Introdction and Sacred Scriptures -6

The Mantra Aum

The mantra AUM stands for the supreme state Of Turiya, without parts, beyond birth and death, symbol of everlasting joy.
Those who know AUM as the Self become the Self; Truly they become the Self.

Om shanti shanti shanti

— Mandukya Upanishad

Astronomy

(Indian Astronomy)

Historical Indian astronomy (Jyotiṣa) develops as a discipline of Vedanga or one of the "auxiliary disciplines" associated with the study of the Vedas.^[1] The oldest extant text of astronomy is the treatise by Lagadha, dated to the Mauryan era (final centuries BCE).
As with other traditions, the original application of astronomy was thus religious, and would be considered astrology in modern terminology. Hindu astrology was heavily influenced by Hellenistic astrology during the early centuries of the Common Era, notably by the Yavanajataka, a Sanskrit translation of a Greek text disseminated from the 2nd century.
Indian astronomy flowered in the 6th century, with Aryabhata, whose Aryabhatiya represented the pinnacle of astronomical knowledge at the time, and significantly influenced medieval Muslim astronomy. Other astronomers of the classical era who further elaborated on Aryabhata's work include Brahmagupta, Varahamihira and Lalla. But an identifiable native Indian astronomical tradition remains active throughout the medieval period and into the 16th or 17th century, especially within the Kerala school of astronomy and mathematics.

History

Some cosmological concepts are present in the Vedas, as are notions of the movement of heavenly bodies and the course of the year.^[1] As in other traditions, there is a close association of astronomy and religion during the early history of the science, astronomical observation being necessitated by spacial and temporal requirements of correct performance of religious ritual. Thus, the Shulba Sutras, texts dedicated to altar construction, discusses basic astronomical concepts such as the cardinal directions.^[2] Jyotiṣa Vedānga as the science of observing the heavens in order to correctly perform Vedic sacrifice arises after the end of the Vedic period, during ca. the 6th to 4th centuries BCE,^[3] and the work of Lagadha is informed by these earlier traditions.
By the early centuries of the Common Era, Indo-Greek influence on the Vedanga tradition becomes evident with texts such as Romaka Siddhānta and Yavanajataka. Later astronomers mention the existence of various siddhantas during this period, among them a text known as the Surya Siddhanta. But these weren't fixed texts but rather an oral tradition of knowledge, and their content is not extant. The text today known as Surya Siddhanta dates to the Gupta period and was received by Aryabhata.
The classical era of Indian astronomy begins in the late Gupta era, in the 5th to 6th centuries. The Pañcasiddhāntikā (Varahimira, 505 CE) approximates the method for determination of the meridian direction from any three positions of the shadow using Gnomon.^[2] By the time of Aryabhata I the motion of planets was treated to be elliptical rather than circular.^[4] Other topics included definitions of different units of time, eccentric models of planetary motion, epicyclic models of planetary motion, and planetary longitude corrections for various terrestrial locations

Calendars

Further information: Hindu calendar

The divisions of the year were on the basis of religious rites and seasons (Rtu).^[5] The duration from mid March—Mid May was taken to be spring (vasanta), mid May—mid July: summer ("grishma"), mid July—mid September: rains (varsha), mid September—mid November: autumn, mid November—mid January: winter, mid January—mid March: dew (śiśira).^[5]

In the Vedānga Jyotiṣa, the year begins with the winter solstice.^[6] Hindu calendars have several eras:

• The Hindu calendar, counting from the start of the Kali Yuga, has its epoch on 18 February 3102 BC Julian (23 January 3102 BCE Gregorian).
• The Vikrama Samvat calendar, introduced about the 12th century, counts from 56–57 BCE.
• The "Saka Era", used in some Hindu calendars and in the Indian national calendar, has its epoch near the vernal equinox of year 78.
• The Saptarshi calendar traditionally has its epoch at 3076 BCE.^[7]

J.A.B. van Buitenen (2008) reports on the calendars in India:

The oldest system, in many respects the basis of the classical one, is known from texts of about 1000 BC. It divides an approximate solar year of 360 days into 12 lunar months of 27 (according to the early Vedic text Taittirīya Saṃhitā 4.4.10.1–3) or 28 (according to the Atharvaveda, the fourth of the Vedas, 19.7.1.) days. The resulting discrepancy was resolved by the intercalation of a leap month every 60 months. Time was reckoned by the position marked off in constellations on the ecliptic in which the Moon rises daily in the course of one lunation (the period from New Moon to New Moon) and the Sun rises monthly in the course of one year. These constellations (nakṣatra) each measure an arc of 13° 20′ of the ecliptic circle. The positions of the Moon were directly observable, and those of the Sun inferred from the Moon's position at Full Moon, when the Sun is on the opposite side of the Moon. The position of the Sun at midnight was calculated from the nakṣatra that culminated on the meridian at that time, the Sun then being in opposition to that nakṣatra.[5]

