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Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t8: Sūrya Siddhānta

Bhāratīya Jyotiḥśāstra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t8

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Sūrya Siddhānta

v2.c12.s2.t8.1

The Pañcasiddhāntikā gives a different method for each of the five siddhāntas as far as the calculation of the sun and the moon is concerned ; but the calculation of the planets is given as from the Sūrya Siddhānta only, and this shows that the Sūrya Siddhānta was given the greatest importance. That “the Sūrya Siddhānta is the most accurate of all” has already been declared at the outset in the fourth couplet ; and it appears to have received such great importance because of its correctness when compared with actual positions in the heavens.

v2.c12.s2.t8.2

The 14th couplet of the Pañcasiddhāntikā states the number of intercalary months and other items as given by the Sūrya Siddhānta. The 26th couplet of the 9th chapter and all the Seven couplets of the 10th chapter, explain the methods of calculating (the places of) the sun, the moon and of eclipses etc. All the six couplets from the 11th chapter appear to give the explanation of only the eclipses as given by the Sūrya Siddhānta itself, and all the 27 couplets from the 16th chapter deal with the mean places of Mars and other planets, and the method of finding their true places, the question of retrograde and direct motions, the rising and setting etc.

v2.c12.s2.t8.3

In the beginning, the author quotes the couplets which mention the number of the intercalary months and other things, the revolutions of the sun, the moon and other planets and mean positions for the epoch assumed by the ‘Karana’ work according to the Sūrya Siddhānta and these are followed by the results calculated therefrom †—

v2.c12.s2.t8.4

† The original copy of the Pañcasiddhāntikā is very inaccurate. The author has quoted here the couplets, corrected by him on the basis of the underlying theory and given in the form in which they must have undoubtedly been originally compiled.

v2.c12.s2.t8.5

वर्षायुते धृतिघ्ने १८०००० नवनसगुणरसराः ६६३८६ स्युरधिमासाः ॥ सावित्रे शरनखेद्वियार्णवाशा १०४५०६५ स्तिथिप्रायाः ॥ १४ ॥

v2.c12.s2.t8.6

∗ See, commentary on Chapter 1.

v2.c12.s2.t8.7

युगणेकोष्टशत ८०० घ्ने विपक्षवेदांणवे ४४२ कंसिद्धांते ।। स्वरखा-चिवद्विनवयमी २६२२०७ द्वते क्रमाद्विनदलेऽवंत्यां ।। १ ।। नवशतसहस्र १००००० गुणिते स्वरैकपक्षाम्बरस्वरनू ६७०२१७ ने ।। षट्द्व्योमेंद्रियनेववसुविषयजिने २४५८९९९६ भंजिते चंद्रः ।। २ ।। नवशत ८०० गुणिने दद्याद्रसविषयगुणांबरतुयमपक्षान् २२६०३५३ ।। नवससुप्ताष्टांबरनबाश्च २९०७८९६ भक्ते शशांकोच्चं ।। ३ ।। राशिविषय ५१ घानींदोः खाकीग्नि ३१२० हतानि मंडलानि ऋणं ।। स्वोच्चे दि १० घ्नानि घनं स्वरदस्यमो २२७ द्वते विकलाः ।। ४ ।।

v2.c12.s2.t8.8

“Chap. 1, (14) According to the Saura (Siddhānta) there are in 180000 years 66389 intercalary months and 1045095 suppressed lunar days.

v2.c12.s2.t8.9

Chapter 9—(1) According to the Sūrya Siddhānta the mean place of the sun is found (i.e. in revolutions and signs etc.) by multiplying the ahargaṇa by 800, deducting 442, and dividing by 292207 successively; the place so found is for the midday at Avanti.

v2.c12.s2.t8.10

(2) Multiply the ahargaṇa by 900000, deduct 670217 and divide by 24589996; the result is the mean place of the moon.

v2.c12.s2.t8.11

(3) Multiply the ahargaṇa by 900, add 2260353, and divide by 2908789; the result is the place of the moon’s Ucca.

v2.c12.s2.t8.12

(4) Multiply the revolutions of the moon by 51 and divide by 3120; deduct the result taken as seconds. Also, multiply the revolutions of the moon’s Ucca by 10 and divide by 227; the resulting seconds are to be added to the moon’s Ucca.”

