GrahalÃÂghavaá¹ is a Sanskrit treatise on astronomy composed by Gaá¹Âeà Âa Daivajna (c. 1507âÂÂ1554), a sixteenth century astronomer, astrologer, and mathematician from western India, probably from the Indian state of Maharashtra. It is a work in the genre of the karaá¹Âa text in the sense that it is in the form of a handbook or manual for the computation of the positions of the planets. Of all the ancient and medieval karaá¹Âa texts on astronomy, GrahalÃÂghavaá¹ is the most popular among the pañcÃÂá¹ gaá¹ makers of most parts of India.It is also considered to be the most comprehensive, exhaustive and easy to use karaá¹Âa text on astronomy. The popularity of this work is attested by the large number of commentaries (at least 14 in number) on it and also by the large number of modern editions (at least 23 in number) of the book. The work is divided into sixteen chapters and covers all the commonly discussed topics in such texts including planetary positions, timekeeping and calendar construction, eclipses, heliacal rising and settings, planetary conjunctions, and the mahÃÂpÃÂta-s.
The most striking features of the work that made it highly popular include its use of an ingenious method to reduce the traditional method of computations involving 'astronomical numbers' to smaller numbers and its meticulous and careful avoidance of the use of the trigonometrical sines by replacing them with simpler, still acceptably accurate, algebraic expressions. The former is effected by introducing the concept of a new cycle called a cakra, a period consisting of 4016 days which is approximately 11 years. Traditional computations make use the concept of ahargaá¹Âa which is the number of civil days elapsed since the kali epoch which falls on 17/18 February 3102 BCE. The traditional ahargaá¹Âa is a huge number. For example, the ahargaá¹Âa corresponding to 1 January 2025 is 1872211. The ahargaá¹Âa as modified in GrahalÃÂghavaá¹ is the remainder number of days after completing full cakra-s of 4016 days each since the beginning of the epoch. Thus the modified ahargaá¹Âa corresponding to 1 January 2025 would be 755, a number less than 4016. To avoid the use of trigonometrical sines, GrahalÃÂghavaá¹ uses several approximations to the sine function. For example, in the context of computing the true longitudes of celestial objects, approximation formulas based on the following approximation to the sine function (known as the BhÃÂskara I's sine approximation formula) is used:
In the context of the computation of eclipses, the following approximation is used:
Full text of the work with commentaries in Sanskrit and with English translation are available at the following sources: