Candravakyas
Encyclopedia
Candravākyās are a collection of numbers, arranged in the form of a list, related to the motion of the Moon
in its orbit around the Earth
. These numbers are couched in the katapayadi system
of representation of numbers and so apparently appear like a list of words, or phrases or short sentences written in Sanskrit
and hence the terminology Candravākyās. In Sanskrit
, Candra is the Moon
and vākya means a sentence. The term Candravākyās could thus be translated as Moon-sentences.
Vararuci
(c. 4th century CE), a legendary figure in the astronomical traditions of Kerala
, is credited with the authorship of the collection of Candravākyās. These were routinely made use of for computations of native almanacs and for predicting the position of the Moon. The work ascribed to Vararuci
is also known as Candravākyāni, or Vararucivākyāni, or Pañcāṅgavākyāni.
Madhava of Sangamagrama
(c. 1350 – c. 1425), the founder of the Kerala school of astronomy and mathematics, had set forth a revised set of Candravākyās, together with a method for computing them, in his work titled Venvaroha
.
Candravākyās were also popular in Tamil Nadu region of South India. There, the astrologers and astronomers used these vākyās to construct almanacs. These almanacs were popularly referred to as the Vākya-pañcāṅgas. This is used in contrast to the modern mode computation of almanacs based on parameters derived from astronomical observations. These modern almanacs are known as Dṛk Pañcāṅgas ( or Thirukanitha Pañcāṅgas).
system of astronomical computations introduced by Haridatta
(ca. 683 CE), though simplified the computational processes, required long tables of numbers for its effective implementation. For timely use of these numbers they had to be memorised in toto and probably the system of constructing astronomical Vākyas arose as an answer to this problem. The katapayadi system
provided the most convenient medium for constructing easily memorable
mnemonic
s for the numbers in these tables. Candravākyās ascribed to Vararuci
are the earliest example of such a set of mnemonic
s. The period of Vararuci
of Kerala
tradition has been determined as around fourth century CE and the year of the promulgation of the Parahita system is known to be 683 CE, Vararuci's Candravākyās should have been around at the time of the institution of the Parahita system.
Besides Vararuci's Vākyas, several other sets of Vākyas had been composed by astronomers and mathematicians of the Kerala school
. While Vararuci's Vākyas contain a list of 248 numbers, another set of Vākyas relating to Moon
's motion contains 3031 numbers. There is a set of 2075 Vākyas called Samudra-vākyas or Maṇḍala-vākyas or Kujādi-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 of Vākyas encoding other mathematical tables like Madhava's sine table
.
's manual on his Parahita system, known as Graha-cāra-nibandhana. The next major work that makes use of the mnemonic system of the Vākyas which has down to us is Vākya-karaṇa (karaṇa, or computations, utilising Vākyas). The authorship of this work is uncertain, but, is apocryphally assigned to Vararuci
. The work is known to have been composed around 1300 CE. It has been extensively commented upon by Sundararaja (c.1500 CE) of Trichinopopy of Tamil Nadu
. The almanac makers of Tamil Nadu
fully make use of this Vākya-karaṇa for computing the almanacs. These almanacs are known as Vākya-pañcāṅgas.
's orbit approximates an ellipse
rather than a circle. The orientation and the shape of this orbit
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 the Moon
longer to return to the same position, perigee
or apogee, because it moved ahead during one revolution. This longer period is called the anomalistic 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. 9 anomalistic months constitute a period of approximately 248 days. The differences in the longitude
s of the Moon on the successive days of a 248-day cycle constitute the Candravākyās. Each set of Candravākyās contains a list of 248 Vākyās or sentences.
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
in its orbit around the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
. These numbers are couched in the katapayadi system
Katapayadi system
Kaṭapayādi system of numerical notation is an ancient Indian system to depict letters to numerals for easy remembrance of numbers as words or verses...
of representation of numbers and so apparently appear like a list of words, or phrases or short sentences written in Sanskrit
Sanskrit
Sanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...
and hence the terminology Candravākyās. In Sanskrit
Sanskrit
Sanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...
, Candra is the Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
and vākya means a sentence. The term Candravākyās could thus be translated as Moon-sentences.
Vararuci
Vararuci
Vararuci is a name associated with several literary and scientific texts in Sanskrit and also with various legends in several parts of India. This Vararuci is often identified with Kātyāyana...
