Aryabhata: the Aryabhatiya · Chapter 7 of 8

#The sphere of the heavens

The fourth and longest section of the Aryabhatiya, the Gola ("the sphere", 50 verses), describes the shape of the universe and the geometry needed to calculate what is seen in the sky.

#The ecliptic and the nodes (Gola 1–3)

• The half of the ecliptic from the start of Aries to the end of Virgo is north of the equator; from the start of Libra to the end of Pisces, south; both deviate equally from the equator (Gola 1).
• The Sun, the planets' nodes and the Moon's node move along the ecliptic, and the Earth's shadow moves along it 180° from the Sun (Gola 2).
• The Moon, and the planets, move north and south of the ecliptic from their nodes (Gola 3).

#Seeing the planets near the Sun (Gola 4–5)

• When the Moon has no latitude it becomes visible when 12° from the Sun; Venus at 9°; the other planets at greater distances (Gola 4). (Compare the Surya Siddhanta's distances for combustion.)
• Half of each sphere — Earth, planets, stars — is dark, and half, turned towards the Sun, is lit (Gola 5). That is why the Moon has phases.

#The round Earth (Gola 6–7)

The sphere of the Earth, being quite round, situated in the center of space, in the middle of the circle of asterisms, surrounded by the orbits of the planets, consists of water, earth, fire and air (Gola 6).

Just as a ball formed by a kadamba flower is surrounded on all sides by blossoms, just so the Earth is surrounded on all sides by all creatures, terrestrial and aquatic (Gola 7).

The image of the kadamba flower — a round ball covered with blossoms on every side — makes the point that people live all round the Earth, with no "underneath" from which they would fall.

#The rotating Earth (Gola 9–10)

As a man in a boat going forward sees a stationary object moving backward, just so at Lanka a man sees the stationary asterisms moving backward (westward) in a straight line (Gola 9).

This is the clearest statement that the daily turning of the sky is an appearance caused by the Earth's own rotation, as the shore seems to move to a person in a moving boat. It fits Dasagitika 1, which counts the Earth's rotations, and Dasagitika 4: "the Earth moves one minute in a prana".

The next verse, however, says: "the cause of their rising and setting is due to the fact that the circle of the asterisms, together with the planets, driven by the provector wind, constantly moves straight westward at Lanka" (Gola 10). Clark notes that the natural reading of verse 9 is the Earth's rotation, and that the commentators struggled with the two verses. Some read verse 10 as describing how things appear, others took it as Aryabhata's real view. Later Indian astronomers generally rejected the rotating Earth; the commentator Parameshvara tried to explain it away (Clark's notes).

#The traditional cosmology (Gola 8, 11–12, 16–17)

Beside these scientific statements, the Gola keeps parts of the traditional cosmology:

• the Earth grows by a yojana in a day of Brahma and shrinks by the same in a night of Brahma (Gola 8);
• Mount Meru, a yojana high, made of jewels, stands at the north pole, and Vadavamukha at the south; "the gods and the dwellers in hell both think constantly that the others are beneath them" (Gola 11–12);
• the gods on Meru see the Sun for half a year; the ancestors on the Moon for half a month; humans for half a day (Gola 16–17).

The last point is good astronomy dressed in myth: at the pole the Sun is indeed above the horizon for half the year, and on the Moon a "day" lasts about half a month.

#Places on the Earth (Gola 13–14)

Aryabhata places four cities 90° apart on the equator: "sunrise at Lanka is sunset at Siddhapura, midday at Yavakoti, and midnight at Romaka" (Gola 13). Lanka here is not Sri Lanka but an ideal point on the equator. Ujjain is due north of Lanka by 22½° (Gola 14) — the meridian of Ujjain became the prime meridian of Indian astronomy.

#Circles of the sky (Gola 18–21)

The observer's sky has the prime vertical (east–west through the zenith), the meridian (north–south), the horizon, the six o'clock circle on which the lengthening and shortening of day and night are measured, and the vertical circles through a planet and through the nonagesimal (Gola 18–21). These are the reference circles of spherical astronomy.

#The self-turning sphere (Gola 22–23)

A light wooden sphere should be made, round, and of equal weight in every part. By ingenuity one should cause it to revolve so as to keep pace with the progress of time by means of quicksilver, oil or water (Gola 22).

