Indian Astronomical Tables of the Saura Paddhati – In Historical Perspective

Abstract

The period including the latter half of the fifteenth century and the earlier half of the sixteenth century witnessed a big resurgence in the development of astronomy, not only in Europe but also in India. In Europe we had great pioneers like Galileo, Copernicus and Tycho Brahe, the illustrious galaxy being crowned by Johannes Kepler (1571–1630) a little later.

On the Indian scene, during that period we had two remarkable stalwarts, Parameśvara Nīlakaņţha and Gaņeśa Daivajña. In the tradition of computation of planetary positions, astronomical phenomena and calendrical data, the role of astronomical tables for Indian calendrical purposes (pañcāṅga) cannot be exaggerated. We have different genres of such tables known differently as sāriṇīs, padakas, koṣṭakas and vākyas.

In this paper we present some salient features of a few prominent handbooks (karaṇas) and tables belonging to the Saurapakṣa School of Astronomy, based on a popular Indian astronomical treatise, the Sūryasiddhānta (SS).

1 Introduction

In the European astronomical tradition, starting with Ptolemy’s second century CE Handy Tables, De la Hire’s tables etc. were used in calculating ephemerides. In an Indian context, for both calendrical purposes and the computation of planetary positions, different schools (pakṣas) viz., Āryapakṣa, Saurapakṣa, Brāhma (Paitāmaha) pakṣa and Gaṇeśapakṣa, were in vogue. In these distinct schools both handbooks with ready-to-use algorithms and astronomical tables emerged in quick succession. The Saurapakṣa tables, based on the Sūryasiddhānta (Burgess and Gangooly 1989) became very popular in the northern part of India. On the other hand, the Āryabhaṭan School—fostered by Bhāskara I (CE 629)—was followed exclusively in Kerala (Southern India).

Around CE 1520 the Grahalāghavam (GL), a text written by the Maharashtrian astronomer Gaṇeśa Daivajña who was based in Banaras, became extremely popular throughout Maharashtra, in the major part of north India, and also in north Karnataka, particularly in the Belgaum and Gulbarga regions. The popularity of Gaṇeśa’s School often exceeded the other schools mainly because Gaṇeśa Daivajña completely dispensed with the use of trigonometric ratios, replacing them with very good algebraic approximations. In fact, this thoughtful innovation relieved the pañcāṅga-makers of the bugbear of handling the cumbersome values of trigonometric ratios. Based on the GL there are many astronomical tables belonging to the Gaṇeśapakṣa.

In the Saurapakṣa, the most popular astronomical tables were the Makaranda sāriṇī of Makaranda (CE 1478), the Pratibhāgī Gaṇakānanda (GNK) and the Tyāgarthi manuscripts. In the following sections we provide a few glimpses of a couple of these Saura tables.

The famous Andhra astronomer Sūrya, son of Bālāditya, composed his famous karaṇa (handbook) called the Gaṇakānanda. His more illustrious protégé, Yalaya, composed his exhaustive commentary, Kalpavallī, on the well-known SS treatise.

Yalaya belonged to kāśyapa Gotra, and his genealogy is as follows: Kalpa Yajvā (great grandfather) – Yalaya (grandfather) – Śridhara (father) – Yalaya.

His father, Śridhara, was an expert in Sanskrit stotras (and was different from his namesake, the author of the Pāṭīgaṇita and the Triśatikā). Yalaya received his training in astronomy from his instructor, Sūryācaryā, the author of the Gaṇakānanda. Yalaya spoke highly of his guru and even compared him with the Vedic sage Brihaspati.

Yalaya quotes from his instructors three works: the Gaṇakānanda (composed in CE 1447), the Daivajñābharaṇa and the Daivajñabhῡṣanạ. Yalaya resided in a small town to the north of Addankī (latitude 15°.49 N, longitude 80°.01 E) called Skandasomeśvara, in Andhra Pradesh. This small town was south-east of Śriśaila, the famous pilgrimage centre.

In his commentary on the Laghumānasa of Mañjula (CE 932), Yalaya provides the astronomical data for Tuesday noon, of the beginning of Chaitra māsa corresponding to 18 March 1482 CE. Yalaya wrote his commentary Kalpavallī on SS in CE 1472 and that on the Āryabhaṭiyam in CE 1480.

Interestingly, Yalaya records some contemporary astronomical events. A few of them are as follows:

• 1. A lunar eclipse on Saturday, Phālguna paurṇimā, śaka 1407, corresponding to 18 February 1486 CE.

• 2. A solar eclipse on Friday, Phālgunā Amāvāsyā, śaka 1389, i.e. on 25 March 1468 CE.

• 3. A solar eclipse on Friday, Bhādrapada Amāvāsyā, śaka 1407, i.e. 9 September 1485 CE, visible from his native place.