(c. 4th century CE), a legendary figure in the astronomical traditions of Kerala
Kerala
or Keralam is an Indian state located on the Malabar coast of south-west India. It was created on 1 November 1956 by the States Reorganisation Act by combining various Malayalam speaking regions....
, is credited with the authorship of the collection of Candravākyās. These were routinely made use of for computations of native almanacs and for predicting the position of the Moon. The work ascribed to Vararuci
Vararuci
Vararuci is a name associated with several literary and scientific texts in Sanskrit and also with various legends in several parts of India. This Vararuci is often identified with Kātyāyana...
is also known as Candravākyāni, or Vararucivākyāni, or Pañcāṅgavākyāni.
Madhava of Sangamagrama
Madhava of Sangamagrama
Mādhava of Sañgamāgrama was a prominent Kerala mathematician-astronomer from the town of Irińńālakkuţa near Cochin, Kerala, India. He is considered the founder of the Kerala School of Astronomy and Mathematics...
(c. 1350 – c. 1425), the founder of the Kerala school of astronomy and mathematics, had set forth a revised set of Candravākyās, together with a method for computing them, in his work titled Venvaroha
Venvaroha
Veṇvāroha is a work in Sanskrit composed by Mādhava of Sangamagrāma the founder of the Kerala school of astronomy and mathematics. It is a work in 74 verses describing methods for the computation of the true positions of the Moon at intervals of about half an hour for various days in an...
.
Candravākyās were also popular in Tamil Nadu region of South India. There, the astrologers and astronomers used these vākyās to construct almanacs. These almanacs were popularly referred to as the Vākya-pañcāṅgas. This is used in contrast to the modern mode computation of almanacs based on parameters derived from astronomical observations. These modern almanacs are known as Dṛk Pañcāṅgas ( or Thirukanitha Pañcāṅgas).
The Vākya tradition
The ParahitaParahita
Parahita is a system of astronomy prevalent in Kerala and Tamil Nadu, India. It was introduced by the Kerala astronomer Haridatta, .Nilakanthan Somayaji , in his DrkkaraNa, relates how Parahita was created based...
system of astronomical computations introduced by Haridatta
Haridatta
Haridatta was an astronomer-mathematician of Kerala, India, who is believed to be the promulgator of the Parahita system of astronomical computations. This system of computations is widely popular in Kerala and Tamil Nadu. According to legends, Haridatta promulgated the Parahita system on the...
(ca. 683 CE), though simplified the computational processes, required long tables of numbers for its effective implementation. For timely use of these numbers they had to be memorised in toto and probably the system of constructing astronomical Vākyas arose as an answer to this problem. The katapayadi system
Katapayadi system
Kaṭapayādi system of numerical notation is an ancient Indian system to depict letters to numerals for easy remembrance of numbers as words or verses...
provided the most convenient medium for constructing easily memorable
mnemonic
Mnemonic
A mnemonic , or mnemonic device, is any learning technique that aids memory. To improve long term memory, mnemonic systems are used to make memorization easier. Commonly encountered mnemonics are often verbal, such as a very short poem or a special word used to help a person remember something,...
s for the numbers in these tables. Candravākyās ascribed to Vararuci
Vararuci
Vararuci is a name associated with several literary and scientific texts in Sanskrit and also with various legends in several parts of India. This Vararuci is often identified with Kātyāyana...
are the earliest example of such a set of mnemonic
Mnemonic
A mnemonic , or mnemonic device, is any learning technique that aids memory. To improve long term memory, mnemonic systems are used to make memorization easier. Commonly encountered mnemonics are often verbal, such as a very short poem or a special word used to help a person remember something,...
s. The period of Vararuci
Vararuci
Vararuci is a name associated with several literary and scientific texts in Sanskrit and also with various legends in several parts of India. This Vararuci is often identified with Kātyāyana...
of Kerala
Kerala
or Keralam is an Indian state located on the Malabar coast of south-west India. It was created on 1 November 1956 by the States Reorganisation Act by combining various Malayalam speaking regions....
tradition has been determined as around fourth century CE and the year of the promulgation of the Parahita system is known to be 683 CE, Vararuci's Candravākyās should have been around at the time of the institution of the Parahita system.
