The Surya Siddhanta · Chapter 4 of 8

#True places and the panchanga

Chapter II turns the mean positions of chapter I into true positions — where the planets actually appear — and ends with the computation of the panchanga.

#Why the planets move unevenly (II.1–11)

The text gives a picture, half physical and half mythic:

Forms of Time, of invisible shape, stationed in the zodiac, called the conjunction (shighrocca), apsis (mandocca) and node (pata), are causes of the motion of the planets. The planets, attached to these beings by cords of air, are drawn away by them, with the right and left hand, forward or backward, according to nearness, toward their own place (II.1–2).

A wind, the "provector" (pravaha), drives them toward their apices (II.3). The apsis pulls a planet forward or back depending on which side of it the planet is (II.4–5); the node pulls the Moon and planets north or south of the ecliptic, producing their latitude (II.6–8). The Sun, being large, is pulled only a little; the Moon, smaller, more; Mars and the others, being small, are pulled "very far" (II.9–11).

#The eight kinds of motion (II.12–14)

Planetary motion is of eight kinds: retrograde, somewhat retrograde, transverse, very swift, swift, slow, very slow and even (II.12–13). The purpose of the chapter: "the planets thus come to an accordance with their observed places — this, their correction, I shall carefully explain" (II.14).

#The sine table (II.15–27)

The sines are built up from the first: "the eighth part of the minutes of a sign is called the first sine" (1,800 ÷ 8 = 225); each next sine is found from the previous ones (II.15–16) — the same second-difference rule as Aryabhata's. The table gives 24 sines: 225, 449, 671, 890, 1105, 1315 ... up to 3,438, the radius (II.17–22), and a table of versed sines (II.22–27).

#The tilt of the ecliptic (II.28)

The sine of greatest declination is thirteen hundred and ninety-seven (II.28).

On a radius of 3,438, a sine of 1,397 corresponds to an angle of about 24° — the tilt of the Earth's axis (the true value in this period was about 23.6°). From it, the declination of any point of the ecliptic follows.

#Epicycles and the two corrections (II.29–51)

Each planet's mean position is corrected twice:

• the manda correction, "from the apsis", for the uneven speed due to the shape of the orbit — the only correction needed for the Sun and Moon (II.43);
• the shighra correction, "from the conjunction", for the effect of the planet's position relative to the Sun — needed for Mars, Mercury, Jupiter, Venus and Saturn.

The sizes of the epicycles are given, slightly different at the ends of the odd and even quadrants: for the Sun's apsis 14° and 13°40′, the Moon's 32° and 31°40′; and so on for the planets (II.34–37). The text then gives the procedure: compute the equations with the sines, apply half of each, then the whole, in a set order (II.38–45). The planets' daily motions are corrected in the same way (II.46–51).

#Retrograde motion (II.52–55)

When at a great distance from its conjunction, a planet, having its substance drawn to the left and right by slack cords, comes then to have a retrograde motion (II.52).

The text gives, for each planet, the angular distance from its "conjunction" at which retrograde motion begins and ends (II.53–55).

#Latitude and declination (II.56–58)

The nodes of the planets, corrected in the same way, give their latitudes north or south of the ecliptic; combined with the declination of the ecliptic, the planet's true declination (II.56–58).

#Day and night (II.59–63)

From the Sun's declination and the latitude of the place, the ascensional difference is found, and from it the length of day and night (II.59–63).

#The panchanga (II.64–69)

The chapter ends with the five limbs of the almanac:

• The nakshatra: from the Moon's longitude divided by the portion of one nakshatra, 800 minutes (II.64).
• The yoga: "From the number of minutes in the sum of the longitudes of the sun and moon are found the yogas, by dividing that sum by the portion of an asterism" (II.65).
• The tithi: "From the number of minutes in the longitude of the moon diminished by that of the sun are found the lunar days, by dividing the difference by the portion of a lunar day" — 720 minutes, 12° (II.66).
• The karanas: the four fixed karanas — Shakuni, Naga, Chatushpada and Kimstughna — from the second half of the fourteenth of the dark half; then the seven movable karanas, Bava and the rest, each eight times a month (II.67–68); a karana is half a tithi (II.69).

And in each case the text gives the time elapsed and remaining from the planets' daily motions. These are the same definitions used in every Indian almanac today.

#Summary

• Uneven motion is caused by "forms of Time" — apsis, conjunction, node — pulling the planets by cords of air (II.1–11); eight kinds of motion (II.12–13).
• The sine table on radius 3,438 (II.15–27); the ecliptic's tilt, sine 1,397 ≈ 24° (II.28).
• Mean planets are made true by the manda (apsis) and shighra (conjunction) corrections with epicycles (II.29–51); retrograde motion (II.52–55); latitude, declination and day length (II.56–63).
• The nakshatra, yoga, tithi and karanas are computed from the longitudes of the Sun and Moon (II.64–69).

#Exercises

1. What pulls the planets out of their even motion, according to II.1–2?
2. Which correction is needed for the Sun and Moon, and which for the other planets?
3. How is the yoga found?
4. How long is a tithi in arc? A karana?
5. Which are the four fixed karanas?

Answers: 1. The "forms of Time" — the conjunction, apsis and node — by cords of air (II.1–2). 2. Only the manda (apsis) for the Sun and Moon; both manda and shighra for the others (II.43). 3. By dividing the sum of the longitudes of the Sun and Moon by the portion of a nakshatra (800′) (II.65). 4. 12°; 6°. 5. Shakuni, Naga, Chatushpada and Kimstughna (II.67).