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'''''Sūrya Siddhānta''''' is an ancient Indian treatise in Astronomy. Like many classical Indian works, the ''Sūrya Siddhānta'' is a poem in [[Sanskrit]] language. It has fourteen chapter and 500 verses. It is composed in ''śloka'' metrical style of Sanskrit. It contain works on Indian sine tables, cosmology, eclipses, planetary motions, conjunctions, star positions, geography, instrumentation, concepts of time and mathematics. Unlike conventional books ''Sūrya Siddhānta'' contains advanced calculation and methods which are not easily comprehensible for a rank beginner. <ref>[https://insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol45_4_1_ANarayan.pdf]</ref> The text had been updated several times and the last update appears to have  been made around 580 CE to the ''Nakshatra'' longitudes. In second chapter, the text contains the calculation of Earth's obliquity of ''1397 jya (R.sine) 23.975°'' modern units indicating the time of calculation around 3000 BCE. There are several other observations in the tradition of ''Indian Astronomy'' that were also recorded in the vicinity of 3000 BCE. This could possibly be the time of the origin of ''Sūrya Siddhānta'' although scholars do not seem to have a consensus on the origin of this text of ''Indian Astronomy''.
+
'''''Sūrya Siddhānta''''' is an ancient Indian treatise in Astronomy. Like many classical Indian works, the ''Sūrya Siddhānta'' is a poem in [[Sanskrit]] language. It has fourteen chapter and 500 verses. It is composed in ''śloka'' metrical style of Sanskrit. It contain works on Indian sine tables, cosmology, eclipses, planetary motions, conjunctions, star positions, geography, instrumentation, concepts of time and mathematics. Unlike conventional books ''Sūrya Siddhānta'' contains advanced calculation and methods which are not easily comprehensible for a rank beginner. <ref>[https://insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol45_4_1_ANarayan.pdf]</ref> In second chapter, the text contains the calculation of Earth's obliquity of ''1397 jya (R.sine) 23.975°'' modern units. The text describes the observation of two pole stars one each at the north pole and the south pole seen at the equatorial region, such phenomena was last seen in the 3rd millennium BCE. This indicates the antiquity of the concepts recorded in the text.<seo title="Surya Siddhanta" titlemode="append" keywords="Surya Siddhanta, surya, Surya Siddhanta dharma, dhammawiki" description="Sūrya Siddhānta is an ancient Indian treatise in Astronomy. Like many classical Indian works, the Sūrya Siddhānta is a poem in Sanskrit language. It has fourteen chapter and 500 verses. It is composed in śloka metrical style of Sanskrit. It contain works on Indian sine tables, cosmology, eclipses, planetary motions, conjunctions, star positions, geography, instrumentation, concepts of time and mathematics."></seo>
−
 
 
 
== History ==
 
== History ==
 
<nowiki>''Sūrya Siddhānta'' is well known, most referred and most esteemed. The original author of ''Sūrya Siddhānta'' is ''Mayasura'' as described in the story in the first chapter that ''Mayasura'' obtained his knowledge from ''Sūrya'' (the Sun). ''Siddhānta'' in Sanskrit means ''treatise'' and it usually has author'</nowiki>s name prefixed to it. There were several other works on Astronomy in ancient India, many of which have since been lost.
 
<nowiki>''Sūrya Siddhānta'' is well known, most referred and most esteemed. The original author of ''Sūrya Siddhānta'' is ''Mayasura'' as described in the story in the first chapter that ''Mayasura'' obtained his knowledge from ''Sūrya'' (the Sun). ''Siddhānta'' in Sanskrit means ''treatise'' and it usually has author'</nowiki>s name prefixed to it. There were several other works on Astronomy in ancient India, many of which have since been lost.
  
