The Surya Siddhanta · Chapter 3 of 8
The revolutions of the planets
Why the planets move east (I.25–27)
The planets, moving westward with exceeding velocity, but constantly beaten by the asterisms, fall behind, at a rate precisely equal, proceeding each in its own path. Hence they have an eastward motion (I.25–26).
The whole sky turns westward once a day; each planet is carried with it but falls a little behind, so that relative to the stars it moves east. All the planets move the same distance each day along their orbits; a planet in a small orbit therefore goes round quickly, one in a large orbit slowly (I.26–27). The circle of the zodiac is complete "at the end of the asterism Revati" (I.27). (The same idea as Aryabhata's; Aryabhata Book, chapter 6.)
The divisions of the circle (I.28)
60 seconds make a minute; 60 minutes a degree; 30 degrees a sign; 12 signs a revolution (I.28).
The revolutions in a great age (I.29–34)
| Body | Revolutions in a great age (4,320,000 years) |
|---|---|
| Sun, Mercury, Venus (mean) | 4,320,000 |
| Moon | 57,753,336 |
| Mars | 2,296,832 |
| Mercury's conjunction (shighra) | 17,937,060 |
| Jupiter | 364,220 |
| Venus's conjunction (shighra) | 7,022,376 |
| Saturn | 146,568 |
| Moon's apsis | 488,203 |
| Moon's node (backwards) | 232,238 |
| The asterisms (sidereal days) | 1,582,237,828 |
(I.29–34.) The numbers differ slightly from Aryabhata's: the Moon's is the same, the others differ in the last digits.
Months and days (I.35–44)
- Lunar months = revolutions of the Moon minus those of the Sun; minus the solar months, they give the intercalary months: 1,593,336 in a great age (I.35, 38).
- Civil days = risings of the asterisms minus revolutions of the Sun: 1,577,917,828 (I.37, 39).
- Lunar days (tithis): 1,603,000,080; minus the civil days, the omitted tithis: 25,082,252 (I.36–38).
- Multiplied by 1,000, these give the numbers in a kalpa (I.40).
The slow motions of the planets' apsides and nodes are given per kalpa: the Sun's apsis 387 revolutions, Mars's 204, Mercury's 368, Jupiter's 900, Venus's 535, Saturn's 39; the nodes of Mars 214, Mercury 488, Saturn 662, and so on (I.41–44).
How accurate?
| Quantity | Surya Siddhanta | Modern |
|---|---|---|
| Sidereal year | 365.258756 days (365 d 6 h 12 m 36.6 s) | 365.256363 days |
| Synodic month | 29.530588 days | 29.530589 days |
| Sidereal month | 27.321674 days | 27.321662 days |
| Sidereal day | 23 h 56 m 4.1 s | 23 h 56 m 4.1 s |
| Saturn | 29.47 years | 29.46 years |
| Jupiter | 11.861 years | 11.862 years |
| Mars | 1.8809 years | 1.8809 years |
| The Moon's node | 18.60 years | 18.61 years |
(Computed from I.29–39.) The synodic month is right to a tenth of a second. The year is about 3½ minutes too long — enough, over the centuries, to move the computed calendar away from the sky.
The mean planets (I.48–58)
From the count of days since the start, the mean position of each planet follows by the rule of three: revolutions × days ÷ days in the age (I.53). The result is for midnight on the prime meridian. The text adds that at the end of the last Golden Age all the mean planets were together at the first point of Aries, with the Moon's apsis at the start of Capricorn and its node at the start of Libra (I.57–58) — a convenient starting point for shorter calculations (I.56) — and gives the rule for the year of Jupiter's sixty-year cycle, counted from Vijaya (I.55).
The prime meridian (I.62)
Situated upon the line which passes through the haunt of the demons [Lanka] and the mountain which is the seat of the gods [Meru], are Rohitaka and Avanti, as also the adjacent lake (I.62).
The prime meridian of Indian astronomy runs from Lanka (an ideal point on the equator) to the north pole through Avanti — Ujjain. Positions computed for this meridian are corrected for places east or west of it (I.61).
The size of the Earth (I.59–60)
Twice eight hundred yojanas are the diameter of the earth: the square root of ten times the square of that is the earth's circumference (I.59).
So the diameter is 1,600 yojanas and the circumference 1,600 × √10 ≈ 5,060 yojanas — using √10 ≈ 3.162 for π. The circumference along a parallel of latitude is found by multiplying by the cosine of the latitude (I.60). (Burgess notes that the true size depends on the uncertain length of the yojana.)
Longitude from eclipses (I.63–65)
If a lunar eclipse is seen earlier than the time calculated for the prime meridian, the observer is west of it; if later, east. The difference in time, multiplied by the Earth's circumference at that latitude and divided by sixty, gives the distance in yojanas (I.63–65). This is the classic method of finding longitude — by observing the same event from two places.
The weekday and the latitudes (I.66–70)
The weekday begins, east of the prime meridian, later than midnight by the difference of longitude, and earlier to the west (I.66). The greatest latitude of the Moon is an eightieth of the circle — 270 minutes, 4½° — and of the planets in proportion (I.68–70).
Summary
- The planets are carried west by the sky but fall behind, so move east; all move equal distances daily (I.25–27).
- The revolutions of each body in a great age (I.29–34) give months, intercalary months, civil days and omitted tithis (I.35–44), with remarkable accuracy except a year 3½ minutes too long.
- Mean positions by the rule of three from the count of days (I.53).
- The prime meridian passes through Ujjain (I.62); the Earth is 1,600 yojanas across, its circumference 1,600√10 (I.59); longitude by timing eclipses (I.63–65).
Exercises
- Why do the planets seem to move east?
- How many civil days are in the Surya Siddhanta's great age? How are they found?
- What value does I.59 use for π?
- Through which city does the prime meridian pass?
- A lunar eclipse is seen 2 nadis earlier than the time calculated for the prime meridian. Is the observer east or west?
Answers: 1. Because the sky carries them west but they fall behind it (I.25–26). 2. 1,577,917,828: the sidereal days minus the Sun's revolutions (I.37, 39). 3. √10 ≈ 3.162. 4. Avanti (Ujjain) (I.62). 5. West (I.64).