• 4. A Jupiter-Moon conjunction on Saturday, Āṣādha paurṇimā śaka 1408, i.e. 17 June 1486 CE.

• 5. Commencement of Adhika (intercalary) Śrāvaṇa-śukla pratipat śaka 1408, i.e. Sunday, 2 July 1486 CE.

Balachandra Rao and Venugopal (2008) have verified the genuineness of the above eclipse recordings by using the software prepared by them based on modern computations.

In the following section we consider a few examples to give a feel of these classical tables and handbooks.

2 The Gaṇakānanda (GNK)

The karaņa text Gaņakānanda is the most popular text in regions of Andhra and Karnataka. Apart from the regular topics the text contains tables of astronomical phenomena. The text belongs to the Saurapakșa and was authored by Sūryācārya, the son of Bālāditya who came from the Andhra region. The text based on the Sūryā-siddhānta is in Telugu, and the script was edited and published by Vella Lakshmi Narasimha Sastri from Machalipatnam in the Andhra region and reprinted in 2006. The epochal date of the text is 16 March 1447 CE.

3 Makaranda Sariṇī (MKS)

A large number of Indian astronomical almanacs (pañcāṅga) which are composed annually according to the Saurapakṣa are based on the MKS. The author of the MKS declares:David Pingree had provided very useful and often exhaustive information on the contents of the MKS and also on the availability of the manuscripts in his two famous catalogues, Sanskrit Astronomical Tables in the United States (SATIUS) and Sanskrit Astronomical Tables in England (SATE).

In the following section, to check the correctness of the MKS and the GNK parameters and procedures, we have computed and compared, as an example, values of the true sidereal (nirayaṇa) longitude of the Sun for the date 3 April 2012 at mean sunrise at Ujjayinī (6^h 27^m IST). These are shown in Table 1.

Table 1 Sun’s sidereal true longitude for 3 April 2012

This particular date was chosen since around that date every year the Sun’s equation of centre (mandaphala) is maximum. In Table 1 we note that the MKS values of mean longitude and the equation of centre are close to the modern ones. But the Sun’s true longitude differs from the modern value by about 9′ 7″ and the equation of centre (mandaphala) by 16′ 16″. These differences are mainly because in modern computations gravitational periodic terms are considered. In the classical Indian texts, even as in the European tradition before Kepler, epicyclic theory was adopted. The results obviously vary a little compared to those of Kepler’s heliocentric elliptical theory. The equation of centre in siddhāntas is governed by the radii of the epicycles.¹

4 The Sun’s Declination (Krānti)

In the computation of solar eclipses and transits we need to use the declination (krānti) of the Sun. In Table 2 we compare the values of the Sun’s declination (δ) for 2 days when the Sun’s rays fall directly on the Shiva lingam at the famous Gavigaṅgadhareśvara Temple in Bangalore (see Vyasanakere et al., 2008).

Table 2 The Sun’s sidereal true longitude on 3 April 2012

From Table 2 we notice that on 2 days of the year 2012, namely 14 January and 28 November, the declination of the Sun has the values 21° 02′ 29.13″ south and 21° 08′ 51.91″ south respectively according to the MKS, and the corresponding values according to the GNK are 21° 10′ 10.64″ south and 21° 16′ 36.97″ south. It should be noted that the declination is calculated according to these texts for the same time. The difference in arcminutes for the two dates according to a particular text indicates that the corresponding azimuths and the altitudes of the Sun differ a little. The difference in the values of δ according to the two classical texts as compared to the modern values is due to the fact that the Indian classical texts considered the obliquity of the ecliptic as 24° while the modern known value is around 23° 26′. It is significant to note that the GNK values are closer to the modern ones.

5 The Conjunction of the Moon and Jupiter on 19 May 1472

In his commentary Kalpavallī on the SS, Yalaya gives an example of the lunar conjunction with Jupiter for (Nandana saṃvatsara, Jyestha Śukla12, Śaka 1394) i.e. Tuesday 19 May 1472. According to his text the conjunction took place around 44 ghaṭis from the midnight between 18 and 19 May 1472, i.e. 17.6 h p.m. (LMT) or around 6 p.m. (IST) on 19 May 1472. Let us compare Yalaya’s result with a modern computation, which comes out to about 20 h (IST). The difference of about 2 h is mainly due to the fact that in Yalaya’s computation the gravitational terms are not taken into consideration. For 2 h the relative motion of the Moon with respect to Jupiter is about 1°, which was not easily perceptible without a telescope. Furthermore, the difference between the ephemeris time and the universal time, Δt, also plays a role, though a marginal one. In Table 3, the true tropical longitudes of the Moon and Jupiter according to Yalaya and modern computations are compared.