 +
{| class="wikitable"
 +
|-
 +
| ''Surya Siddhānta'' || ''Brahma Siddhānta'' || ''Soma Siddhānta''
 +
|-
 +
| ''Vyasa Siddhānta'' || ''Vashishtha Siddhānta'' || ''Atri Siddhānta''
 +
|-
 +
| ''Parashira Siddhānta'' || ''Kashyap Siddhānta'' || ''Nārad Siddhānta''
 +
|-
 +
| ''Garga Siddhānta'' || ''Marici Siddhānta'' || ''Manu Siddhānta''
 +
|-
 +
| ''Angiras Siddhānta'' || ''Lomasha Siddhānta'' || ''Pulisha Siddhānta''
 +
|-
 +
| ''Cyavana Siddhānta'' || ''Yavana Siddhānta'' || ''Bhrigu Siddhānta''
 +
|}
 +
 +
== Content ==
 +
''Sūrya Siddhānta'' contains 14 chapters and 500 verses. The chapters contain observations, methods, instruments and calculations of various astronomical phenomenas. There is a scarcity of scientific analysis done on the text of ''Surya Siddhanta''. Majority western work is based on Indology dates which in itself is controversial and based on their biased opinion of granting the origin of any science or mathematics to the ancient Greek or babylonians despite of immense textual evidence pointing otherwise. Their analysis of Surya Siddhanta primarily avoids the study of actual data and observations recorded within the ''Surya Siddhanta''.
 +
 +
=== Indian origin of seconds, minutes and degrees ===
 +
''Surya Siddhanta'' in chapter 2 describes the units of seconds, minutes and degrees. These units of measurement are primary basis of the calculations of earth's obliquity and sine tables of ''Surya Siddhanta''. Essentially ''Surya Siddhanta'' describes that Rashi has 30 degrees (Ansh) implying it has 1800 minutes (Kala). The data is as as described in the table
  
 
{| class="wikitable"
 
