Chandravākyas (IAST:Candravākyas) are a collection of numbers, arranged in the form of a list, related to the motion of theMoon in its orbit around theEarth. These numbers are couched in thekatapayadi system of representation of numbers and so apparently appear like a list of words, or phrases or short sentences written inSanskrit and hence the terminologyChandravākyas.[1] InSanskrit,Chandra is theMoon andvākya means a sentence. The termChandravākyas could thus be translated asMoon-sentences.[2]
Vararuchi (c. 4th centuryCE), a legendary figure in the astronomical traditions ofKerala, is credited with the authorship of the collection ofChandravākyas. These were routinely made use of for computations of native almanacs and for predicting the position of the Moon.[3] The work ascribed to Vararuchi is also known asChandravākyāni, orVararucivākyāni, orPañcāṅgavākyāni.[4]
Madhava of Sangamagrama (c. 1350 – c. 1425), the founder of theKerala school of astronomy and mathematics, had set forth a revised set ofChandravākyās, together with a method for computing them, in his work titledVenvaroha.[2]
Chandravākyas were also popular in Tamil Nadu region of South India. There, the astrologers and astronomers used thesevākyās to construct almanacs. These almanacs were popularly referred to as theVākya-pañcāṅgas.[5] This is used in contrast to the modern mode computation of almanacs based on parameters derived from astronomical observations that are known asDṛk Pañcāṅgas ( orThirukanitha Pañcāṅgas).
TheParahita system of astronomical computations introduced byHaridatta (ca. 683CE), though simplified the computational processes, required long tables of numbers for its effective implementation.[1] For timely use of these numbers they had to be memorised in toto and probably the system of constructing astronomicalVākyas arose as an answer to this problem. Thekatapayadi system provided the most convenient medium for constructing easily memorablemnemonics for the numbers in these tables.Chandravākyās ascribed toVararuci are the earliest example of such a set ofmnemonics. The period ofVararuci ofKerala tradition has been determined as around fourth centuryCE and the year of the promulgation of theParahita system is known to be 683CE, Vararuci'sChandravākyās should have been around at the time of the institution of theParahita system.
Besides Vararuci'sVākyas, several other sets ofVākyas had been composed by astronomers and mathematicians of theKerala school. While Vararuci'sVākyas contain a list of 248 numbers, another set ofVākyas relating toMoon's motion contains 3031 numbers. There is a set of 2075Vākyas calledSamudra-vākyas orMaṇḍala-vākyas orKujādi-pañcagraha-mahāvākyas relating to the motion of the five planets Kuja (Mars), Budha (Mercury), Guru (Jupiter), Bhrigu (Venus) and Sani (Saturn). There are also lists ofVākyas encoding other mathematical tables likeMadhava's sine table.[1]
The first known text to use theseChandravākyass isHaridatta's manual on hisParahita system, known asGraha-cāra-nibandhana. The next major work that makes use of the mnemonic system of theVākyas which has come down to us isVākya-karaṇa (karaṇa, or computations, utilisingVākyas). The authorship of this work is uncertain, but, is apocryphally assigned toVararuci. The work is known to have been composed around 1300CE. It has been extensively commented upon by Sundararaja (c.1500CE) of Trichinopopy ofTamil Nadu. The almanac makers ofTamil Nadu fully make use of thisVākya-karaṇa for computing the almanacs. These almanacs are known asVākya-pañcāṅgas.[1]
TheMoon's orbit approximates anellipse rather than a circle. The orientation and the shape of thisorbit is not fixed. In particular, the positions of the extreme points,the point of closest approach (perigee) and the point of farthest excursion (apogee), make a full circle in about nine years. It takes theMoon longer to return to the same position,perigee orapogee, because it moved ahead during one revolution. This longer period is called theanomalistic month, and has an average length of 27.554551 days (27 d 13 h 18 min 33.2 s). The apparent diameter of the Moon varies with this period. 9anomalistic months constitute a period of approximately 248 days. The differences in thelongitudes of the Moon on the successive days of a 248-day cycle constitute theChandravākyas. Each set ofChandravākyas contains a list of 248Vākyās or sentences.[6]
