Page 25 - Guidelines for Training/ Orientation of Faculty on IKS

Guidelines for Training/ Orientation of Faculty on IKS

Course 6: Basics of Indian Astronomy
1. Introduction
 The science of Astronomy. Astronomy as one of earliest sciences; observational
astronomy in the Vedic corpus. Emergence of Jyotiḥśāstra encompassing the three
skandhas of Gaṇita (Astronomy), Horā (Horoscopic Astrology and Saṃhitā (Omens and
Natural Phenomena). The purpose of Astronomy—as stated in the texts. Contents of a
typical Indian astronomical Siddhānta text. Broad classification of the texts in Indian
astronomy. Names of some of the prominent astronomers and their important
contributions. Highlight the continuity of the Indian astronomical tradition (1400 BCE –
19th cent CE).
2. The different units of time discussed in the texts
 Brief introduction to the concept of time (approach of physics and philosophy). Quote
from Bhāskara I’s commentary at the beginning of Kālakriyā; also quote the verse in the
famous text Sūryasiddhānta. Recount the currently used units of time—duration of year,
month, week, etc. in the Gregorian calendrical system—subtly point out that they do not
have any astronomical basis whatsoever. Introduce the different shorter units of time
discussed in Indian astronomical texts year, month, fortnight, tithi, etc. Introduce larger
units or time like yuga, mahāyuga, manvantara and kalpa.
3. Systems employed for representing numbers
 Highlight the need for having different systems for representing numbers in those days.
Explain the three systems adopted - Bhūtasaṅkhyā, Kaṭapayādi and
Āryabhaṭīyapaddhati. With illustrative examples, bring out their beauty and ingenuity.
Briefly discuss the advantages in each of these systems.
4. Spherical trigonometry
 Introduce the notion of shortest path on a non-Euclidean surface. Definition of great
circle, small circle, spherical triangle, etc. Their illustration using the Earth as an
example, which the students will be familiar with. Compare and contrast the properties
of a spherical triangle with a planar triangle. Derive the cosine and sine formula from
‘first’ principles. Introduce the four-part formula. Work out a few illustrative problems
(such as distance travelled by a flight along the great circle arc, small circle arc, etc) that
would help visualise the circles on a sphere, as well as assimilate the application of the
formulae. Demonstrate how to derive the sine formula simply using the planar triangles,
and their projections inside the sphere.
5. Celestial Sphere
 The notion of celestial sphere and the need for its conception. The different coordinate
systems (horizontal, equatorial and ecliptic) employed. The range of the coordinates in
each of these systems. The advantages and disadvantages of one system over the other.
Some illustrative examples for converting one set of coordinates into another. Indian
names for the fundamental circles and the coordinates used in these systems.
6. What is Pañcāṅga?
 Division of the celestial sphere/ecliptic into 12 and 27 equal parts — rāśi and nakṣatra
division. Explain their significance by pointing out their basis; that is, they are connected
with the duration of 12 lunar months and the period of moon’s revolution around the
earth, and not introduced arbitrarily. Explain the five elements that constitute Pañcāṅga
– and also bring out their astronomical significance. Also point out that they are
essentially different units of time. Illustrate with numerical examples the computation of

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