Lalla

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Lalla was an early Indian astronomer.

He wrote the Template:Ref-SiDhVr. It contains an extensive discussion of matters regarding the Celestial Sphere. He discusses how it appears to the residents of the South Pole (demons) and the residents of the North Pole (gods), what would happen if they walked towards the equator, and how they see the sun. He discusses calculations of the latitudes. [1] He also mentioned many of the ideas of the Purāṇas that contemporary astronomers did not agree with, such as the earth being flat, infinite, riding on an animal, having two suns and moons, the sun being in front of the moon, the earth floating on water, riding on a tortoise, the eclipses being a monster Rāhu, etc etc. [2] He goes on to make several logical arguments against these notions, using counter-examples &c. [3]

He also disupted notions of eclipses, using the concept of parallax. One was that Rāhu was the cause of eclipses. Rāhu he describes as the decapitated head of a demon who had been 'drinking the nectar' when Hari chopped it off. Due to a boon of Brahmā, his decapitated, floating head shows up on new-moon and full-moon days and eats the sun. Or the moon. Depending. Lalla also describes the theory of a snake eating the sun and moon. [4]

He also criticizes the theory of a 'moving earth', including Āryabhaṭa's rotating earth theory. He makes several arguments against both theories. Of the latter, he asks why arrows shot up do not fall to the west, and why clouds move the way they do.[5]

Celestial sphere

Lalla's celestial sphere [6][7]
Samamaṇḍala prime vertical great circle through E-W points of horizon
yāmyottaramaṇḍala meridian great circle through N-W points of horizon
koṇamaṇḍala NE/SW-NW/SE long. great circles of loingitude going at 45°/135°
kṣitija horizon where the planets rise and set
unmaṇḍala 6oclock circle through two points where samamaṇḍala meets the celestial equator and kṣitija, goes near poles, shows increase/decrease in day/night lengths.
viṣuvadvṛtta / nāḍīvṛtta celestial equator sphere of fixed stars, below celestial sphere, split into 60 nāḍi/ghaṭikā
Bhagola starry sphere where the nakṣatras are
dhruvayaṣti polar axis line thru N & S poles
apamaṇḍala ecliptic path of planets. intersects equator at points in aries / libra
vikṣepamaṇḍala half orbit orbit of a planet after it goes north of ecliptic plane.

Armillary sphere

Lalla's armillary sphere[8][9]
madhyajyāvṛtta meridian
madhyalagna merdiain ecliptic point
ḍṛṇmaṇḍala above the madhyalagna, where planet is seen
dṛggatijivāvalaya ahead of the madhyalagna
agrā amplitude, measured on celestial horizon
kujyā Earth-sine
lagna orient ecliptic point - where the ecliptic meets the eastern horizon.
astalagna setting ecliptic point - like lagna, but western horizon
śaṅku altitude of Sun above eastern or western horizon
samaśaṅku jyā of the Sun when it is on the prime vertical
koṇaśaṅku jyā altitude of sun on koṇamaṇḍala (intermediate vertical circle)
dyudalaśaṅku śaṅku at midday, north & south horizon points are equal distance from Sun
natajyā jyā of the arc from zenith to sun (when sun is on meridian)
dṛgjyā distance between earth center and 'the foot' of jyā altitude
trijya line from zenith to lines-of-direction intersection (aka radius / hypotenuse)
line from top of ko-jyā latitude to lines-of-direction intersection
nati latitudinal parallax
lambana longitudinal parallax
Bhagola Sphere of the asterisms
Khagola Sphere of the sky, celestial sphere (outside the Bhagola)

Each of the 7 planets gets a set of the following:[8]

Each of the 5 star-planets gets:

The moon also gets a vimaṇḍala

12 instruments of astronomy

In Template:Ref-SiDhVr, Lalla describes his "twelve instruments of astronomy". They were:

He also listed 'accessories' needed to use the instruments: [10]

References

  1. Template:Refia-expand-title
  2. Template:Refia5.2.1
  3. See all of section 5, Template:Refia
  4. Template:Refia5.13.1
  5. See all of section 5, Template:Refia, Lalla's work translated by Template:Ref-BC.
  6. Template:Refia8.3.1
  7. Template:Refia8.4.1
  8. 8.0 8.1 Template:Refia8.6.1
  9. Template:Refia8.6.2
  10. Template:Refia10.1.2