v2.c12.s2.t8.13

एष निशाधैर्वंत्यां ताराग्रहणेर्कसिद्धांतै ।। तत्रैदुपत्रशुक्रौ तुल्यगतौ मध्यमार्केण ।। १ ।। जीवस्य शता १०० म्यस्तं द्वित्रियमाग्नित्रिसागरै ४३३२३२ र्विभजेत् ।। युगणं कुजस्य चंद्रा १ हतं तु सप्ताष्टषष्ट ६८७ भक्तं ।। २ ।। सौरस्य सहस्र १००० गूणं ऋतुरसशून्यतुषदकमुनिखैः १०७६६०६६ ।। यल्लब्धं ते भगणाः शेषा मध्याग्रहाः क्रमेणैव ।। ३ ।। राशिचतुष्टय ४ मंर्शद्वयं २ कलाविंशतिवंसुसमेताः २८ ।। नववेदा ४९ श्व विलप्ताः शनेर्धनं मध्यमस्यैवं ।। ५ ।। अष्टौ ८ भागालिप्ततैवः ६ खमक्षी २० गुरो विलप्ताश्च ।। क्षेपः कुजस्य यम २ तिथि १५ पंचत्रिशच्च ३५ राश्याद्यः ।। ६ ।। शत १०० गुणितां बुधशीघ्रं खरनवसप्ताष्टभाजिते ८७९५ ।। क्रमशः ।। अत्राधपंचमा ४।३० स्तत्पराश्च भगणाहताः क्षेप्याः ।। ७ ।। सितशीघ्रं दश १० गुणिते युगणे भक्ते स्वरार्णवाशिवयमैः २२४७ ।। अर्धैकादश देया विलप्तिका भगणसंगुणिताः ।। ८ ।।

v2.c12.s2.t8.14

सिंहस्य वसुयमांशा: २८ खरेंदवो १७ लिप्तिका ज्ञशीघ्रघ्नं ॥ शोध्या: सितस्य बिकाला: शशिरसनवपक्षगुणदहता: ३३२६६१ ॥ ६ ॥

v2.c12.s2.t8.15

(1) The determination of the mean places of the smaller planets for midnight at Avantī is, according to the Sūrya Siddhānta, as follows :— Mercury and Venus have the same motion as the mean sun.

v2.c12.s2.t8.16

(2) For Jupiter, multiply the ahargaṇa by 100 and divide by 433232. For Mars multiply the ahargaṇa by one and divide by 687.

v2.c12.s2.t8.17

(3) For Saturn, multiply the ahargaṇa by 1000 and divide by 10766066 The quotients are the entire revolutions ; from the remainders, the mean places of the planets are ascertained in signs, degrees and so on.

v2.c12.s2.t8.18

(4) For each revolution of Jupiter 10 ‘tatparas’ (i.e. sixtieth parts of seconds) have to be deducted. 14 ‘tatparas’ are to be added for each revolution of Mars ; five have to be deducted for each revolution of Saturn.

v2.c12.s2.t8.19

(5) Four signs, two degrees, twenty-eight mirutes and forty-nine seconds have to be added to the mean place of Saturn.

v2.c12.s2.t8.20

(6) Eight degrees, six minutes and twenty seconds constitute the additive quantity for Jupiter. For Mars that quantity amounts to two signs fifteen degrees and thirty-five minutes.

v2.c12.s2.t8.21

(7) For the ‘śīghra’ of Mercury, multiply the ahargaṇa by 100, and divide by 8797. Add the product of the completed revolutions, and four and a half ‘tatparas’.

v2.c12.s2.t8.22

(8) For the ‘śīghra’ of Verus, multiply the ahargaṇa by 10 and divide by 2247. Add ten and a half seconds, multiplied by the revolutions. .

v2.c12.s2.t8.23

(9) Twenty eight degrees of Leo (i.e. 4 signs plus 28 degrees) and seven teen minutes are the additive quantity for the ‘śīghra’ of Mercury. From the ‘śīghra’ of Venus 332961 seconds are to be deducted”.

v2.c12.s2.t8.24

The first two couplets above give 365d-15gh-31pal-30vip as the measure of the year, and assuming the Kaliyuga to have commenced on Thursday, at midnight (when the longitudes of the sun and the moon were nil), the mean Sun's entry into Aries in Śaka 427 falls on Sunday, the 14th tithi of Caitra, dark-half at 48gh-9pal. (The mean longitude of the sun was zero at the moment). The couplet “dyugaṇerko....” gives 11ˢ 29° 27' 20" as the mean position of the sun at the epoch, and the couplet clearly states it to be true for the noon at Avantī, but what day it refers to is not stated therein. The mean longitude of the sun for the noon of Sunday, the 14th tithi of Caitra, dark half, as calculated for the moment 33gh-9p, before the mean sun's entry into Aries, tallies exactly with the epochal position given. This shows that the Sūrya Siddhānta of the Pañcasiddhāntikā has assumed the commencement of the yuga at midnight and that it postulates the Yuga system. These conclusions prove* to be true from the fact that the figures for the revolutions of planets as giver below agree with the planetary positions calculated on the assumption of the beginning of the Kali yuga at midnight.

