Page 29 - Guidelines for Training/ Orientation of Faculty on IKS

Guidelines for Training/ Orientation of Faculty on IKS

SEMESTER II
1. Planetary longitudes and latitudes and Nīlakaṇṭha Somayājī’s revised planetary model
 True longitudes of planets: Manda and Śīghra corrections in detail. Geometrical
description. Comparison with Kepler’s model. Latitudes of planets.
 Nīlakaṇṭha Somayājī’s revision of the planetary model: Nīlakaṇṭha’s analysis of the
motion of the interior planets (Mercury and Venus). His geometrical model which is
geometrically similar to the Tycho Brahe model (planets moving around the Sun which
itself orbits the Earth), but computationally approximates the Kepler model.
2. Rates of motion of planets
 Idea of derivative in finding the Mandagatiphala (manda-correction to the mean rate of
motion). The correct formula due to Nīlakaṇṭha. True rates of motion of planets: Correct
expression due to Bhāskara. Application to calculate retrograde motion of planets.
3. Tripraśna topics
 Latitudinal triangles (of Bhāskara) and applications. Agrajyā or the distance between
rising-setting line and the east-west line. Correction to the east-west line due to change in
Sun’s declination. Zenith distance in terms of the declination, hour angle and latitude (cos
z = sin φ sin δ + cos φ cos δ cos H). Derivation of this formula as in Siddhāntaśiromaṇi.
Relation among Śaṅkutala (Śaṅkvagra), Bhujā, Agrajyā and its applications.
4. Rising times of Rāśis and finding Lagna
 Relation between the right ascension and longitude and rising times of rāśis at the
equator. Rising times at an arbitrary latitude. Finding the Lagna at any instant after
Sunrise (approximate).
5. Eclipse calculations
 Details of calculations of the middle of a lunar eclipse and half-durations iteratively,
using the correct expression for the rate of motion of the Moon. Parallax and the
calculation of the middle of a solar eclipse.
6. The Vākya system
 Longitude of the Sun from the ‘subtractive minutes’ at any time (‘Bhūpajña etc. vākyas).
Vākyas for zodiacal transit times (‘Śrīrguṇamitra’ etc.). Longitude of the Moon using
the Candravākyas (‘gīrnaśreyaḥ’ etc). More accurate values due to Mādhava.
7. Astronomical Instruments
 Gnomon . Cakra and Dhanur yantras for measuring the zenith distance of the Sun.
Approximate and exact times from a ‘yaṣṭi’. Phalakayantra to measure the hour angle.
Equatorial sundial to measure time. Clepsydra for measuring time. Celestial globe and
Armillary sphere for explaining celestial coordinates and various circles.
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8. Indian Astronomy in the 18 and 19 centiries
 Astronomical endeavours of Savai Jayasiṃha. Samrat-yantra and other instruments in the
observatories of Jayasiṃha. European observers on the simplicity and accuracy of Indian
eclipse computations. The work of Śaṅkaravarman and Candraśekhara Sāmanta. Efforts to
update the Indian calendar.

References
1. M. S. Sriram, Man and the Universe- An elementary account of Indian Astronomy,
(Unpublished 1993).
2. M. S. Sriram, Elements of Indian astronomy- 5 Lectures, Instructional Course on Indian
Sciences, Prof. K.V. Sarma Research Foundation, 2019.

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