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Surya Siddhanta (सूर्य सिद्धांता) (view source)

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{| class="wikitable"
 
{| class="wikitable"
 
|-
 
|-
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| ''Surya Siddhānta'' || ''Brahma Siddhānta'' || Soma Siddhānta
+
| ''Surya Siddhānta'' || ''Brahma Siddhānta'' || ''Soma Siddhānta''
 
|-
 
|-
−
| Vyasa Siddhānta || Vashishtha Siddhānta || Atri Siddhānta
+
| ''Vyasa Siddhānta'' || ''Vashishtha Siddhānta'' || ''Atri Siddhānta''
 
|-
 
|-
−
| Parashira Siddhānta || Kashyap Siddhānta || Nārad Siddhānta
+
| ''Parashira Siddhānta'' || ''Kashyap Siddhānta'' || ''Nārad Siddhānta''
 
|-
 
|-
−
| Garga Siddhānta || Marici Siddhānta || Manu Siddhānta
+
| ''Garga Siddhānta'' || ''Marici Siddhānta'' || ''Manu Siddhānta''
 
|-
 
|-
−
| Angiras Siddhānta || Lomasha Siddhānta || Pulisha Siddhānta
+
| ''Angiras Siddhānta'' || ''Lomasha Siddhānta'' || ''Pulisha Siddhānta''
 
|-
 
|-
−
| Cyavana Siddhānta || Yavana Siddhānta || Bhrigu Siddhānta
+
| ''Cyavana Siddhānta'' || ''Yavana Siddhānta'' || ''Bhrigu Siddhānta''
 
|}
 
|}
   −
== References ==
+
== 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''. It is reasonable to think that these units or concepts had been in existence prior to other calculations and observation made in the epoch of 6th millennium BC as discussed in this article. The descriptions are
 +
 
 +
{| 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 seconds
 +
|-
 +
| Degree || Ansh || 60 minutes
 +
|-
 +
| Zodiac Sign || Rashi || 30 degrees
 +
|-
 +
| Revolution || Bhagan || 12 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 - 580 AD ===
 +
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 - 3000 BC ===
 +
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''. The epoch this obliquity calculation provides is around 3000BC.<ref>Anil Narayanan, "Dating the Surya Siddhanta using Computer simulation of Proper Motions and Ecliptic variations", ''Indian Journal of History of Science'', Volume 45, issue 4, 23 March 2010.</ref>
 +
 
 +
=== North Pole Star and South Pole Star - 3000 BC ===
 +
''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 3000 BC 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>
 +
 
 +
=== The Pulsating Indian Epicycle of the Sun - 5000-5500 BC ===
 +
For determining the Sun’s longitude, the pulsating Indian epicycle is far more accurate than the Greek eccentric-epicycle model. The pulsating Indian epicycle for the Sun becomes progressively more accurate as one goes back in time. Peak accuracy, of about 1 minute of arc, is reached around 5200 BC. The current values of the Surya Siddhanta’s pulsating epicycle parameters for the Sun appear to have been set in the 5000-5500 BC timeframe.<ref>Anil Narayanan, "The Pulsating Indian Epicycle of the Sun", ''Indian Journal of History of Science'', Volume 46, issue 3, p15, 30 June 2011.</ref>
 +
 
 +
=== The Latitudinal data - 7300-7500BC ===
 +
Using computer simulation of nakshatra latitudinal data by varying ecliptic obliquity, ecliptic-node-location and ecliptic-sink together with proper motion, a match for the Surya Siddhanta latitudinal data was obtained in the timeframe 7300-7800 BC.<ref>Anil Narayanan, "Dating the Surya Siddhanta using Computer simulation of Proper Motions and Ecliptic variations", ''Indian Journal of History of Science'', Volume 45, issue 4, p21, 23 March 2010.</ref> Although the author notes that a major assumption made in this investigation is that star proper motion is fairly constant over several thousands of years. The results may be adversely affected if this were found untrue for the star set under consideration. It should also be noted that this time frame matches with the establishment of the oldest archaeological site of Bhirrana found along the Saraswati river paleochannel. In the 8th millennium BC this site shows that the people were living in the dwelling pits.<ref>Bhirrana, "Archaeological Survey of India", http://excnagasi.in/excavation_bhirrana.html</ref> This stands in contrast with the above time frame, the question arises whether people could be that scientifically advanced while they were inhabiting the dwelling pits. Although this view is subject to change given older more advanced archaeological sites are found within the Indian subcontinent.
 +
 