{| class="wikitable"
 +
|+ ''Surya Siddhanta'' units: seconds, minutes and degrees<ref>Pundit Bapu Deva Shastri, "English Translation of Surya Siddhanta",p11, 1861</ref>
 +
|-
 +
! Modern SI units !! Surya Siddhanta units !! Value
 +
|-
 +
| Second || Vikala || -
 +
|-
 +
| Minute || Kala || 60 Vikala/seconds
 +
|-
 +
| Degree || Ansh || 60 Kala/minutes or 3600 Vikala/seconds
 +
|-
 +
| Zodiac Sign || Rashi || 30 Ansh/degrees or 1800 Kala/minutes
 +
|-
 +
| Revolution || Bhagan || 12 Rashi/zodiac signs
 +
|}
 +
 +
These units are used in several calculations done through out the text of ''Surya Siddhanta''. In the sine tables of ''Surya Siddhanta'' the first sine or Jyā is described as the value equal to 1/8th of the number of minutes (Kalas) in a zodiac sign (Rashi).
 +
 +
=== Indian standard circle ===
 +
The ''Surya Siddhanta'' is using the [[Indian standard circle]] in various calculations through out the text. This standard circle is based on radius of 3,438 minutes. The significance lies in the precision of 1/3438 that the ancient Indian astronomers were able to work with. It is evident from the calculation of obliquity of the earth's axis in chapter 2 where 1397 units is the measured R-sine value.
 +
Another interesting outcome of this radius of 3,438 minutes is that the circumference of the standard Indian circle is calculated as 21,600 minutes using the formula of Pi multiply by diameter (twice the radius).
 +
 +
=== Nakshatra (Asterism) System ===
 +
 +
The ''Surya Siddhanta'' uses the 27 [[Nakshatra system]] throughout the text. The Nakshatra is a smaller constellation typically consisting of 1 to 5 stars. The brightest star is called as Yogtara. Each Nakshatra spans 13° 20' on the ecliptic. Each Nakshatra has its own primary star which is usually the junction star but not always.
 +
 +
=== Longitudinal updates  ===
 +
Chapter 8 of ''Surya Siddhanta'' primarily focuses on the stellar data. It provides the longitudinal data for the Asterisms. In comparison to the present day longitudinal values of these stars and the data of Surya Siddhanta, it becomes clear that this update to Surya Siddhanta was made around 580 AD. THe longitude of the stars change by 1° in every 71 years. From the data it is clear that the data does not represent observation but rather is obtained by adding precessional increment to each of the previously calculated data.
 +
 +
=== Obliquity (tilt) of the Earth's axis ===
 +
Obliquity or the axial tilt of earth is the angle which the earth's axis of rotation makes with the perpendicular of orbital plane. This angle varies between 22.1° and 24.5° and it is cyclic phenomena over a period of 41,000 years. Currently the obliquity is 23.4 degrees.<ref>Alan Buis, "Milankovitch (Orbital) Cycles and Their Role in Earth's Climate", "NASA's Jet Propulsion Laboratory" https://climate.nasa.gov/news/2948/milankovitch-orbital-cycles-and-their-role-in-earths-climate/</ref> ''Sūrya Siddhānta'' in two different chapters calculate and provide the value of obliquity.
 +
 +
Chapter 2, verse 28 translates as
 +
{{Quote
 +
|text = ''The sine of the greatest declination is 1397 units; Multiply the sine by the said sine 1397; Divide the product by the radius 3438 units; Find the arc whose sine is equal to the quotient. This arc is the mean declination of the planet''<ref>E. Burgess, "Translation of Surya Siddhanta", p26, Accessible at https://www.jstor.org/stable/pdf/592174.pdf</ref>
 +
}}
 +
This way we obtain the obliquity as Sin<sup>-1</sup>(1397/3438) = 23.975°
 +
 +
 +
Chapter 12, verse 68 translates as
 +
{{Quote
 +
|text = ''At the distance of the fifteenth part of the Earth's circumference (from the equator) in the regions of the Gods or the Asuras (i.e. at the north and south terrestrial tropic) the sun passes through the zenith when it arrives at the north or south solstitial point (respectively)''''<ref>Pundit Bapu Deva Shastri, "Translation of Surya Siddhanta", "Baptist Mission Press", 1861, Accessible at https://www.wilbourhall.org/pdfs/suryaEnglish.pdf</ref>
