Karmic Astrology—a Study
by Sunita Anant Chavan | 2017 | 68,707 words
This page relates ‘Ganita of the Siddhanta Period’ of the study on Karmic Astrology and its presentation in Vedic and the later Sanskrit literature. Astrology (in Sanskrit: Jyotish-shastra) is based upon perceptive natural phenomenon of cosmic light forms while the Concept of Karman basically means “action according to Vedic injunction” such as the performance of meritorious sacrificial work.
Part 2.2.6 - Gaṇita of the Siddhānta Period
[Full title: Classification of Jyotiḥśāstra (2): Gaṇita of the Siddhānta Period]
The advent of the Siddhāntas bifurcate the Gaṇita branch of Jyotiḥśāstra into pre-scientific and scientific period.[1] Gaṇita branch is also termed as the Siddhānta branch. Siddhāntas chiefly dealt with the study of planetary phenomenon. The study rest on independent Indian observations and refute any supposed Greek influence.[2]
a. Characteristics of a Siddhānta
Siddhāntas deal with topics related to physical Astronomy, with the calculations related to the mean and true longitudes of Planets and the difference between them at a certain point of time.[3] Bhaskarācārya[4] characterizes a Siddhānta specifying that Siddhānta must deal with enumerations of the units of time from truṭi to the end of the pralaya. Thereby Siddhānta and Tantra deal with planetary calculations, cosmogony and calculations of units of time.
Siddhāntas work on planetary calculations beginning from a Kalpa, the Tantra texts calculate from a Mahāyuga and Karaṇa[5] texts on the mean motions of planets in a given epoch close to the date of their composition.
b. Schools of Siddhāntas
The Siddhānta works differed amongst themselves in calculation related to the length of the year and the calculation related to the motion of planets in a Kalpa or a Mahāyuga. This difference gave rise to three main schools of Astronomy, the Saurya, the Ārya and the Brahma.[6]
The features which differentiated one school (Pakṣa) from another were the choice of subdivisions of the Kalpa and the number of rotations of each of the planets within the Kalpa or the Mahāyuga.
c. The Peculiarities of the Siddhāntas
The Paitāmaha Siddhānta[7] is later and closer to Vedāṅga Jyotiṣa[8] where as the Vasiṣṭha Siddhānta in PS (Pañcasiddhāntikā) mentions the concept of lagna somewhat similar to the present one[9] Sūrya Siddhāṇṭa in the PS is the most clear of the five (4th Āryā) and Romaka which is the latest of the PS matches in year length with Hipparchus[10] and does not mention the pattern of Yuga.[11] Āryabhaṭīya or Āryasiddhānta is the oldest of the Pauruṣa Siddhāntas and the most independent one. It includes both Astronomy as well as Mathematics.
Āryasiddhānta refers to the diurnal rotation as a rotation of the Earth (in the first part named Daśagītikā. 3 and also in Golapāda 9 and 10). The concept of motion to the Earth was an innovation in comparison to the traditional ideas of Earth believed to be a fixed sphere placed at the centre of the universe around which the whole world including the heavenly bodies revolved.
Siddhāntas deal with calculations of Ahargaṇa (the number of days lapsed since cpoch), it also includes the calculations of the number of years, the intercalary months and also the tithis (omitted) in a Yuga. The Romaka[12] specifies the method of calculating an Ahargaṇa. Pauliṣa almost matches with Romaka in Ahargaṇa (Pañcasiddhāntikā I. 10)
The motion of the planets was determined in relation with the Nakṣatras which move faster than the planets. Thereby the planets appear to move from west to East. Jyotiḥśāstra deals with this Eastward motion of planets which is in a relative scale with reference to the Nakṣatras. The Sūrya Siddhānta[13] comments on this relatively lacking behind and thus eastward daily motion of planets.
The Siddhāntas also talk about the cause of the motion of planets and Nakṣatras due to a wind named Pravaha[14]
The Siddhāṇṭas also work on the pole star Dhruva and its distance from various places on earth.
In the initial stage of the Siddhāntas, Gaṇita appears in an intermingled form with Astrology[15] which later bifurcated on an advancement in the Gaṇita branch and Astrology came to be a topic dealt with the other two branches.
Footnotes and references:
[1]:
Siddhāntaprākkāla and Jyotiḥsiddhāntakāla Bhāratīya Jyotiṣaśāstra. P.11. 67
[2]:
[3]:
Bhāratīya Jyotiṣaśāstra, p. 185.
[4]:
Siddhānta Shiromaṇi I. 6.
[5]:
[6]:
Pingree mentions five schools the other two being Ardharātrika (= Āryapakṣa) and Ganeṣa. Jyotiḥśāstra p. 13,14.
[7]:
Paitāmahasiddhānta in Varāhas Pañcasiddhāntikā (12.1-5) is the oldest amongst the Prācinsiddhāntapañcaka and relates it to the Brahmasiddhānta referred or mentioned by Brahmagupta in his Siddhānta (I-2) Bhāratīya Jyotiṣaśāstra, p. 152. Pingree, Jyotiḥśāstra p.17 differs as Paitāmahasiddhānta incorporated in the Viṣṇudharmottara is according to him the earliest. A third Paitāmaha or Brahmasiddhānta is related to Śākalyasaṃhitā Bhāratīya Jyotiṣaśāstra p.151. The Prācinsiddhāntapañcaka are mentioned in Varāhas Pañcasiddhāntikā. These are non-extant and composed before the Śaka era. According to Thibaut they are composed around 400 A.D. Bhāratiya Jyotiṣaśāstra p.160. the Prācinsiddhāntapañcaka, the modern five viz. Sūrya, Soma, Vasiṣṭha, Romaśa and Brahmasiddhānta (in Śākalya Saṃhitā) and Brahmasiddhānta (Paitāmahasiddhānta) in Viṣṇudharmottara are Apauruṣeya. Bhārtīya Jyotiṣaśāstra p.169.
[8]:
[9]:
Bhāratīya Jyotiṣaśāstra, p. 151.
[11]:
For which accused by Brahmagupta. While the other Romaka by Sriṣena mentions Yuga. (11.55).
[12]:
Romaka Siddhānta I. 1 (Pañcasiddhāntikā verse 8)
[13]:
Sūrya Siddhānta (Madhyamādhikāra verse 25).
[14]:
Sūrya Siddhāanta II. 3, Hindu Astronomy, p. 85.
[15]:
Paitāmahasiddhānta chap. I and II deal with Astrology, Jyotiḥśāstra, p. 17.; such a composite form is also displayed in Śārdulakarṇāvdāna, a divination text in its chap. 33 (Divyāvadāna) which deals with Astronomy. Jyotiḥśāstra,, p. 10.