Page 23 - Guidelines for Training/ Orientation of Faculty on IKS

1. 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.

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Guidelines for Incorporating Indian Knowledge in Higher Education Curricula