Celestial sphere

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The celestial sphere is an imaginary sphere of arbitrarily large radius, concentric with the Earth and rotating upon the same axis. All objects in the sky can be thought of as projected upon the celestial sphere. [1]

Many early Indian astronomers distinguished the 'Khagola' (sphere of the sky, celestial sphere) from the Bhagola (sphere of the asterisms, or stars). For example, Lalla in his description of an armillary sphere instrument. [2]

Features

The early Indian astronomers created names for the features of the celestial sphere.

Features of the celestial sphere
English Sanskrit description references
Zenith The direction directly above the observer's head
Nadir The opposite of the Zenith (the direction straight down from the observer)
Meridian Yāmyottara-vṛtta A great circle going through the North and South celestial poles, and the observer. [3]
Prime Meridian - The meridian at which longitude is considered 0 degrees [4]
Prime Vertical Samamaṇḍala A great circle going through the North and South celestial poles, and the east-west points of the horizon, at a right angle to the Meridian [3][5]
Horizon Kṣitija A plane stretching out from the observer, perpendiculuar to the Zenith and Nadir [3]
Celestial Equator Vāyugola / Visuvaṇṃandala the Earth's Equator projected outwards onto the celestial sphere [6]
Celestial Poles The North Pole and South Pole of the Earth, projected onto the celestial sphere
Ecliptic Apakrama-vṛtta
Apama-vṛtta
The great circle formed by the apparent path of the Sun on the celestial sphere. [7][8]
Celestial latitude viksepa Latitude on the celestial sphere [9]
- dṛñmaṇḍala great circle vertical to observer, passes through planet [10]
- dṛkkṣepavṛtta vertical circle thru ecliptic 3-signs behind ecliptics rising point [10]
line of rising and setting Astodaya-sūtra joins rising point and setting point, goes east-west [11]
east or west point svastika [11]
sine amplitude arkāgrā [11]
sine declination krāntijyā jyā of the arc between sun and svastika [11]
altitude bhujā - [11]
diurnal circle dyuvṛtta circle of sun's position [11]
- kṣitijyā arc of dyuvṛtta between horizon and unmaṇḍala [11]
Solstiital Colure Dakṣiṇottara a north-south circle [8]
Equinoctial celestial equator Ghaṭikāmaṇḍala perpendicular to Dakṣiṇottara [8]
Equinoctial colure - perpendicular to Ghaṭikāmaṇḍala and Dakṣiṇottara [8]
- svastika 4 crosses made by the equinoctial colure, at the 'cardinal points' [8]
- viṣuvad circles 3 great circles: Equinoctial colure, Ghaṭikāmaṇḍala, and Dakṣiṇottara [8]

The Sphere along the ecliptic was in earlier times divided into 27 asterisms, called Nakṣatras. Later on the 12 signs of the Zodiac were adopted, and given the name of the rāśis.

The prime meridian (longitude 0) went through the real city of Ujjain, the mythical city of Laṅkā,[12][13][14] and a number of other cities as well. [15]

The astronomer Lalla, in his Template:Ref-SiDhVr, gives a 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 also discusses calculations of the latitudes. [16] Many other astronomers gave similar pictures of how the heavens might appear the different inhabitants of the Earth at different times of the day or year. [17]

Pṛthūdaka-svāmi, Makkibhaṭṭa, and Āryabhaṭa I postulated a rotating Earth causing the apparent movement of the stars. [18][19][20][21] This notion was rejected by others because the Vedas had described the Earth as fixed. [22][23]

Kamalākara wrote that the Pole Star was not fixed. [24]

Size

Size of star sphere (in yojana)
Source Distance
to Earth
Circumference
Nīlakaṇṭha[25] 60 * Sun's orbit -
Bhāskara I[26] revolutions of the moon in a yuga / 10 * 32,40,000 -
Bhāskara II[27] - 18,71,20,69,20,00,00,000


Size of circle of sky (in yojana)
Source Distance
to Earth
Circumference
Vaṭeśvara[28] - 1,24,74,72,05,76,000

Arrangement of the planets

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, from highest to lowest:[29][30][31]

  • Stars, Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon, Earth

Āryabhaṭa says the Earth is at the end, "like a hitching peg". [31]

Nīlakaṇṭha wrote a great deal on the arrangement of the heavens in his Golasāra. The Earth he viewed as 'down' from everywhere. The atmosphere went up so far, and then the Pravaha winds blew the stars around the Earth, 21,600 arcminutes around each day. The ecliptic was divided into 30° sections called rāśis. He also discusses several great circles of the sphere, including the Ghaṭikā-maṇḍala, the Unmaṇḍala, and the Samamaṇḍala. Also described are the Lagna, epicycles, the equation of center, higher apsis, etc. He also mentions the planets' Śīgha circles and Manda circles. [7]

Details of motion can be found in the article on the planets.

Earth centered vs sun centered

The Celestial Sphere model of the solar system, being geocentric, differs greatly from the modern sun-centered model. However, many of the ideas and methods apply to both systems. For example, the ecliptic plane in the sun-centered model is the orbit of the Earth around the sun. In the Earth-centered model, it is the orbit of the Sun around the Earth. Both of these orbits define the exact same plane, regardless of the viewpoint used as the center, or what name the plane is called by. [32]

See Also

References

  1. Based on the article: Celestial sphere from wikipedia
  2. Template:Refia8.6.2
  3. 3.0 3.1 3.2 Template:Ref-indian-astronomy, p. XXXI
  4. The modern prime meridian is at Greenwich, England. This happened in the late 1800s/early 1900s. See Template:Ref-millar
  5. Template:Refia8.3.1
  6. Template:Refia4.24.2
  7. 7.0 7.1 Template:Refia4.16.1
  8. 8.0 8.1 8.2 8.3 8.4 8.5 Template:Refia8.2.1
  9. Template:Refia, p 34, including footnotes
  10. 10.0 10.1 Template:Refia4.23.1
  11. 11.0 11.1 11.2 11.3 11.4 11.5 11.6 Template:Refia4.25.1
  12. Template:Refia4.5.2
  13. Template:Ref-indian-astronomy, APPENDIX IV
  14. Template:Refia4.3.2
  15. See the article on Earth
  16. Template:Refia4.3.1
  17. See Template:Refia, sections 4.1, 4.2, 4.3
  18. Template:Refia4.9.2
  19. Template:Refia4.9.3
  20. Template:Refia4.9.4
  21. Template:Refia4.9.5
  22. Template:Refia4.9.6
  23. For a discussion of Āryabhaṭa's theory and the reaction of others, plase see footnote of pg 26 of Template:Refia
  24. Template:Refia4.13.5
  25. Template:Refia4.26.1
  26. Template:Refia4.27.1
  27. Template:Refia4.28.1
  28. Template:Refia7.14.2
  29. Template:Refia4.15.1
  30. Template:Refia4.15.2
  31. 31.0 31.1 Template:Refia4.17.1
  32. The Path of the Sun, the Ecliptic nasa.gov, via www-istp.gsfc.nasa.gov on 2011 02 09