v2.c12.s2.t8.25

*The figures as calculated from the Couplets quotea above are as follows* —

v2.c12.s2.t8.26

| | d | gh | pal | vipal |
| The length of the year | 365 | 15 | 31 | 30 |

v2.c12.s2.t8.27

*In a Mahāyuga (i.e. 4320000 years)*

v2.c12.s2.t8.28

| The No. of revolutions of | | The No. of revolutions of | |
| The stars | 1582237800 | Jupiter | 364220 |
| The Sun | 4320000 | Venus | 7022388 |
| Sāvana days | 1577917800 | Saturn | 146564 |
| Moon's revolutions | 57753336 | Solar months | 51840000 |
| Revolutions of Moon's apogee | 488219 | Intercalary months | 1593336 |
| Moon's asc. node | | Lunar months | 53433336 |
| Revolutions of Mars | 2296824 | Tithis | 1603000080 |
| Revolutions of Mercury | 17937000 | Suppressed days | 25082280 |

v2.c12.s2.t8.29

The epochal positions as ‘emerging’ from the above couplets (i.e. the positions at the epoch, calculated on the basis of the Sūrya-Siddhānta of Pañcasiddhāntikā) are as follows :—

v2.c12.s2.t8.30

| | s | ° | ' | " | |
| Sun | 11 | 29 | 27 | 20 | |
| Moon | 11 | 20 | 11 | 16 | These positions are true for the noor of Sunday, the 14th tithi of the dark half of Caitra, śaka 427 (elapsed). |
| Moon's Apogee | 9 | 9 | 44 | 53 | |

v2.c12.s2.t8.31

*Assuming at first that the yuga commenced on Thursday at midnight and adjusting planetary positions true for the moment, and then, arguing on the basis of the agreement of the two that the assumption was correct, appear like “arguing in a circle”. But one is forced to follow this method in the case of many problems in astronomy when nothing certain is known about them in the beginning. I have stated above only the final results obtained after the full consideration of the facts embodied in the above couplets. But only experienced persons can realize what pains I must have had to take over before arriving at the conclusion, and in how many ways I had to make different assumptions and to attempt the verification of their truth. When in August 1887 and Feb. 1888, inspite of several difficultes enumerated below, I could establish a correspondence between the multipliers and divisors with the epochal elements, and could particularly explain how the planetary positions mentioned by the Bhāśwat karana and Khaṇḍakhādyaka almost agree with the figures given by the Sūrya,Siddhānta of the Pañcasiddhāntikā, and could establish a certainty about the three works, my delight knew no bounds. The difficulties were (i) the Pañcasiddhāntikā was compiled about 1400 years ago (ii) it had no commentary, (iii) the copy which I had obtained was very inaccurate (iv) suspicion about the reliability of the words denoting the numerical quantities indicated by them and written below, in the above couplets, since the manuscript was incorrect, and (v) the fact that the figures indicating the length of the year and revolutions of planets do not fully agree with any of the modern siddhāntas. It must, however, be recorded here that this research does not deserve any more importance than what it is worth from the historical point of view. I enjoyed some more such moments of delight while writing this work—The author.

v2.c12.s2.t8.32

| | s | o | ' | " |
| Moon's asc. node | . | . | . | . |
| Mars | . | 2 | 15 | 35 | 4 |
| Mercury | . | 4 | 28 | 17 | 7 |
| Jupiter | . | 0 | 8 | 6 | 20 |
| Venus | . | 8 | 27 | 30 | 35 |
| Saturr | . | 4 | 2 | 28 | 49 |

v2.c12.s2.t8.33

The epochal positions of Mars and other planets are true for the midnight of Sunday, the 14th tithi of the dark half of Caitra.