Astronomers

Name	Year	Contributions
Lagadha	1st millennium BCE	The earliest astronomical text—named Vedānga Jyotiṣa details several astronomical attributes generally applied for timing social and religious events.[8] The Vedānga Jyotiṣa also details astronomical calculations, calendrical studies, and establishes rules for empirical observation.[8] Since the texts written by 1200 BCE were largely religious compositions the Vedānga Jyotiṣa has connections with Indian astrology and details several important aspects of the time and seasons, including lunar months, solar months, and their adjustment by a lunar leap month of Adhimāsa.[9] Ritus and Yugas are also described.[9] Tripathi (2008) holds that ' Twenty-seven constellations, eclipses, seven planets, and twelve signs of the zodiac were also known at that time.'[9]
Aryabhata	476–550 CE	Aryabhata was the author of the Āryabhatīya and the Aryabhatasiddhanta, which, according to Hayashi (2008): 'circulated mainly in the northwest of India and, through the Sāsānian dynasty (224–651) of Iran, had a profound influence on the development of Islamic astronomy. Its contents are preserved to some extent in the works of Varahamihira (flourished c. 550), Bhaskara I (flourished c. 629), Brahmagupta (598–c. 665), and others. It is one of the earliest astronomical works to assign the start of each day to midnight.'[4] Aryabhata explicitly mentioned that the earth rotates about its axis, thereby causing what appears to be an apparent westward motion of the stars.[4] Aryabhata also mentioned that reflected sunlight is the cause behind the shining of the moon.[4] Ayrabhata's followers were particularly strong in South India, where his principles of the diurnal rotation of the earth, among others, were followed and a number of secondary works were based on them.[1]
Brahmagupta	598–668 CE	Brahmasphuta-siddhanta (Correctly Established Doctrine of Brahma, 628 CE) dealt with both Indian mathematics and astronomy. Hayashi (2008) writes: 'It was translated into Arabic in Baghdad about 771 and had a major impact on Islamic mathematics and astronomy.'[10] In Khandakhadyaka (A Piece Eatable, 665 CE) Brahmagupta reinforced Aryabhata's idea of another day beginning at midnight.[10] Bahmagupta also calculated the instantaneous motion of a planet, gave correct equations for parallax, and some information related to the computation of eclipses.[1] His works introduced Indian concept of mathematics based astronomy into the Arab world.[1]
Varāhamihira	505 CE	Varāhamihira was an astronomer and mathematician who studied and Indian astronomy as well as the many principles of Greek, Egyptian, and Roman astronomical sciences.[11] His Pañcasiddhāntikā is a treatise and compendium drawing from several knowledge systems.[11]
Bhāskara I	629 CE	Authored the astronomical works Mahabhaskariya (Great Book of Bhaskara), Laghubhaskariya (Small Book of Bhaskara), and the Aryabhatiyabhashya (629 CE)—a commentary on the Āryabhatīya written by Aryabhata.[12] Hayashi (2008) writes 'Planetary longitudes, heliacal rising and setting of the planets, conjunctions among the planets and stars, solar and lunar eclipses, and the phases of the Moon are among the topics Bhaskara discusses in his astronomical treatises.'[12] Baskara I's works were followed by Vateśvara (880 CE), who in his eight chapter Vateśvarasiddhānta devised methods for determining the parallax in longitude directly, the motion of the equinoxes and the solstices, and the quadrant of the sun at any given time.[1]
Lalla	8th century CE	Author of the Śisyadhīvrddhida (Treatise Which Expands the Intellect of Students), which corrects several assumptions of Āryabhata.[13] The Śisyadhīvrddhida of Lalla itself is divided into two parts:Grahādhyāya and Golādhyāya.[13] Grahādhyāya (Chapter I-XIII) deals with planetary calculations, determination of the mean and true planets, three problems pertaining to diurnal motion of Earth, eclipses, rising and setting of the planets, the various cusps of the moon, planetary and astral conjunctions, and complementary situations of the sun and the moon.[13] The second part—titled Golādhyāya (chapter XIV–XXII)—deals with graphical representation of planetary motion, astronomical instruments, spherics, and emphasizes on corrections and rejection of flawed principles.[13] Lalla shows influence of Āryabhata, Brahmagupta, and Bhāskara I.[13] His works were followed by later astronomers Śrīpati, Vateśvara, and Bhāskara II.[13] Lalla also authored the Siddhāntatilaka.[13]
Bhāskara II	1114 CE	Authored Siddhāntaśiromaṇi (Head Jewel of Accuracy) and Karaṇakutūhala (Calculation of Astronomical Wonders) and reported on his observations of planetary positions, conjunctions, eclipses, cosmography, geography, mathematics, and astronomical equipment used in his research at the observatory in Ujjain, which he headed.[14]
Śrīpati	1045 CE	Śrīpati was an astronomer and mathematician who followed the Brhmagupta school and authored the Siddhāntaśekhara (The Crest of Established Doctrines) in 20 chapters, thereby introducing several new concepts, including moon's second ineuqlity.[1][15]
Mahendra Suri	14th century CE	Mahendra Suri authored the Yantra-rāja (The King of Instruments, written in 1370 CE)—a Sanskrit work on the astrolabe, itself introduced in India during the reign of the 14th century Tughlaq dynasty ruler Firuz Shah Tughluq (1351–1388 CE).[16] Suri seems to have been a Jain astronomer in the service of Firuz Shah Tughluq.[16] The 182 verse Yantra-rāja mentions the astrolabe from the first chapter onwards, and also presents a fundamental formula along with a numerical table for drawing an astrolabe although the proof itself has not been detailed.[16] Longitudes of 32 stars as well as their latitudes have also been mentioned.[16] Mahendra Suri also explained the Gnomon, equatorial co-ordinates, and elliptical co-ordinates.[16] The works of Mahendra Suri may have influenced later astronomers like Padmanābha (1423 CE)—author of the Yantra-rāja-adhikāra, the first chapter of his Yantra-kirnāvali.[16]
Nilakanthan Somayaji	1444–1544 CE	In 1500, Nilakanthan Somayaji of the Kerala school of astronomy and mathematics, in his Tantrasangraha, revised Aryabhata's model for the planets Mercury and Venus. His equation of the centre for these planets remained the most accurate until the time of Johannes Kepler in the 17th century.[17] Nilakanthan Somayaji, in his Aryabhatiyabhasya, a commentary on Aryabhata's Aryabhatiya, developed his own computational system for a partially heliocentric planetary model, in which Mercury, Venus, Mars, Jupiter and Saturn orbit the Sun, which in turn orbits the Earth, similar to the Tychonic system later proposed by Tycho Brahe in the late 16th century. Nilakantha's system, however, was mathematically more efficient than the Tychonic system, due to correctly taking into account the equation of the centre and latitudinal motion of Mercury and Venus. Most astronomers of the Kerala school of astronomy and mathematics who followed him accepted his planetary model.[17][18] He also authored a treatise titled Jyotirmimamsa stressing the necessity and importance of astronomical observations to obtain correct parameters for computations.
Acyuta Pisārati	1550–1621 CE	Sphutanirnaya (Determination of True Planets) details an elliptical correction to existing notions.[19] Sphutanirnaya was later expanded to Rāśigolasphutānīti (True Longitude Computation of the Sphere of the Zodiac).[19] Another work, Karanottama deals with eclipses, complementary relationship between the sun and the moon, and 'the derivation of the mean and true planets'.[19] In Uparāgakriyākrama (Method of Computing Eclipses), Acyuta Pisārati suggests improvements in methods of calculation of eclipses.