 +
}}
 +
It essentially provides information to calculate the axial tilt of earth which in this case can be calculated as 360°/15 = 24°.
 +
 +
The significance of these verses is that they pin points the exact time when the obliquity calculations were made by ancient Indian astronomers and added into the ''Sūrya Siddhānta''.
 +
 +
=== North Pole Star and South Pole Star ===
 +
''Surya Siddhanta'' contains an observation of the presence of pole stars at both north celestial pole and south celestial pole. Because of the precession of the earth's axis it is known that the pole star changes over a period of time which is normally more than thousand years. In present times our North Pole star is Polaris.<ref>Bruce McClure, "Polaris is the North Pole Star", "Earthsky", 21 May 2019, Accessible at https://earthsky.org/brightest-stars/polaris-the-present-day-north-star</ref> This observation is recorded in chapter 12, verse 43-44 and translates as
 +
{{Quote
 +
|text = ''There are two pole stars, one each, near North Celestial Pole (NCP) and near South Celestial Pole (SCP). From equatorial regions, these stars are seen along the horizon. The pole stars are seen along the horizon, thus the place latitude is close to zero, while declination of NCP and SCP is 90 degrees.''
 +
}}
 +
 +
Such phenomena was last seen around 3rd millennium BCE when Thuban was the North Pole Star and Alpha Hydri was the South Pole star.<ref>Nilesh N Oak and Rupa Bhatty, "Ancient Updates to Surya Siddhanta", 09 March 2019, "India Facts" Accessible at http://indiafacts.org/ancient-updates-to-surya-siddhanta/</ref> <ref>Anil Narayanan, "Wonders, Mysteries and Misconceptions in Indian Astronomy – I", 'India facts", 09 Sept 2019, Accessible at http://indiafacts.org/wonders-mysteries-and-misconceptions-in-indian-astronomy-i/</ref> This indicates the antiquity of the concepts written in the text.
 +
 +
=== ''Surya Siddhanta'' sine table ===
 +
The ''Surya Siddhanta'' provides methods to calculate the sine value in chapter 2. It is among the earliest form of [[Indian sine tables]]. The sine tables had been improved upon by many ancient Indian mathematicians. ''Surya Siddhanta'' uses an ''Indian standard circle'' of radius 3438 minutes. It divides the quadrant into 24 equal segments with each segment sweeping an angle of 3.75° and an arc length of 225 minutes. The verse 15-16 translates as
 +
{{Quote
 +
|text = ''The eighth part of the number of minutes contained in a zodiac sign (Rashi) (i.e. 1800) is the first sine (Jya). Divide the first sine by itself, subtract the quotient by that sine and add the remainder to that sine: the sum will be the second sine. In this manner divide successively the sines by the first sine, subtract the quotient from the divisor and add the remainder to the sine last found and the sum will be next sine. Thus you get twenty four sines (in a quadrant of a circle whose radius is 3438 minutes)''<ref>Deva Shastri, Pundit Bapu (1861). Translation of the Surya Siddhanta. pp. 15–16.</ref>
 +
}}
 +
 +
The verse 17-22 translates as
 +
{{Quote
 +
|text = ''The Twenty four sines are 225, 449, 671, 890, 1105, 1315, 1520, 1719, 1910, 2093, 2267, 2431, 2585, 2728, 2859, 2978, 3084, 3177, 3256, 3321, 3372, 3409, 3431, 3438.
 +
Subtract the sines separately from 3438 in the inverse order, the remainders are the versed sines. ''<ref>Deva Shastri, Pundit Bapu (1861). Translation of the Surya Siddhanta. pp. 16.</ref>
 +
}}
 +
 +
The verse 23-27 translates as
 +
{{Quote
 +
|text = ''The versed sines in a quadrant are 7, 29, 66, 117, 182, 261, 354, 460, 579, 710, 853, 1007, 1171, 1345, 1528, 1719, 1918, 2123, 2333, 2548, 2767, 2989, 3213, 3438.''<ref>Deva Shastri, Pundit Bapu (1861). Translation of the Surya Siddhanta. pp. 16.</ref>
 +
}}
 +
 +