v2.c12.s2.t8.34

The motion and position of Rāhu (moon's asc. node) has been mentioned in the 5th couplet of the 9th Chapter, but the couplet is unintelligible. The first couplet of the 16th Chapter clearly states that the epochal positions are true for the midnight, but which day it refers to has not been mentioned. The positions of planets, calculated on the basis of planetary revolutions mentioned above and true for the midnight of Sunday, the 14th tithi of the dark-half of Caitra, i.e. a moment 3gh-9 palas before the mean Sun's entry into Aries, completely agree with the epochal positions given by the couplets. The 6th couplet gives the ‘kṣepakas’ (epochal positions) for Mars, and the figures for seconds (of arc) appear to have been left out from it. The 9th couplet mentions Mercury's positions which contain no figures for seconds; and the position of Venus is given shorter by four seconds. But there would be no harm if it be said that the difference of a few seconds in the epochal positions should be regarded as negligible.

v2.c12.s2.t8.35

The above mentioned figures denoting revolutions and the length of a year do not agree with the corresponding measures of revolutions etc. given by the modern Sūrya Siddhānta. This shows that the Sūrya Siddhānta of Pañcasiddhāntikā and the modern Sūrya Siddhānta differ from each other in respect of elements and revolutions etc. That the former is older than the latter is evident from the fact that Varāhamihira has incorporated only the former. The date of the latter will be considered later on.

v2.c12.s2.t8.36

The above figures from the Sūrya Siddhānta of the Pañcasiddhāntikā completely agree with those from the Pulīśa Siddhānta and cited from Utpala above. It will be shown later on that Brahmagupta has adopted in his work, “Khaṇḍakhādyaka”, all these elements except those for the Moon's Apogee and the Ascending Node. It will be seen that all the elements from the Sūrya Siddhānta of the Pañcasiddhāntikā, except those for the length of the year and the revolutions of Mercury and Jupiter, completely agree with those of the Siddhānta of Āryabhaṭa which are given later on. It will be shown* further, that the mean planetary positions for the epoch, have been obtained from the Bhāsvatikaraṇa, by borrowing from the Sūrya Siddhānta of Pañcasiddhāntikā, the elements for all planets, except Jupiter, and applying the corrections suggested by Varāhamihira separately, in the 10th and 11th couplets of the 16th Chapter of the Pañcasiddhāntikā.

v2.c12.s2.t8.37

∗ Jupiter's ‘Kṣepaka’ (epochal position) as given by Bhāsvatikaraṇa agrees with the calculated result, if 364224 be assumed as the Jupiter's bhagaṇas (revolutions) instead of 364220; but this (364220) can be proved to be the Jupiter's ‘bhagaṇas’ according to Pañcasiddhāntikā, the multipliers and divisors, as mentioned in the first half of the 2nd couplet of the 16th Chapter, given above. Accepting 364224 as the correct number, 100 revolutions require 433227 days. Utpala's Pulīśa Siddhānta and the modern Sūrya Siddhānta give 364220 as the number of Jupiter's revolutions and on the basis of this very number one can arrive at the Jupiter's ‘Kṣepaka’ according to Khaṇḍakhādyaka. The Siddhānta of Āryabhaṭa states 364224 to be Jupiter's bhagaṇa; and Varāhamihira, while describing in the 8th chapter of Bṛhatsaṃhitā, the method of finding the ‘Barhaspatyasamvatsra’ (Jovian year) for any śaka year, assumes a Kṣepaka which can be obtained by assuming 364224 as the Jupiter's bhagaṇa.

v2.c12.s2.t8.38

Albiruṇī states† that the Sūrya Siddhānta was compiled by Lāṭa ; but, the Sūrya Siddhānta of the Pañcasiddhāntikā is not compiled by Lāṭa. Prof. Weber says‡ that the Sūrya Siddhānta must have some connection with Ptolemy. Both these points will be discussed later on in the course of the study of the modern Sūryasiddhānta.

v2.c12.s2.t8.39

† See Dr. Kern's Preface to the Bṛhatsaṃhitā and page 2 of the Translation of the Sūrya Siddhānta by Burgess.

v2.c12.s2.t8.40

‡ See page 3 of Translation of Sūrya Siddhānta by Burgess.

v2.c12.s2.t8.41

The above study of the five Siddhāntas, includes that of their dates also. They are, Paitāmaha, Vāsiṣṭha, Paulīśa, Saura, and Romaka as seen in their chronological order. It seems that Romaka belongs to a pre Śaka period and the remaining four were older than it.

v2.c12.s2.t8.42

THE PAURUṢA (HUMAN) AUTHORS OF ASTRONOMICAL WORKS BEFORE ŚAKA 420

v2.c12.s2.t8.43

The Pañcasiddhāntikā mentions names of some authors of astronomical works and no other source than this is available for obtaining any information about authors or writers of works before Śaka 420.

