Tracing Chãyã and Bimba: Mathematical Harmony of Indian Eclipse Computations and Modern Astronomy

Abstract

Eclipses are the natural phenomena occurring periodically. In modern astronomy
i.e., after Kepler and Newton, an eclipse is a syzygy that is a straight-line configuration
of three heavenly bodies in a gravitational system. In this phenomenon the participating
three heavenly bodies are the Sun, the Earth and the Moon. By definition, the times of
New Moon, First Quarter, Full Moon, and the Last Quarter are excess of the apparent
geocentric longitude of the Moon over the apparent geocentric longitude of the Sun is 0
0
,
900
, 1800
, and 2700
respectively. To calculate timings of the lunar eclipse, here we used
the algorithms based on the phases of the Moon. In Indian classical astronomy texts,
the computation of lunar eclipse is given based on the positions of the Sun and the Moon
and with their true daily motions. In modern astronomy the gravitational parameters
are also involved for calculations. The algorithms of both Indian and modern methods
are discussed using mathematical software Scilab and compared these results NASA
data. In this paper we discussed Improved Siddhantic Procedure of Indian method and
modern procedure using number of periodic terms and the number of lunations from
the epoch 2000 C.E which are comparable to those of modern data.