Planets

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The planets, in old Indian Astronomy, are categorized as follows:[1]

Luminous planets:

Star planets (the Tārāgrahas[2])

Dark / Invisible planets (The lunar nodes)

Arrangement

Many astronomers gave an ordering of the heavens. Āryabhaṭa I's, Template:Ref-VM, and Template:Ref-par all wrote of the order of the heavens from highest to lowest, as follows:[3][4][5]

Size

Astronomers described the distances to the heavenly objects as follows:

Sizes of celestial objects (units in yojanas)
Source Earth Moon Mercury Venus Sun Mars Jupiter Saturn
Āryabhaṭa (diameters)[6] 1050 315 1/15 moon 1/5 moon 4410 1/25 moon 1/10 moon 1/20 moon

Motion

Vaṭeśvara described eight types of planetary motion. In the normal direction he broke it down into very fast, fast, mean, slow, and very slow. He also described retrograde, very retrograde, and re-retrograde motion. [7]

Lalla described 6 types: Normal (east), retrograde (west), declination (to the north or the south), and finally two speeds: slow, when above mean orbit, and fast when below. [8]

Āryabhaṭa I mentioned the north-south movement of the planets. [9]

Epicycle

The planets sometimes appear to move 'backwards' (retrograde) against the background of the distant stars. This was explained in many civilizations by the concept of an 'epicycle', for example Ptolemy, circa 200 AD. [10]

Kuppanna Sastry postulates the independent Indian discovery of the epicyclic / eccentric model. Part of his reasoning is that the Romaka Siddhānta and Pauliśa Siddhānta were 'clearly western' and did not contain these theories. [11]

Vedic astronomers also used the concept of an epicycle to explain the planetary motions. See for example, Nīlakaṇṭha's Template:Ref-SiDar, which describes śīghra and manda cycles, the pratimaṇḍala (eccentric) and kaksyā-maṇḍala (orbital) circles, ucca and nica (upper and lower) circles, jñātabhoga-vṛtta (eccentric) and jñeyabhoga-vṛtta (orbital) circles. He also describes how doḥ-bhuja and koṭi-bhuja are used to measure the position of the planets. [12][13]

Āryabhaṭa I described the kaksyā-maṇḍala and prati-maṇḍala circles as well. He also mentions the śighroccas, the ucca, describes the epicycles, and says that the mean planet is at the center of the planet's epicycle. [14]

Lalla also describes the epicycle. He describes the kakṣāvṛtta (orbit of the planet), antyaphalajyā (jyā of maximum correction), the kendra-vṛtta (eccentric circle), nīcoccavṛta (epicycle), ucca (apogee), nīca (perigee), mandocca (apogee of manda), the śīghrocca ("apogee of quick motion"), the mean planet vs the true motion, the anomaly, the phala (or correction - the distance from the true planet to the mean planet), using jyā (sine) and cosine to calculate correction, the koṭīphala, the koṭī, the karṇa (distance from the center of the earth to the true planet, aka hypotenuse), and bāhujyā (the jyā of the anomaly, the distance between the planet and the line through apogee & perigee) [15]

Nīlakaṇṭha did as well, in his Golasāra. He discusses the Lagna, epicycles, the equation of center, higher apsis, etc. He also mentions the planets' Śīgha circles and Manda circles. [16]

See Also

References

  1. Template:Refia13.1.1
  2. Template:Refia2.4.1
  3. Template:Refia4.15.1
  4. Template:Refia4.15.2
  5. Template:Refia4.17.1
  6. Template:Refia4.20.2
  7. Template:Refias
  8. Template:Refia4.17.2
  9. {{refias|4.24.1|AB|ABh|4.1-3|KSS
  10. Template:Ref-indian-astronomy, pgs. xxxi-xxxii
  11. Indian Journal of History of Science, 9 (1974), 37-41, as cited in Template:Refia, pgs. xxxii-xxxiii
  12. Template:Refia4.18.1
  13. Template:Refia4.19.1
  14. Template:Refia4.19.2
  15. Template:Refia4.19.3
  16. Template:Refia4.16.1