The ''Surya Siddhanta'' derived Sin(θ) or Sine values show astonishing precision of 3 to 4 decimal places in comparison to the modern Sine values. The 1st order difference is the value by which each successive sine increases from the previous and similarly 2nd order difference is the increment in the 1st order difference values. ''Burgess'' notes that it is remarkable to see that the 2nd order differences increase as the sines and each, in fact, is about 1/225th part of the corresponding sine.<ref>Burgess, Rev. Ebenezer (1860). Translation of the Surya Siddhanta. p. 115.</ref>
 +
 +
{| class="wikitable" style="margin: 1em auto 1em auto;"
 +
!Sl. No
 +
!Angle (in degrees, arcminutes)
 +
![[Surya Siddhanta]] value of ''[[Indian_sine_tables|Jyā]]'' (R.sine)
 +
!Surya Siddhanta versed sines [[Indian_sine_tables#Terminology|Utkramā-jyā]] (R - R.cosine)
 +
!Modern value of ''[[Indian_sine_tables|Jyā]]'' (R.sine)
 +
!SS derived sine values (''[[Indian_sine_tables|Jyā]]'' / 3438)
 +
!Modern sine values
 +
|-
 +
|&nbsp;&nbsp; 1
 +
|{{center|03° &nbsp; 45′}}
 +
|{{center|225′}}
 +
|{{center|7'}}
 +
|{{center|224.8560}}
 +
|{{center|0.06544503}}
 +
|{{center|0.06540313}}
 +
|-
 +
|&nbsp;&nbsp; 2
 +
|{{center|07° &nbsp; 30′}}
 +
|{{center|449′}}
 +
|{{center|29'}}
 +
|{{center|448.7490}}
 +
|{{center|0.13059919}}
 +
|{{center|0.13052619}}
 +
|-
 +
|&nbsp;&nbsp; 3
 +
|{{center|11° &nbsp; 15′}}
 +
|{{center|671′}}
 +
|{{center|66'}}
 +
|{{center|670.7205}}
 +
|{{center|0.19517161}}
 +
|{{center|0.19509032}}
 +
|-
 +
|&nbsp;&nbsp; 4
 +
|{{center|15° &nbsp; 00′}}
 +
|{{center|890′}}
 +
|{{center|117′}}
 +
|{{center|889.8199}}
 +
|{{center|0.25887144}}
 +
|{{center|0.25881905}}
 +
|-
 +
|&nbsp;&nbsp; 5
 +
|{{center|18° &nbsp; 45′}}
 +
|{{center|1105′}}
 +
|{{center|182′}}
 +
|{{center|1105.1089}}
 +
|{{center|0.3212078}}
 +
|{{center|0.32143947}}
 +
|-
 +
|&nbsp;&nbsp; 6
 +
|{{center|22° &nbsp; 30′}}
 +
|{{center|1315′}}
 +
|{{center|261′}}
 +
|{{center|1315.6656}}
 +
|{{center|0.38248982}}
 +
|{{center|0.38268343}}
 +
|-
 +
|&nbsp;&nbsp; 7
 +
|{{center|26° &nbsp; 15′}}
 +
|{{center|1520′}}
 +
|{{center|354′}}
 +
|{{center|1520.5885}}
 +
|{{center|0.44211751}}
 +
|{{center|0.44228869}}
 +
|-
 +
|&nbsp;&nbsp; 8
 +
|{{center|30° &nbsp; 00′}}
 +
|{{center|1719′}}
 +
|{{center|460′}}
 +
|{{center|1719.0000}}
 +
|{{center|0.50000000}}
 +
|{{center|0.50000000}}
 +
|-
 +
|&nbsp;&nbsp; 9
 +
|{{center|33° &nbsp; 45′}}
 +
|{{center|1910′}}
 +
|{{center|579′}}
 +
|{{center|1910.0505}}
 +
|{{center|0.55555556}}
 +
|{{center|0.55557023}}
 +
|-
 +
|&nbsp;&nbsp; 10
 +
|{{center|37° &nbsp; 30′}}
 +
|{{center|2093′}}
 +
|{{center|710′}}
 +
|{{center|2092.9218}}
 +
|{{center|0.60878418}}
 +
|{{center|0.60876143}}
 +
|-
 +
|&nbsp;&nbsp; 11
 +
|{{center|41° &nbsp; 15′}}
 +
|{{center|2267′}}
 +
|{{center|853′}}
 +
|{{center|2266.8309}}
 +
|{{center|0.65939500}}
 +
|{{center|0.65934582}}
 +
|-
 +
|&nbsp;&nbsp; 12
 +
|{{center|45° &nbsp; 00′}}
 +
|{{center|2431′}}
 +
|{{center|1007′}}
 +
|{{center|2431.0331}}
 +
|{{center|0.70709715}}
 +
|{{center|0.70710678}}
 +
|-
 +
|&nbsp;&nbsp; 13
 +
|{{center|48° &nbsp; 45′}}
 +
|{{center|2585′}}
 +
|{{center|1171′}}
 +
|{{center|2584.8253}}
 +
|{{center|0.75189063}}
 +
|{{center|0.75183981}}
 +
|-
 +
|&nbsp;&nbsp; 14
 +
|{{center|52° &nbsp; 30′}}
 +
|{{center|2728′}}
 +
|{{center|1345′}}
 +
|{{center|2727.5488}}
 +
|{{center|0.79348458}}
 +
|{{center|0.79335334}}
 +
|-
 +
|&nbsp;&nbsp; 15
 +
|{{center|56° &nbsp; 15′}}
 +
|{{center|2859′}}
 +
|{{center|1528′}}
 +
|{{center|2858.5925}}
 +
|{{center|0.83158813}}
 +
|{{center|0.83146961}}
 +
|-
 +
|&nbsp;&nbsp; 16
 +
|{{center|60° &nbsp; 00′}}
 +
|{{center|2978′}}
 +
|{{center|1719′}}
 +
|{{center|2977.3953}}
 +
|{{center|0.86620128}}
 +
|{{center|0.86602540}}
 +
|-
 +
|&nbsp;&nbsp; 17
 +
|{{center|63° &nbsp; 45′}}
 +
|{{center|3084′}}
 +
|{{center|1918′}}
 +
|{{center|3083.4485}}
 +
|{{center|0.89703316}}
 +
|{{center|0.89687274}}
 
