Saturday, 8 September 2012

Titbits’ from ancient Indian Astronomy

Revolution of planets:

In a yuga1, the eastward revolutions of the sun are 43, 20,000 2; of the Moon 5, 77, 53,336; of the Earth 3 1,58,22,37,500; of the Saturn 1,46,564; of the Jupiter 3,64,224 of the Mars 22,96,824; of the Mercury and Venus, the same as those of the Sun; of the Moon’s apogee, 4,88,219; of the sighrocca of Mercury, 1,7937,020; of the sighrocca of Venus 70,22,388; of the sighrocca of the other planets. The same as those of the Sun; of the Moon’s ascending node in the opposite direction (i.e. westward), 2, 32,226.4.

These revolutions commenced at the beginning of the sign Aries on Wednesday at Sunrise at Lanka ( when it was the commencement of the current yuga 5) .

The Moon’s apogee is that point of the Moon’s orbit which is at the remotest distance from the Earth and the Moon’s ascending node is that point of the ecliptic where the Moon crosses it in its northward motion.

The sighroccas of Mercury and Venus are the imaginary bodies which are supposed to revolve around the Earth with the heliocentric mean angular velocities of Mercury and Venus respectively, their directions from the Earth being always the same as those of the mean positions of Mercury and Venus from the Sun. It will thus mean that the revolutions of Mars, the sighrocca of Mercury, Jupiter, the sighrocca of Venus and Saturn given above are equal to the revolutions of Mars, Mercury, Jupiter, Venus and Saturn respectively round the sun.

The following table gives the revolutions of the Sun, The Moon and the planets along with their periods of one sidereal revolution. The sidereal periods according to the Greek Astronomer Ptolemy (AD circa 100 – circa 178) and the modern astronomers are also given for the sake of comparison.

Mean motion of planets                   sidereal period  in terms of days  planet  revolutions in
43,20,000 years                                            Aryabatta I          Ptolemy 6         Modern 7

SUN    43,20,000                                             365.25868           365.24666      365.25636

Moon   5,77,53,336                                           27.32167               27.32167       27.32166

Moon's Apogee    4,88,219                                3231.98708          3231.61655  3232.37543

Moon's asc. Node   2,32,226                               6794.74951         6796.45587     6793.39108

Mars                      22,96,824                              686.99974              686.94462       686.9797

Sighrocca of Mercury  1,79,37,020                        87.96988               87.96935             87.9693

Jupiter                              3,64,224                        4332.27217          4330.96064         4332.5887

Sighrocca of Venus              70,22,388                     224.69814              224.6989           224.7008

Saturn                                     1,46,564                    10766.06465       10749.94640        10759.201

The epoch of the planetary motion mentioned in the text marks the beginning of the current yuga and not the beginning of current Kalpa as was supposed by P.C. Sengupta. The current Kalpa according to Aryabatta I, started on Thursday 1,98,28,80,000 years or 7, 24,44,75,70,625 days before the beginning of the current Kaliyuga began on Friday, February 18, 3102 BC at sunrise at Linka (a hypothetical place on the equator where the meridian of Ujjain intersects it), which synchronised with the beginning of the light half of the lunar (synodic) month of Caitra or Chitra.
One thing that deservs special notice is the statement of the Earth’s rotations. Aryabatta I is perhaps, the earliest Astronomer in India who advanced the theory of the Earth’s rotation and gave the number of rotations that the Earth perfoms in a period of 43, 20,000 years. That period of one sidereal  rotation of the Earth according to Aryabatta I’s value is 23h56m 4s .1. The corresponding modern value is 23h 56m 4s.091. The accuracy of the Aryabatta I’s value is remarkable.

The final two parts of his Sanskrit magnum opus the Aryabhatiya, which were named the Kalakriya ("reckoning of time") and the Gola ("sphere"), state that the Earth is spherical and that its circumference is 4,967 yojanas, which in modern units is 39,968 km (24,835 mi), which is close to the current modern equatorial value of 40,075 km (24,901 mi).
Of the other Indian astronomers who upheld the theory of the Earht’s rotation mention may be made of Prthudaka (AD 860) and Makkibhatta (AD 1377). In the Skanda-Purana (, too, the Earth is described as revolviong like a Bhramarika (Spinning top/potter’s wheel / whirlpool).

The commentators of the Aryabhatiya, who hold the opinion that the Earth is stationary, think that Aryabatta I states the rotations of the Earth because the asterisms, which revolve westward around the earth by the force of the pro-vector wind, see that the Earth rotates eastward.

