Page 26 - Guidelines for Training/ Orientation of Faculty on IKS

I. INTRODUCTION TO INDIAN ASTRONOMY

1. Preliminaries

Sky viewed as the inside of a hemisphere. Cardinal directions, zenith, horizon, pole star at any
location. Daily motion of celestial objects (Sun, Moon, planets, stars) and diurnal circles. Motion in
the stellar background. Ecliptic. Basic time units: Day, Month and Year. Celestial coordinates and
elementary spherical trigonometry. Cosine and Sine formulae. Horizontal (z,A), Equatorial (δ, α and
H), and Ecliptic (λ, β) systems. cos z = sin φ sin δ + cos φ cosδ cos H, and other relations. Planetary
positions.

2. Developments from the Vedic period up to the Siddhāntic period
Vedic Astronomy: Astronomical concepts in Vedic literature regarding Sun, Moon, Stars, Earth.
Months, seasons, year. 27 nakṣatras. Ecliptic and ayana. Planets, Comets etc. Pole star in an earlier

era. Nakṣatra division of the ecliptic and motion of the Sun along it in Vedāṅga Jyotiṣa (VJ) and
other texts. VJ calendar. VJ computations. Duration of a day. Better value for an year in Vedic
literature.

Siddhāntic astronomy: Earlier Siddhāntas and Pañcasiddhāntikā. Introduction of trigonometry,
Indian jyā–astronomy. Āryabhaṭīya . Mahāyuga. (Kalpa etc., and also smaller units of time can be
introduced at this stage). Revolution numbers of planets. Ahargaṇa and Mean longitudes, Examples.
Obtaining the true longitudes by applying corrections to mean longitudes.

Epicycle models: Manda correction (Equation of centre) in detail. Its significance. Latitude of Moon.

Śīghra correction to planets and its significance: Essential features only with the aid of diagrams and
final formulae. Latitudes of planets.

Precession of equinoxes— Nirayana and Sāyana longitudes.

Nature and organisation of texts. Sūtra (algorithmic) format. Siddhānta, Tantra, Karaṇa and Vākya
texts. Sāraṇis or Tables.

3. Indian Calendar
Pañcāṅga. Adhikamāsas. Solar and Luni-Solar systems.

4. Solar and Lunar Eclipses

Angular diameters of the Sun, Moon and Earth’s shadow. Possibility of eclipses. Finding the middle
of an eclipse by iteration. Amount of obscuration at any time.

5. Tripraśna Topics (Diurnal problems)

Description of the celestial spheres and various circles. Similarity to modern description.
Determination of the East-West directions. Derivation of the expression for the declination in terms
of the longitude. Shadow of a gnomon. Equinoctial day when the locus of the tip of the shadow is a
straight line. Finding the latitude. Mid-day shadow. Finding the declination. Relation between the
time and the shadow at an arbitrary instant (no derivation).

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