|-
 
|-
−
| ''Surya Siddhānta'' || ''Brahma Siddhānta'' || Soma Siddhānta
+
|&nbsp;&nbsp; 18
 +
|{{center|67° &nbsp; 30′}}
 +
|{{center|3177′}}
 +
|{{center|2123′}}
 +
|{{center|3176.2978}}
 +
|{{center|0.92408377}}
 +
|{{center|0.92387953}}
 
|-
 
|-
−
| Vyasa Siddhānta || Vashishtha Siddhānta || Atri Siddhānta
+
|&nbsp;&nbsp; 19
 +
|{{center|71° &nbsp; 15′}}
 +
|{{center|3256′}}
 +
|{{center|2333′}}
 +
|{{center|3255.5458}}
 +
|{{center|0.94706225}}
 +
|{{center|0.94693013}}
 
|-
 
|-
−
| Parashira Siddhānta || Kashyap Siddhānta || Nārad Siddhānta
+
|&nbsp;&nbsp; 20
 +
|{{center|75° &nbsp; 00′}}
 +
|{{center|3321′}}
 +
|{{center|2548′}}
 +
|{{center|3320.8530}}
 +
|{{center|0.96596859}}
 +
|{{center|0.96592583}}
 
|-
 
|-
−
| Garga Siddhānta || Marici Siddhānta || Manu Siddhānta
+
|&nbsp;&nbsp; 21
 +
|{{center|78° &nbsp; 45′}}
 +
|{{center|3372′}}
 +
|{{center|2767′}}
 +
|{{center|3371.9398}}
 +
|{{center|0.98080279}}
 +
|{{center|0.98078528}}
 
|-
 
|-
−
| Angiras Siddhānta || Lomasha Siddhānta || Pulisha Siddhānta
+
|&nbsp;&nbsp; 22
 +
|{{center|82° &nbsp; 30′}}
 +
|{{center|3409′}}
 +
|{{center|2989′}}
 +
|{{center|3408.5874}}
 +
|{{center|0.99156486}}
 +
|{{center|0.99144486}}
 +
|-
 +
|&nbsp;&nbsp; 23
 +
|{{center|86° &nbsp; 15′}}
 +
|{{center|3431′}}
 +
|{{center|3213′}}
 +
|{{center|3430.6390}}
 +
|{{center|0.99796393}}
 +
|{{center|0.99785892}}
 +
|-
 +
|&nbsp;&nbsp; 24
 +
|{{center|90° &nbsp; 00′}}
 +
|{{center|3438′}}
 +
|{{center|3438′}}
 +
|{{center|3438.0000}}
 +
|{{center|1.00000000}}
 +
|{{center|1.00000000}}
 
|-
 
|-
−
| Cyavana Siddhānta || Yavana Siddhānta || Bhrigu Siddhānta
 
 
|}
 
|}
 +
 +
== See Also ==
 +
*[[Indian sine tables]]
 +
*[[Indian standard circle]]
 +
*[[Madhava's sine table]]
 +
 +
== References and notes==
 +
<references />

Latest revision as of 01:05, 18 September 2021

Sūrya Siddhānta is an ancient Indian treatise in Astronomy. Like many classical Indian works, the Sūrya Siddhānta is a poem in Sanskrit language. It has fourteen chapter and 500 verses. It is composed in śloka metrical style of Sanskrit. It contain works on Indian sine tables, cosmology, eclipses, planetary motions, conjunctions, star positions, geography, instrumentation, concepts of time and mathematics. Unlike conventional books Sūrya Siddhānta contains advanced calculation and methods which are not easily comprehensible for a rank beginner. [1] In second chapter, the text contains the calculation of Earth's obliquity of 1397 jya (R.sine) 23.975° modern units. The text describes the observation of two pole stars one each at the north pole and the south pole seen at the equatorial region, such phenomena was last seen in the 3rd millennium BCE. This indicates the antiquity of the concepts recorded in the text.

History

''Sūrya Siddhānta'' is well known, most referred and most esteemed. The original author of ''Sūrya Siddhānta'' is ''Mayasura'' as described in the story in the first chapter that ''Mayasura'' obtained his knowledge from ''Sūrya'' (the Sun). ''Siddhānta'' in Sanskrit means ''treatise'' and it usually has author's name prefixed to it. There were several other works on Astronomy in ancient India, many of which have since been lost.

Surya Siddhānta Brahma Siddhānta Soma Siddhānta
Vyasa Siddhānta Vashishtha Siddhānta Atri Siddhānta
Parashira Siddhānta Kashyap Siddhānta Nārad Siddhānta
Garga Siddhānta Marici Siddhānta Manu Siddhānta
Angiras Siddhānta Lomasha Siddhānta Pulisha Siddhānta
Cyavana Siddhānta Yavana Siddhānta Bhrigu Siddhānta

Content

Sūrya Siddhānta contains 14 chapters and 500 verses. The chapters contain observations, methods, instruments and calculations of various astronomical phenomenas. There is a scarcity of scientific analysis done on the text of Surya Siddhanta. Majority western work is based on Indology dates which in itself is controversial and based on their biased opinion of granting the origin of any science or mathematics to the ancient Greek or babylonians despite of immense textual evidence pointing otherwise. Their analysis of Surya Siddhanta primarily avoids the study of actual data and observations recorded within the Surya Siddhanta.

