Understanding astronomy through verses, prose and phrases

Transcription

1 Understanding astronomy through verses, prose and phrases Venketeswara Pai R Indian Institute of Science Education and Research Pune INSA-AGM IISER Pune December 27, 2017

2 Research Focus Field of Specialization and mode of Research History and Development of Astronomy and Mathematics in India from 12th to 17th centuary AD Deciphering the manuscripts pertaining to Astronomy/Mathematics Editing, and Translating/decoding the contents Critical study of the text Preparing the detailed mathematical notes in terms of modern mathematical parameters/notation Comparing the algorithms and results with modern ones 2

3 Indian Astronomical literature Evolution from Siddhāntik to Karaṇa School The huge corpus of astronomical literature that has been produced in India from the time of Āryabhaṭa (c 499 CE) is generally divided into Siddhāntas, Tantras, Karaṇas and Vākyas, in decreasing order of the theoretical contents Astronomical parameters given in Siddha ntik texts are very large Complex and lengthy computational algorithms are employed in finding the planetary longitudes and other astronomical quantities Hence evolved a new school of astronomy which is known as Karaṇa school The epoch is chosen to a closer date and observed planetary longitudes documented Astronomical parameters are made smaller in magnitude Karaṇa texts describes the simplfied algorithms and the mathematical equations are modified for computational ease 3

4 Instantaneous velocity in Siddhāntaśiromaṇi 4 dθ dt dθ 0 dt r 0 R R cos(m)dm dt θ θ 0 r 0 R R sin(m)

5 Instantaneous velocity in Siddhāntaśiromaṇi 5 dθ dt dθ 0 dt r 0 R R cos(m)dm dt θ θ 0 r 0 R R sin(m)

6 Instantaneous velocity in Siddhāntaśiromaṇi 6 dθ dt dθ 0 dt r 0 R R cos(m)dm dt θ θ 0 r 0 R R sin(m)

7 Instantaneous velocity in Siddhāntaśiromaṇi 7 dθ dt dθ 0 dt r 0 R R cos(m)dm dt θ θ 0 r 0 R R sin(m)

8 Rationale in prose

9 Rationale in prose

10 Geometrical construction from the Commentary 10 P1 T 1 P T 2 2 X Ψ s Ψ + Μ Ks Μt S Μ s P 10 P 20 E

11 Vākya system of Astronomy The term Vākya literally means a sentence consisting of one or more words In the context of astronomy, it refers to a phrase or a string of letters in which numerical values associated with various astronomical parameters are encoded The vākyas are composed using the kaṭapayādi system of numerations The strings used in composing vākyas are chosen so that they not only represent numerical values, but are also in the form of beautiful meaningful phrases and sentences that convey worldly wisdom and moral values

12 Vākya system of Astronomy 12 The term Vākya literally means a sentence consisting of one or more words In the context of astronomy, it refers to a phrase or a string of letters in which numerical values associated with various astronomical parameters are encoded The vākyas are composed using the kaṭapayādi system of numerations The strings used in composing vākyas are chosen so that they not only represent numerical values, but are also in the form of beautiful meaningful phrases and sentences that convey worldly wisdom and moral values

13 Vākya system of Astronomy 13 The term Vākya literally means a sentence consisting of one or more words In the context of astronomy, it refers to a phrase or a string of letters in which numerical values associated with various astronomical parameters are encoded The vākyas are composed using the kaṭapayādi system of numerations The strings used in composing vākyas are chosen so that they not only represent numerical values, but are also in the form of beautiful meaningful phrases and sentences that convey worldly wisdom and moral values

14 Vākya system of Astronomy 14 The term Vākya literally means a sentence consisting of one or more words In the context of astronomy, it refers to a phrase or a string of letters in which numerical values associated with various astronomical parameters are encoded The vākyas are composed using the kaṭapayādi system of numerations The strings used in composing vākyas are chosen so that they not only represent numerical values, but are also in the form of beautiful meaningful phrases and sentences that convey worldly wisdom and moral values

15 Vākya system of Astronomy 15 The term Vākya literally means a sentence consisting of one or more words In the context of astronomy, it refers to a phrase or a string of letters in which numerical values associated with various astronomical parameters are encoded The vākyas are composed using the kaṭapayādi system of numerations The strings used in composing vākyas are chosen so that they not only represent numerical values, but are also in the form of beautiful meaningful phrases and sentences that convey worldly wisdom and moral values

16 Candravākyas of Vararuci 16 No The Vākya The Numerical Value 1 gīrnaḥ śreyaḥ dhenavaḥ śrīḥ rudrastu namyaḥ rāmā gīyate atyāhārastu kaveḥ śakyam bhavet sukham The desired numerical value is coded in these vākyas using Kaṭapayādi system

17 Period of Moon s anomaly Significance of the khaṇḍa 17 Time axis ahargana khanda desired day Epoch The day at the end of khanda U (Moon s apogee) At Surise Moon Γ E Conjunction of Moon and its apogee at Sunrise

18 Candravākyas of Vararuci 18 No The Vākya The Numerical Value 1 gīrnaḥ śreyaḥ dhenavaḥ śrīḥ rudrastu namyaḥ rāmā gīyate atyāhārastu kaveḥ śakyam bhavet sukham The desired numerical value is coded in these vākyas using Kaṭapayādi system

19 Rate of anomaly of Moon 19 Application of Vallyupasaṃhāra or Continued fraction alpa-hārakas alpa-guṇakāras (H i ) (G i )

20 20 THANK YOU for your patience