v2.c12.s2.t8.44

The following references are found in the Pañcasiddhāntikā—

v2.c12.s2.t8.45

पञ्चम्यो द्वावाद्यौ (पौलिशरोमकसिद्धान्तौ) व्यारव्यातो लाटदेवेन ॥ ३ ॥ अ० १. लाटाचार्येणोक्तो यवनपुरे चास्तगे सूर्ये ॥ रव्युदये लंकायां सिंहाचार्येण दिनगणौभिहितः ॥ ४४ ॥ यवनानां निशि दशाभिगतंर्मुहूर्तैश्च तद्गुरुणा ॥ लंकाधरात्रसमये दिनप्रवृत्ति जगाद चायर्भटः ॥ ४५ ॥ सूर्य: स एव सूर्योदयात् प्रभृत्याह लंकायां ॥ अ० १४.

v2.c12.s2.t8.46

(3) The first two of the five (viz. Paulīśa and Romaka) have been described by Lāṭadeva.

v2.c12.s2.t8.47

(44 & 45) The purport of these very important lines from the 14th chapter is as follows—Lāṭācārya has enjoined the calculation of ahargaṇa from the moment of sunset (on the horizon) of Yavanapur.

v2.c12.s2.t8.48

(The moment of sunset at Yavanapur coincides with that of midnight at Laṅkā). Siṃhācārya has enjoined the calculation of ahargaṇa from the sunrise at Laṅkā, while his preceptor enjoins the adoption of ten muhūrtas (i.e. 20 ghaṭis) in the night for the calculation of ahargaṇa in the Yavana country. Āryabhaṭa after stating the commencement of the day as from the midnight at Laṅkā, has again defined the day as begining from the sunrise* there. The name of Siṃha's preceptor referred to here is not known. Here is a reference quoting some more names :—

v2.c12.s2.t8.49

∗ Āryabhaṭa's reference of the commencement of a day at sunrise at Laṅkā will be given later on. The reference of the day commencing at midnight in Laṅkā is not found in the Āryabhaṭīya.

v2.c12.s2.t8.50

प्रद्युम्नो भूत नये जीवे सौरे च विजयनंदी ॥ ५६ ॥ शेवटचा अध्याय.

v2.c12.s2.t8.51

“Pradyumna broke down in the matter of Mars and Vijayanandi in the matter of Jupiter and Saturn…………”

v2.c12.s2.t8.52

These are the names mentioned by the Pañcasiddhāntikā. Of these, an account of Āryabhaṭa will be given later on. All these names occur in Brahmagupta’s Siddhānta also. All of them have been criticised by Brahmagupta in some way or other. We do not come across any mention of their merits. The statement that Śrīṣeṇa has adopted some elements from Lāṭa in his work, Romaka, has already been given above. Varāha remarks that Lāṭa has commented upon the Puliśa and Romaka Siddhāntas and this commentary cannot possibly contain his own views. This shows that Lāṭa must have compiled a separate work. Brahmagupta elsewhere observes :—

v2.c12.s2.t8.53

श्रौषेणविष्णुचंद्रप्रद्युम्नार्यभटलाटसिहानां ॥ ग्रहणादिविसंवादात् प्रतिदिवसं सिद्धमकृतत्वं ॥ ४६ ॥ †अंकचितिविजयनंदिप्रद्युम्नादीनि पादकरणानि ॥ यस्मात्तस्मात्तेषां न दूषणान्यत्र लिखितानि ॥ ५८ ॥

v2.c12.s2.t8.54

† The word ‘aṅkaciti’ also seems to be a proper noun.

v2.c12.s2.t8.55

It shows that Lāṭācārya had perhaps compiled a work. Similarly Simhācārya also had compiled one. Even Varāhamihira has remarked in one of the above mentioned couplets that Pradyumna broke down in respect of Mars and Vijayanandi about Jupiter and Saturn. The ‘Karaṇa’ works of both these authors are described as ‘pādakaraṇa’. In one of the couplets given before, Brahmagupta says that Śrīṣeṇa has borrowed the Vijayanandi’s pādas. This remark is unintelligible, and it is not clear if ‘pāda’ means a ‘yugapāda’.

v2.c12.s2.t8.56

Anyway, it appears that Lāṭa*, Simhā, Pradyumna and Vijayanandi were authors of astronomical works who lived before Śaka 420.

Cites (11)