Indian origin of seconds, minutes and degrees

Surya Siddhanta in chapter 2 describes the units of seconds, minutes and degrees. These units of measurement are primary basis of the calculations of earth's obliquity and sine tables of Surya Siddhanta. Essentially Surya Siddhanta describes that Rashi has 30 degrees (Ansh) implying it has 1800 minutes (Kala). The data is as as described in the table

Surya Siddhanta units: seconds, minutes and degrees[2]
Modern SI units Surya Siddhanta units Value
Second Vikala -
Minute Kala 60 Vikala/seconds
Degree Ansh 60 Kala/minutes or 3600 Vikala/seconds
Zodiac Sign Rashi 30 Ansh/degrees or 1800 Kala/minutes
Revolution Bhagan 12 Rashi/zodiac signs

These units are used in several calculations done through out the text of Surya Siddhanta. In the sine tables of Surya Siddhanta the first sine or Jyā is described as the value equal to 1/8th of the number of minutes (Kalas) in a zodiac sign (Rashi).

Indian standard circle

The Surya Siddhanta is using the Indian standard circle in various calculations through out the text. This standard circle is based on radius of 3,438 minutes. The significance lies in the precision of 1/3438 that the ancient Indian astronomers were able to work with. It is evident from the calculation of obliquity of the earth's axis in chapter 2 where 1397 units is the measured R-sine value. Another interesting outcome of this radius of 3,438 minutes is that the circumference of the standard Indian circle is calculated as 21,600 minutes using the formula of Pi multiply by diameter (twice the radius).

Nakshatra (Asterism) System

The Surya Siddhanta uses the 27 Nakshatra system throughout the text. The Nakshatra is a smaller constellation typically consisting of 1 to 5 stars. The brightest star is called as Yogtara. Each Nakshatra spans 13° 20' on the ecliptic. Each Nakshatra has its own primary star which is usually the junction star but not always.

Longitudinal updates

Chapter 8 of Surya Siddhanta primarily focuses on the stellar data. It provides the longitudinal data for the Asterisms. In comparison to the present day longitudinal values of these stars and the data of Surya Siddhanta, it becomes clear that this update to Surya Siddhanta was made around 580 AD. THe longitude of the stars change by 1° in every 71 years. From the data it is clear that the data does not represent observation but rather is obtained by adding precessional increment to each of the previously calculated data.

Obliquity (tilt) of the Earth's axis

Obliquity or the axial tilt of earth is the angle which the earth's axis of rotation makes with the perpendicular of orbital plane. This angle varies between 22.1° and 24.5° and it is cyclic phenomena over a period of 41,000 years. Currently the obliquity is 23.4 degrees.[3] Sūrya Siddhānta in two different chapters calculate and provide the value of obliquity.

Chapter 2, verse 28 translates as

The sine of the greatest declination is 1397 units; Multiply the sine by the said sine 1397; Divide the product by the radius 3438 units; Find the arc whose sine is equal to the quotient. This arc is the mean declination of the planet[4] 

This way we obtain the obliquity as Sin-1(1397/3438) = 23.975°


Chapter 12, verse 68 translates as

At the distance of the fifteenth part of the Earth's circumference (from the equator) in the regions of the Gods or the Asuras (i.e. at the north and south terrestrial tropic) the sun passes through the zenith when it arrives at the north or south solstitial point (respectively)''[5] 

It essentially provides information to calculate the axial tilt of earth which in this case can be calculated as 360°/15 = 24°.

The significance of these verses is that they pin points the exact time when the obliquity calculations were made by ancient Indian astronomers and added into the Sūrya Siddhānta.

North Pole Star and South Pole Star

Surya Siddhanta contains an observation of the presence of pole stars at both north celestial pole and south celestial pole. Because of the precession of the earth's axis it is known that the pole star changes over a period of time which is normally more than thousand years. In present times our North Pole star is Polaris.[6] This observation is recorded in chapter 12, verse 43-44 and translates as

There are two pole stars, one each, near North Celestial Pole (NCP) and near South Celestial Pole (SCP). From equatorial regions, these stars are seen along the horizon. The pole stars are seen along the horizon, thus the place latitude is close to zero, while declination of NCP and SCP is 90 degrees.

