Page 27 - Guidelines for Training/ Orientation of Faculty on IKS

6. 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.

7. 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.

8. 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.

9. 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).

10. 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.

11. 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.

12. 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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Guidelines for Incorporating Indian Knowledge in Higher Education Curricula