Surya Siddhanta

01Maya’s tapas

The first chapter opens with a bow to Brahman, beyond thought and form, the support of all the worlds. Then the katha. When only a little of the Krita Yuga remained, Maya, a great asura, longing for the highest and most secret knowledge, the foremost limb of the Veda that explains the motions of the lights of heaven, did hard tapas to Vivasvan, the Sun. Pleased, Surya spoke: no one can bear my radiance, and I have no moment to spare; this man born of my own amsha will tell you everything. He vanished, and the amsha-purusha turned to Maya, standing with folded hands.

02The same shastra, age after age

The amsha-purusha tells Maya that this is the very knowledge Vivasvan himself gave to the maharshis in yuga after yuga. The shastra is the first and the same; only time, turning through the yugas, has made the difference in its numbers. The text then places itself exactly. Six Manus and their sandhis have passed in this kalpa, and twenty-seven Mahayugas of the Vaivasvata Manu; of the twenty-eighth, the Krita has just ended. By its own count 1,95,37,20,000 years of the kalpa had gone by at that moment. The last chapter closes the frame: Maya, his task fulfilled, passed the knowledge on to the rishis who came to him.

03The text in human history

In recorded history a Surya Siddhanta first appears in the Panchasiddhantika of Varahamihira, written at Ujjain with an epoch of 505 CE. He summarises five siddhantas, the Paitamaha, Vasishtha, Romaka, Paulisha and Saura, and calls the Saura the clearest of them all. The text read today differs from his summary in several constants, and it has been kept in step with the sky over the centuries by bija, small corrections. Scholars who compare the two place the present recension some centuries after Varahamihira. The tradition sees one shastra given again and refined, which is what the text says of itself.

04The measure of time

Time, says the text, is of two kinds: the time that ends the worlds, and the time that can be counted. Counted time is either gross or subtle. The prana, one breath of about four seconds, begins the gross scale; the truti, too small to perceive, begins the subtle. Six pranas make a vinadi, sixty vinadis a nadi, sixty nadis a sidereal day. Twelve months make a year, which is one day of the devas. Twelve thousand divine years make a Mahayuga of 43,20,000 solar years, shared among the Krita, Treta, Dvapara and Kali as 4:3:2:1. Seventy-one Mahayugas make a Manvantara, fourteen Manvantaras with their sandhis a kalpa, one day of Brahma.

05Fourteen chapters

The first chapter gives time and the mean motions: how many times each planet circles the sky in a Mahayuga, and how to find its mean place on any day by counting the days since creation. The second corrects mean to true, with the sine table, and defines tithi, nakshatra, yoga and karana. The third answers direction, place and time from the gnomon. Chapters four to six are eclipses, seven and eight conjunctions of planets and stars, nine to eleven risings, the moon’s horns and the patas. Twelve describes creation and the earth, thirteen the armillary sphere and instruments, and fourteen the nine kinds of time measure.

06225 and the sine table

The second chapter builds its sine table from one number. Take the minutes in one sign of the zodiac, 1,800, and an eighth of them, 225, is the first sine. Each following sine is found from the one before by a simple rule of subtraction and division, until twenty-four sines cover the quarter circle at steps of 3¾ degrees, on a radius of 3,438. With these and with epicycles that shrink and swell, the text turns a planet’s mean place into the place where it will actually be seen. From the true sun and moon come the tithi, the nakshatra and the yoga, the five limbs of every panchanga.

07Earth in space

The earth, says chapter twelve, stands in space at the centre of the brahmanda, holding the supreme power of Brahma that sustains it. The first chapter gives its size: the diameter is 1,600 yojanas, and the square root of ten times its square is the circumference, about 5,059 yojanas. At other latitudes the circle shrinks by the cosine of the latitude. The prime meridian runs from Lanka on the equator to Meru, passing through Rohitaka, Avanti, which is Ujjain, and the lake at Kurukshetra. Panchanga makers still correct their reckonings by a place’s distance east or west of that line.

08In the panchanga today

Many traditional panchanga makers in Varanasi, Odisha, Bengal, Andhra and the south still compute tithi, nakshatra and eclipses from the Surya Siddhanta, with its bija corrections, and in many regions the solar months and Makar Sankranti are reckoned by its sun. Others now follow drik-ganita, positions computed from modern observation, and the two schools sometimes differ by a day. The fourteenth chapter names the nine measures of time, Brahma, divine, ancestral, Prajapati’s, Jupiter’s, solar, civil, lunar and sidereal, and says which belongs to which rite. A panchanga is still built from those measures.