Such phenomena was last seen around 3rd millennium BCE when Thuban was the North Pole Star and Alpha Hydri was the South Pole star.[7] [8] This indicates the antiquity of the concepts written in the text.

Surya Siddhanta sine table

The Surya Siddhanta provides methods to calculate the sine value in chapter 2. It is among the earliest form of Indian sine tables. The sine tables had been improved upon by many ancient Indian mathematicians. Surya Siddhanta uses an Indian standard circle of radius 3438 minutes. It divides the quadrant into 24 equal segments with each segment sweeping an angle of 3.75° and an arc length of 225 minutes. The verse 15-16 translates as

The eighth part of the number of minutes contained in a zodiac sign (Rashi) (i.e. 1800) is the first sine (Jya). Divide the first sine by itself, subtract the quotient by that sine and add the remainder to that sine: the sum will be the second sine. In this manner divide successively the sines by the first sine, subtract the quotient from the divisor and add the remainder to the sine last found and the sum will be next sine. Thus you get twenty four sines (in a quadrant of a circle whose radius is 3438 minutes)[9]

The verse 17-22 translates as

The Twenty four sines are 225, 449, 671, 890, 1105, 1315, 1520, 1719, 1910, 2093, 2267, 2431, 2585, 2728, 2859, 2978, 3084, 3177, 3256, 3321, 3372, 3409, 3431, 3438.

Subtract the sines separately from 3438 in the inverse order, the remainders are the versed sines. [10]

The verse 23-27 translates as

The versed sines in a quadrant are 7, 29, 66, 117, 182, 261, 354, 460, 579, 710, 853, 1007, 1171, 1345, 1528, 1719, 1918, 2123, 2333, 2548, 2767, 2989, 3213, 3438.[11]

The Surya Siddhanta derived Sin(θ) or Sine values show astonishing precision of 3 to 4 decimal places in comparison to the modern Sine values. The 1st order difference is the value by which each successive sine increases from the previous and similarly 2nd order difference is the increment in the 1st order difference values. Burgess notes that it is remarkable to see that the 2nd order differences increase as the sines and each, in fact, is about 1/225th part of the corresponding sine.[12]

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See Also

References and notes

  1. ↑ [1]
  2. ↑ Pundit Bapu Deva Shastri, "English Translation of Surya Siddhanta",p11, 1861
  3. ↑ Alan Buis, "Milankovitch (Orbital) Cycles and Their Role in Earth's Climate", "NASA's Jet Propulsion Laboratory" https://climate.nasa.gov/news/2948/milankovitch-orbital-cycles-and-their-role-in-earths-climate/
  4. ↑ E. Burgess, "Translation of Surya Siddhanta", p26, Accessible at https://www.jstor.org/stable/pdf/592174.pdf
  5. ↑ Pundit Bapu Deva Shastri, "Translation of Surya Siddhanta", "Baptist Mission Press", 1861, Accessible at https://www.wilbourhall.org/pdfs/suryaEnglish.pdf
  6. ↑ Bruce McClure, "Polaris is the North Pole Star", "Earthsky", 21 May 2019, Accessible at https://earthsky.org/brightest-stars/polaris-the-present-day-north-star
  7. ↑ Nilesh N Oak and Rupa Bhatty, "Ancient Updates to Surya Siddhanta", 09 March 2019, "India Facts" Accessible at http://indiafacts.org/ancient-updates-to-surya-siddhanta/
  8. ↑ Anil Narayanan, "Wonders, Mysteries and Misconceptions in Indian Astronomy – I", 'India facts", 09 Sept 2019, Accessible at http://indiafacts.org/wonders-mysteries-and-misconceptions-in-indian-astronomy-i/
  9. ↑ Deva Shastri, Pundit Bapu (1861). Translation of the Surya Siddhanta. pp. 15–16.
  10. ↑ Deva Shastri, Pundit Bapu (1861). Translation of the Surya Siddhanta. pp. 16.
  11. ↑ Deva Shastri, Pundit Bapu (1861). Translation of the Surya Siddhanta. pp. 16.
  12. ↑ Burgess, Rev. Ebenezer (1860). Translation of the Surya Siddhanta. p. 115.
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