These commentators indeed were helpless because Aryabatta I’s theory of the Earth rotation received a severe blow at the hands if Varahamihira (d. AD 587) and Brahmagupta ( AD 628 ) whose arguments against this theory could not refuted by any Indian astronomer.

It is note worthy that the Greek astronomer Ptolemy, following Aristotle (384 – 322 BC), believed that the Earth was stationary and adduced arguments in support of his view.

  1. Yuga (Devanāgari: युग) in Hindu philosophy is the name of an 'epoch' or 'era' within a cycle of four ages. These are the Satya Yuga, the Treta Yuga, the Dvapara Yuga, and finally the Kali Yuga.
  2. Suppose to be a total period of kali yuga
  3. These are the rotations of the Earth eastward
  4. These very revolutions, excepting those of the Earth are stated in MBh. Vii. 1-5; LBh, i.9-14; and SiDvr, Grahaganitha. I, 3-6.
  5. Kali Yuga (Devanāgarī: कलियुग [kəli juɡə], lit. "age of [the demon] Kali", or "age of vice") is the last of the four stages the world goes through as part of the cycle of yugas described in the Indian scriptures. The other ages are Satya Yuga, Treta Yuga and Dvapara Yuga. The duration and chronological starting point in human history of Kali Yuga has given rise to different evaluations and interpretations. According to one of them, the Surya Siddhanta, Kali Yuga began at midnight (00:00) on 18 February 3102 BCE in the proleptic Julian calendar, or 23 January 3102 BC in the proleptic Gregorian calendar. This date is also considered by many Hindus to be the day that Krishna left Earth to return to his abode. Most interpreters of Hindu scriptures believe that Earth is currently in Kali Yuga. Many authorities such as Swami Sri Yukteswar, and Paramhansa Yogananda believe that it is now Dvapara Yuga. Many others like Aurbindo Ghosh have stated that Kali Yuga is now over. The Kali Yuga is sometimes thought to last 432,000 years, although other durations have been proposed.
  6. Taken from Bina Chatterjee, “The Khanda – Khadyaka of Brahmagupta “. World Press, Calcutta 1970 Vol 1, Appendix VII p 281.
  7. Taken from H.N. Russell, Dugan and J.Q. Stewart, Astronomy, Part 1: The Solar System, Revised editon, Ginn and Company, Boston, Appendix. Also The Sideral period of Moon’s apogee and ascending node are taken from P.C. Sengupta and N.C. Lahari’s introduction (P.xiv) to Babuaji Misra’s edition of Sripati Siddhanta sekhara.
  8. See W.M. Smart, Text book on Sperical Astronomy, Cambridge. 1940, p 420 & p 621 of Bharatiya Sastra Manjusha of M.S. Sreedharan

9. ( Sanskrit) ( both Sanskrit and Tamil months follow same line of calender days). The days are also similar to western days. Sunday to Saturday it same.
  1. Chaitra
  2. Vaishākha
  3. Jyaishtha
  4. Āshādha
  5. Shrāvana
  6. Bhaadra or, Bhādrapada
  7. Āshwini
  8. Kārtika
  9. Agrahayana or, Mārgashīrsha
  10. Pausha
  11. Māgha
  12. Phālguna
Tamil Calendar consists of 12 months starts with ‘Chithirai’ ends with ‘Panguni’.

It is a Solar Calendar, whose dates indicate the position of the earth on its revolution around the sun.
So the number of days varies between 29 and 32.
The following list compiles the months of the Tamil Calendar.

    Tamil                                 Gregorian Calendar equivalent        Western
1  Chithirai       mid-April to mid-May                                                           Aries
2  Vaikasi        mid-May to mid-June                                                           Taurus 
3  Aani           mid-June to mid-July                                                            Gemini
4  Aadi             mid-July to mid-August                                                      Cancer
5  Aavani       mid-August to mid-September                                            Leo
6  Puratasi    mid-September to mid-October                                             Virgo
7  Aippasi     mid-October to mid-November                                            Libra
8  Karthikai  mid-November to mid-December                                         Scorpio
9 Markazhi      mid-December to mid-January                                         Sagittarius
10 Thai        mid-January to mid-February                                              Capricorn
11 Masi      mid-February to mid-March                                                    Aquarius
12 Pankuni   mid-March to mid-April                                                       Pisces

Sunday - Nayiru or ravi var or Solar day
Monday - Thingal or somavar or Moon's day
Tuesday - Sevvai  or mangalvar or Mars day
Wednesday - Bhudan or budhvar or  Mercury day
Thursday - Vizayan or Birgaspathi var or guruvar or Jupiter day
Friday - Velli or Sukkravar or Venus day
Saturday - Sani / kari or Sani var or Saturn day

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