09Commentaries and translations

In Kerala Parameshvara wrote a commentary on it in the fifteenth century. At Kashi, Ranganatha’s Gudharthaprakashika of 1603 became the standard reading, and Kamalakara Bhatta built his Siddhantatattvaviveka of 1658 on its system. Palm-leaf copies in Grantha, Malayalam, Telugu and Odia scripts are found across the south and east. Ebenezer Burgess, an American missionary, published an English translation with W. D. Whitney’s notes in 1860, and Bapu Deva Sastri brought out another in the Bibliotheca Indica in 1861. Mahavir Prasad Srivastava’s Hindi Vijnana Bhashya opened it to Hindi readers.

What it contains

1. 1
   1. Madhyamadhikara

   Opens with the katha of Maya’s tapas. Then the units of time from prana to kalpa, the place of the present moment in the kalpa, the revolutions of each planet in a Mahayuga, and the mean place of a planet on any day. The size of the earth and the prime meridian through Ujjain close it.

2. 2
   2. Spashtadhikara

   Why planets move unevenly, explained by beings of invisible form at the apsides and nodes who draw them with cords of air. Then the sine table, the equations of centre and of conjunction, and the true places of the planets. It ends with tithi, nakshatra, yoga and karana.

3. 3
   3. Triprashnadhikara

   The three questions of direction, place and time, answered with the gnomon’s shadow. It also gives the precession of the equinoxes, the rising times of the signs and the length of day and night at a place.

4. 4
   4–6. Eclipses

   The lunar eclipse, the solar eclipse with its correction for parallax, and the parilekha, how to draw an eclipse on the ground to show its phases, colour and direction. These chapters let a panchanga give the exact minute of sparsha and moksha.

5. 5
   7–8. Grahayuti and nakshatras

   Conjunctions of the planets with one another, and which is the victor when two come close. Then the positions of the junction stars of the twenty-seven nakshatras, with Agastya, Brahmahridaya and other bright stars.

6. 6
   9–11. Risings, the moon and patas

   Heliacal risings and settings of planets and stars, the elevation of the moon’s horns, and the vyatipata and vaidhriti, inauspicious moments when the sun and moon stand in certain relations. These timings are still marked in the panchanga.

7. 7
   12. Bhugoladhyaya

   Maya asks about the size and shape of the earth and the order of creation. The answer describes creation from Vasudeva and Brahma, the earth held in space at the centre of the brahmanda, Meru at its north pole, and the orbits of the planets one above another.

8. 8
   13. Jyotishopanishad

   How to build an armillary sphere of wood with its rings, and other instruments: water clocks, the gnomon, and self-moving devices. The text asks that this knowledge be given only to a worthy student.

9. 9
   14. Manadhyaya

   The nine measures of time, Brahma, divine, ancestral, Prajapati’s, Jupiter’s, solar, civil, lunar and sidereal, and what each governs: the year, the samskaras, the fasts. It ends with Maya giving the knowledge to the rishis.

Famous verses

अल्पावशिष्टे तु कृते मयो नाम महासुरः। रहस्यं परमं पुण्यं जिज्ञासुर्ज्ञानमुत्तमम्॥

When only a little of the Krita Yuga remained, the great asura named Maya, wishing to know the supreme, secret and holy knowledge…Surya Siddhanta 1.2

न मे तेजःसहः कश्चिदाख्यातुं नास्ति मे क्षणः। मदंशः पुरुषोऽयं ते निःशेषं कथयिष्यति॥

No one can bear my radiance, and I have no moment to spare for telling it. This man, born of my own amsha, will tell it to you in full.Surya Siddhanta 1.6

तद्द्वादशसहस्राणि चतुर्युगमुदाहृतम्। सूर्याब्दसंख्यया द्वित्रिसागरैरयुताहतैः॥

Twelve thousand of these divine years are called a chaturyuga. In solar years it is two, three and four, the oceans, multiplied by ten thousand: 43,20,000.Surya Siddhanta 1.15

योजनानि शतान्यष्टौ भूकर्णो द्विगुणानि तु। तद्वर्गतो दशगुणात्पदं भूपरिधिर्भवेत्॥

The diameter of the earth is twice eight hundred yojanas. The square root of ten times its square is the circumference of the earth.Surya Siddhanta 1.59

मध्ये समन्तादण्डस्य भूगोलो व्योम्नि तिष्ठति। बिभ्राणः परमां शक्तिं ब्रह्मणो धारणात्मिकाम्॥

In the very middle of the brahmanda the globe of the earth stands in space, bearing the supreme power of Brahma whose nature is to uphold.Surya Siddhanta 12.32