Table 3 The conjunction of the Moon and Jupiter on 19 May 1472

According to the SS, the accumulated precession of the equinox (i.e. the ayanāṃśa) works out to be 14° 25′. The example given by Yalaya is a valid one.

6 The Lunar Eclipse of Friday 22 May 1472 (i.e. Nandana samvatsara, Jyeṣṭha śῡkla paurṇimā, Friday)

Yalaya explains the procedure for the computation of a lunar eclipse with his contemporary example dated 22 May 1472. According to him, the middle of the eclipse is 3–33 ghaṭis after sunset. The instants of the beginning and the end of the eclipse are 1–13 ghaṭis before and 8–13 ghaṭis after the sunset, respectively. Similarly, the beginning and the end of totality are 1–25 ghatis and 5–37 ghatis after sunset, respectively. The duration of the entire eclipse is 9–26 ghatis. In Table 4 Yalaya’s results are compared with those derived from modern computations.

Table 4 Circumstances of the lunar eclipse dated 22 May 1472^a

From Table 4, we observe that the timings recorded by Yalaya are close to those we get from the modern computations for that date.

7 The Inscriptional Evidence, 1148

7.1 The Solar Eclipse of 20 April 1148

The reference for this eclipse is: EKU Vol. 1 No. 23, Source: 20 April 1148, 11th regnal yr., Vibhava, Chaitra 30, Chalukya of Kalyana, Jagade-kamalla.

The inscriptional data are very interesting since on the very same day three important phenomena occurred: a solar eclipse, a lunar occultation of Mercury and vyatipata (see Table 5). We computed that a transit of Mercury occurred 3 days later, but this was not recorded. Following are the parameters required for the computation of the eclipse:

• Tropical long. of the Sun: 36° 13′ 8″.

• Tropical long. of the Moon: 33° 52′ 36″.

• Latitude of the Moon: 0° 16′ S.

• Instant of New Moon: 10^h 34^m.

Table 5 Vyatipata on 20 April 1148

The eclipse turned out to be total. Here are the details:

• Beginning of Eclipse: 7^h 50^m.

• Beginning of Totality: 8^h 46^m.

• Middle: 10^h 34^m.

• End of Totality: 12^h 21^m.

• End of Eclipse: 13^h 18^m.

Re Table 5, it should be noted that if the declinations of the Sun and the Moon are equal in both magnitude and direction then that phenomena is called Vyatipata. During the solar eclipse it can be observed that the declinations of the Sun and the Moon are equal.

7.2 Transits and Occultations

The procedure for recording transits and occultations is similar to that of solar eclipse. The participating bodies in the case of transits will be Sun and the planets Mercury or Venus, and for occultation, the Moon and the planet or a star. Transits of Mercury and Venus occur when either of them is in conjunction with Sun as observed from the Earth, and subject to prescribed limits (see Balachandra Rao and Venugopal, 2009).

Transits of Venus occur less frequently than transits of Mercury. For example, after the transit of Venus in June 2004 the next occurrence was on 6 June 2012. After that, the subsequent Venus transit will be about 105.5 years later (i.e. in December 2117).

While detailed working of planetary conjuncttions is discussed in all traditional Indian astronomical texts in the chapter titled Grahayuti, it has to be noted that the transits of Mercury and Venus are not explicitly mentioned. This is mainly because when either of these inferior planets is close to Sun it is said to be ‘combust’ (asta) and hence not visible to the naked eye. Transits of Mercury or Venus are called sankramaņa (of the relevant planet), or ‘gādhāsta’. In a transit of Mercury or Venus the planet passes across the bright disc of Sun as a small black dot.

7.3 The Lunar Occultation of Mercury on 19/20 April 1148

The computational procedure is similar to that for a solar eclipse. The details are as follows:

• Instant of conjunction: 17^h IST

• Sidereal longitude of the (retrograde) Mercury: 29° 6′

• Sidereal longitude of the Moon: 29° 1′

• Mercury’s latitude: 0° 49′ N

7.4 The Transit of Mercury of 23 April 1148

The computed details are as follows:

• Instant of conjunction: 13^h IST

• Beginning of the transit: 14^h 0^m 31^s

• Internal ingress: 14^h 0^m 48^s

• Middle of the transit: 15^h 45^m 0^s

• External Ingress: 17^h 29^m 11^s

• End of the transit: 17^h 29^m 28^s

8 Conclusion

In the preceding sections we have introduced some features of the astronomical tables belonging to the Saurapaksa. Using the tables of the MKS and the GNK, both from the Saurapaksa, we have computed and compared some events, like a lunar eclipse, a lunar conjunction of Jupiter, a lunar occultation of Mercury, and the equality of the Sun’s declination when the Sun’s rays fall directly on the deity at a famous shrine in Bangalore. In all of these cases the related parameters according to the traditional tables were compared and found to be close to those obtained by modern procedures.