Burgess. "Translation of the Surya-Siddhanta, a text-book of Hindu Astronomy", Journal of the American Oriental Society 6 (1860): 141–498.
• Victor J. Katz. A History of Mathematics: An Introduction, 1998.
• Dwight William Johnson. Exegesis of Hindu Cosmological Time Cycles, 2003.
• Alaska Mark. Surya Siddhanta, Chapter I with Commentary and Illustrations, 2005.
• Vinay Jha,Deduction of Modern Astronomy from Surya Siddhanta,Sky Research Centre,364 Lancer's Road,Timarpur,Delhi-54,India; AD 2006. Tel: (+91)9431219630,(+91)9931360854,(+91)06272222730.

See also

• Indian science and technology
• Indian mathematics
• Hindu astronomy