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Astronomy

Brahmagupta directed a great deal of criticism towards the work of rival astronomers, and his Brāhmasphuṭasiddhānta displays one of the earliest schisms among Indian mathematicians. The division was primarily about the application of mathematics to the physical world, rather than about the mathematics itself. In Brahmagupta's case, the disagreements stemmed largely from the choice of astronomical parameters and theories. Critiques of rival theories appear throughout the first ten astronomical chapters and the eleventh chapter is entirely devoted to criticism of these theories, although no criticisms appear in the twelfth and eighteenth chapters.

In chapter seven of his Brāhmasphuṭasiddhānta, entitled Lunar Crescent, Brahmagupta rebuts the idea that the Moon is farther from the Earth than the Sun. He does this by explaining the illumination of the Moon by the Sun.

1. If the moon were above the sun, how would the power of waxing and waning, etc., be produced from calculation of the longitude of the moon? The near half would always be bright.

2. In the same way that the half seen by the sun of a pot standing in sunlight is bright, and the unseen half dark, so is of the moon beneath the sun.

3. The brightness is increased in the direction of the sun. At the end of a bright half-month, the near half is bright and the far half dark. Hence, the elevation of the horns from calculation.

He explains that since the Moon is closer to the Earth than the Sun, the degree of the illuminated part of the Moon depends on the relative positions of the Sun and the Moon, and this can be computed from the size of the angle between the two bodies.

Further work exploring the longitudes of the planets, diurnal rotation, lunar and solar eclipses, risings and settings, the moon's crescent and conjunctions of the planets, are discussed in his treatise Khandakhadyaka.