An armillary sphere turned by a water-driven mechanism — a model of the sky that keeps time. On its visible half the stars are marked using sines (Gola 23).

#Day length, altitude and shadows (Gola 24–36)

These verses give the trigonometry of the sphere:

• the radius of the Sun's day-circle at a given declination (Gola 24);
• the ascensional difference, which makes days longer in summer and shorter in winter (Gola 26);
• how long each quarter of the ecliptic takes to rise (Gola 27);
• the Sun's altitude at any time of day, and the length of the gnomon's shadow (Gola 28–32);
• the angles needed to correct the Moon's position for parallax and for its latitude (Gola 33–36).

These rules let an astronomer compute the time from a shadow, the shadow from the time, and the exact times of rising and setting — everything needed for the calendar and for casting a chart.

#Eclipses (Gola 37–47)

The final part of the Gola is a complete theory of eclipses.

• The cause (Gola 37): "The Moon obscures the Sun and the great shadow of the Earth obscures the Moon."
• When (Gola 38): when, at new moon, the Moon is near a node and "enters the Sun", or, at full moon, enters the Earth's shadow.
• The Earth's shadow (Gola 39–40): its length, from the sizes of the Earth and Sun and their distance, and its width at the Moon's distance — a cone of shadow tapering away from the Earth.
• The duration (Gola 41–42): half the duration of the eclipse, and of totality, from the sizes of the two discs and the Moon's latitude — using the overlapping-circles rule of Ganita 18.
• How much is covered (Gola 43–44) at any moment.
• The direction of the eclipse on the disc (Gola 45).
• The colours of the eclipsed Moon (Gola 46): smoky at the beginning, black when half covered, tawny when wholly covered, coppery-black at the middle.
• A solar eclipse of less than an eighth of the Sun's disc is not noticed, because of the Sun's brightness (Gola 47).

This is a fully physical account: no demon, only the bodies and their shadows. A generation later Varahamihira gave the same explanation and rejected the Rahu story outright (Brihat Samhita 5).

#The closing verses (Gola 48–50)

Aryabhata says his values were obtained from conjunctions: the Sun from the conjunction of the Earth and Sun, the Moon from that of the Sun and Moon, the other planets from their conjunctions with the Moon (Gola 48). Then the image of the jewel rescued from the ocean of true and false knowledge (Gola 49), and a warning that whoever disparages this science, "formerly revealed by Svayambhu and now described by me", loses his good deeds and long life (Gola 50).

#Summary

• The ecliptic's halves, the nodes and the Earth's shadow 180° from the Sun (Gola 1–3); visibility distances from the Sun; half of every sphere lit (Gola 4–5).
• The Earth is a round ball in the centre of space, peopled all round (Gola 6–7).
• The stars' daily motion is an appearance caused by the Earth's rotation, like the shore seen from a moving boat (Gola 9) — though Gola 10 speaks of a wind moving the stars, and later astronomers rejected the rotation.
• Traditional cosmology (Meru, the Earth growing in a day of Brahma) stands beside the scientific account (Gola 8, 11–17).
• Lanka on the equator, Ujjain 22½° north of it (Gola 13–14); the circles of the sky (Gola 18–21); a water-driven armillary sphere (Gola 22).
• Spherical astronomy: day length, rising times, altitude, shadows, parallax (Gola 24–36).
• Eclipses: the Moon covers the Sun, the Earth's shadow covers the Moon; with rules for timing, extent, direction and colour (Gola 37–47).

#Exercises

1. What image does Aryabhata use to show that people live all round the Earth?
2. Explain the moving-boat simile of Gola 9 in your own words.
3. Why do the gods on Meru see the Sun for half a year? Is there a real fact behind this?
4. What causes a lunar eclipse, according to Gola 37–38? When can it happen?
5. Why, according to Gola 47, is a small solar eclipse not noticed?

Answers: 1. A kadamba flower, a ball covered with blossoms on all sides (Gola 7). 2. A person in a moving boat sees the stationary shore move backwards; so the stars, which are stationary, seem to move west because the Earth turns east. 3. Because Meru is at the north pole, where the Sun is above the horizon for half the year — a real fact of polar day and night. 4. The Moon entering the Earth's shadow; at full moon, when the Moon is near a node. 5. Because the Sun is so bright that covering less than an eighth of it makes no visible difference.