Besides Vararuci's Vākyas, several other sets of Vākyas had been composed by astronomers and mathematicians of the Kerala school
Kerala school
Kerala school may refer to*Kerala school of astronomy and mathematics, a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala, South India which flourished between the 14th and 16th centuries CE....
. While Vararuci's Vākyas contain a list of 248 numbers, another set of Vākyas relating to Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
's motion contains 3031 numbers. There is a set of 2075 Vākyas called Samudra-vākyas or Maṇḍala-vākyas or Kujādi-pañcagraha-mahāvākyas relating to the motion of the five planets Kuja (Mars), Budha (Mercury
Mercury (planet)
Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...
), Guru (Jupiter), Bhrigu (Venus) and Sani (Saturn). There are also lists of Vākyas encoding other mathematical tables like Madhava's sine table
Madhava's sine table
Madhava's sine table is the table of trigonometric sines of various angles constructed by the 14th century Kerala mathematician-astronomer Madhava of Sangamagrama. The table lists the trigonometric sines of the twenty-four angles 3.75°, 7.50°, 11.25°, ... , and 90.00°...
.
Vākya-pañcāṅga
The first known text to use these Candravākyāss is HaridattaHaridatta
Haridatta was an astronomer-mathematician of Kerala, India, who is believed to be the promulgator of the Parahita system of astronomical computations. This system of computations is widely popular in Kerala and Tamil Nadu. According to legends, Haridatta promulgated the Parahita system on the...
's manual on his Parahita system, known as Graha-cāra-nibandhana. The next major work that makes use of the mnemonic system of the Vākyas which has down to us is Vākya-karaṇa (karaṇa, or computations, utilising Vākyas). The authorship of this work is uncertain, but, is apocryphally assigned to Vararuci
Vararuci
Vararuci is a name associated with several literary and scientific texts in Sanskrit and also with various legends in several parts of India. This Vararuci is often identified with Kātyāyana...
. The work is known to have been composed around 1300 CE. It has been extensively commented upon by Sundararaja (c.1500 CE) of Trichinopopy of Tamil Nadu
Tamil Nadu
Tamil Nadu is one of the 28 states of India. Its capital and largest city is Chennai. Tamil Nadu lies in the southernmost part of the Indian Peninsula and is bordered by the union territory of Pondicherry, and the states of Kerala, Karnataka, and Andhra Pradesh...
. The almanac makers of Tamil Nadu
Tamil Nadu
Tamil Nadu is one of the 28 states of India. Its capital and largest city is Chennai. Tamil Nadu lies in the southernmost part of the Indian Peninsula and is bordered by the union territory of Pondicherry, and the states of Kerala, Karnataka, and Andhra Pradesh...
fully make use of this Vākya-karaṇa for computing the almanacs. These almanacs are known as Vākya-pañcāṅgas.
The numbers encoded in Candravākyās
The MoonMoon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
's orbit approximates an ellipse
Ellipse
In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...
rather than a circle. The orientation and the shape of this orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...
is not fixed. In particular, the positions of the extreme points,
the point of closest approach (perigee
Perigee
Perigee is the point at which an object makes its closest approach to the Earth.. Often the term is used in a broader sense to define the point in an orbit where the orbiting body is closest to the body it orbits. The opposite is the apogee, the farthest or highest point.The Greek prefix "peri"...
) and the point of farthest excursion (apogee), make a full circle in about nine years. It takes the Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
longer to return to the same position, perigee
Perigee
Perigee is the point at which an object makes its closest approach to the Earth.. Often the term is used in a broader sense to define the point in an orbit where the orbiting body is closest to the body it orbits. The opposite is the apogee, the farthest or highest point.The Greek prefix "peri"...
or apogee, because it moved ahead during one revolution. This longer period is called the anomalistic 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. 9 anomalistic months constitute a period of approximately 248 days. The differences in the longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
s of the Moon on the successive days of a 248-day cycle constitute the Candravākyās. Each set of Candravākyās contains a list of 248 Vākyās or sentences.
Further reading
- For details on Madhava's method of computation of Candravakyas see :
- For a discussion on the history of the 248-day schemes see :
- For a discussion of the 248-day schemes in Babylonian astronomy see: (Chapter II)