 +
=== ''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)
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!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′}}
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|{{center|225′}}
 +
|{{center|7'}}
 +
|{{center|224.8560}}
 +
|{{center|0.06544503}}
 +
|{{center|0.06540313}}
 +
|-
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|&nbsp;&nbsp; 2
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|{{center|07° &nbsp; 30′}}
 +
|{{center|449′}}
 +
|{{center|29'}}
 +
|{{center|448.7490}}
 +
|{{center|0.13059919}}
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|{{center|0.13052619}}
 +
|-
 +
|&nbsp;&nbsp; 3
 +
|{{center|11° &nbsp; 15′}}
 +
|{{center|671′}}
 +
|{{center|66'}}
 +
|{{center|670.7205}}
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|{{center|0.19517161}}
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|{{center|0.19509032}}
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|-
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|&nbsp;&nbsp; 4
 +
|{{center|15° &nbsp; 00′}}
 +
|{{center|890′}}
 +
|{{center|117′}}
 +
|{{center|889.8199}}
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|{{center|0.25887144}}
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|{{center|0.25881905}}
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|-
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|&nbsp;&nbsp; 5
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|{{center|18° &nbsp; 45′}}
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|{{center|1105′}}
 +
|{{center|182′}}
 +
|{{center|1105.1089}}
 +
|{{center|0.3212078}}
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|{{center|0.32143947}}
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|-
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|&nbsp;&nbsp; 6
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|{{center|22° &nbsp; 30′}}
 +
|{{center|1315′}}
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|{{center|261′}}
 +
|{{center|1315.6656}}
 +
|{{center|0.38248982}}
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|{{center|0.38268343}}
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|-
 +
|&nbsp;&nbsp; 7
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|{{center|26° &nbsp; 15′}}
 +
|{{center|1520′}}
 +
|{{center|354′}}
 +
|{{center|1520.5885}}
 +
|{{center|0.44211751}}
 +
|{{center|0.44228869}}
 +
|-
 +
|&nbsp;&nbsp; 8
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|{{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}}
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|{{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
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|{{center|41° &nbsp; 15′}}
 +
|{{center|2267′}}
 +
|{{center|853′}}
 +
|{{center|2266.8309}}
 +
|{{center|0.65939500}}
 +
|{{center|0.65934582}}
 +
|-
 +
|&nbsp;&nbsp; 12
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|{{center|45° &nbsp; 00′}}
 +
|{{center|2431′}}
 +
|{{center|1007′}}
 +
|{{center|2431.0331}}
 +
|{{center|0.70709715}}
 +
|{{center|0.70710678}}
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|-
 +
|&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}}
 +
|-
 +
|&nbsp;&nbsp; 18
 +
|{{center|67° &nbsp; 30′}}
 +
|{{center|3177′}}
 +
|{{center|2123′}}
 +
|{{center|3176.2978}}
 +
|{{center|0.92408377}}
 +
|{{center|0.92387953}}
 +
|-
 +
|&nbsp;&nbsp; 19
 +
|{{center|71° &nbsp; 15′}}
 +
|{{center|3256′}}
 +
|{{center|2333′}}
 +
|{{center|3255.5458}}
 +
|{{center|0.94706225}}
 +
|{{center|0.94693013}}
 +
|-
 +
|&nbsp;&nbsp; 20
 +
|{{center|75° &nbsp; 00′}}
 +
|{{center|3321′}}
 +
|{{center|2548′}}
 +
|{{center|3320.8530}}
 +
|{{center|0.96596859}}
 +
|{{center|0.96592583}}
 +
|-
 +
|&nbsp;&nbsp; 21
 +
|{{center|78° &nbsp; 45′}}
 +
|{{center|3372′}}
 +
|{{center|2767′}}
 +
|{{center|3371.9398}}
 +
|{{center|0.98080279}}
 +
|{{center|0.98078528}}
 +
|-
 +
|&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}}
 +
|-
 +
|}
 +
 
 +
== See Also ==
 +
*[[Indian sine tables]]
 +
*[[Indian standard circle]]
 +
*[[Madhava's sine table]]
 +
 
 +
== References and notes==
 
<references />
 
<references />
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