Instruments used

Among the devices used for astronomy was Gnomon, known as Sanku, in which the shadow of a vertical rod is applied on a horizontal plane in order to ascertain the cardinal directions, the latitude of the point of observation, and the time of observation.^[20] This device finds mention in the works of Varāhamihira, Āryabhata, Bhāskara, Brahmagupta, among others.^[2] The Cross-staff, known as Yasti-yantra, was used by the time of Bhaskara II (1114–1185 CE).^[20] This device could vary from a simple stick to V-shaped staffs designed specifically for determining angles with the help of a calibrated scale.^[20] The clepsydra (Ghatī -yantra) was used in India for astronomical purposes until recent times.^[20] Ōhashi (2008) notes that: "Several astronomers also described water-driven instruments such as the model of fighting sheep."^[20]
The armillary sphere was used for observation in India since early times, and finds mention in the works of Āryabhata (476 CE).^[21] The Goladīpikā—a detailed treatise dealing with globes and the armillary sphere was composed between 1380–1460 CE by Parameśvara.^[21] On the subject of the usage of the armillary sphere in India, Ōhashi (2008) writes: "The Indian armillary sphere (gola-yantra) was based on equatorial coordinates, unlike the Greek armillary sphere, which was based on ecliptical coordinates, although the Indian armillary sphere also had an ecliptical hoop. Probably, the celestial coordinates of the junction stars of the lunar mansions were determined by the armillary sphere since the seventh century or so. There was also a celestial globe rotated by flowing water."^[20]
An instrument invented by the mathematician and astronomer Bhaskara II (1114–1185 CE) consisted of a rectangular board with a pin and an index arm.^[20] This device—called the Phalaka-yantra—was used to determine time from the sun's altitude.^[20] The Kapālayantra was a equatorial sundial instrument used to determine the sun’s azimuth.^[20] Kartarī-yantra combined two semicircular board instruments to give rise to a 'scissors instrument'.^[20] Introduced from the Islamic world and first finding mention in the works of Mahendra Sūri—the court astronomer of Firuz Shah Tughluq (1309–1388 CE)—the astrolabe was further mentioned by Padmanābha (1423 CE) and Rāmacandra (1428 CE) as its use grew in India.^[20]
Invented by Padmanābha, a nocturnal polar rotation instrument consisted of a rectangular board with a slit and a set of pointers with concentric graduated circles.^[20] Time and other astronomical quantities could be calculated by adjusting the slit to the directions of α and β Ursa Minor.^[20] Ōhashi (2008) further explains that: "Its backside was made as a quadrant with a plumb and an index arm. Thirty parallel lines were drawn inside the quadrant, and trigonometrical calculations were done graphically. After determining the sun’s altitude with the help of the plumb, time was calculated graphically with the help of the index arm."^[20]
Ōhashi (2008) reports on the observatories constructed by Jai Singh II of Amber:

The Mahārāja of Jaipur, Sawai Jai Singh (AD 1688–1743), constructed five astronomical observatories at the beginning of the eighteenth century. The observatory in Mathura is not extant, but those in Delhi, Jaipur, Ujjain, and Banaras are. There are several huge instruments based on Hindu and Islamic astronomy. For example, the samrāt.-yantra (emperor instrument) is a huge sundial which consists of a triangular gnomon wall and a pair of quadrants toward the east and west of the gnomon wall. Time has been graduated on the quadrants.[20]

The seamless celestial globe invented in Mughal India, specifically Lahore and Kashmir, is considered to be one of the most impressive astronomical instruments and remarkable feats in metallurgy and engineering. All globes before and after this were seamed, and in the 20th century, it was believed by metallurgists to be technically impossible to create a metal globe without any seams, even with modern technology. It was in the 1980s, however, that Emilie Savage-Smith discovered several celestial globes without any seams in Lahore and Kashmir. The earliest was invented in Kashmir by Ali Kashmiri ibn Luqman in 998 AH (1589–90 CE) during Akbar the Great's reign; another was produced in 1070 AH (1659–60 CE) by Muhammad Salih Tahtawi with Arabic and Sanskrit inscriptions; and the last was produced in Lahore by a Hindu metallurgist Lala Balhumal Lahuri in 1842 during Jagatjit Singh Bahadur's reign. 21 such globes were produced, and these remain the only examples of seamless metal globes. These Mughal metallurgists developed the method of lost-wax casting in order to produce these globes.

Global discourse

With the rise of Greek culture in the east, Hellenistic astronomy filtered eastwards to India where its profound influence became apparent in the early centuries AD.^[23] For example, Hellenistic astronomy is known to have been practiced near India in the Greco-Bactrian city of Ai-Khanoum from the 3rd century BCE. Various sun-dials, including an equatorial sundial adjusted to the latitude of Ujjain have been found in archaeological excavations there.^[24] Numerous interactions with the Mauryan Empire, and the later expansion of the Indo-Greeks into India suggest that transmission of Greek astronomical ideas to India occurred during this period.^[25] The Greek concept of a spherical earth surrounded by the spheres of planets, vehemently supported by astronomers like Varahamihira and Brahmagupta, supplanted the long-standing Indian cosmological belief into a flat and circular earth disk.^[23][26]
Several Greco-Roman astrological treatises are also known to have been imported into India during the first few centuries of our era. The Yavanajataka ("Sayings of the Greeks") was translated from Greek to Sanskrit by Yavanesvara during the 2nd century CE, under the patronage of the Western Satrap Saka king Rudradaman I.^{[citation needed]} Rudradaman's capital at Ujjain "became the Greenwich of Indian astronomers and the Arin of the Arabic and Latin astronomical treatises; for it was he and his successors who encouraged the introduction of Greek horoscopy and astronomy into India."^[27]
Later in the 6th century, the Romaka Siddhanta ("Doctrine of the Romans"), and the Paulisa Siddhanta ("Doctrine of Paul") were considered as two of the five main astrological treatises, which were compiled by Varahamihira in his Pañca-siddhāntikā ("Five Treatises").^[28] Varahamihira wrote in the Brihat-Samhita: "The Greeks, though impure, must be honored since they were trained in sciences and therein, excelled others....."^[29] Another Indian text, the Gargi-Samhita, also similarly compliments the Yavanas (Greeks) saying: "The Yavanas are barbarians yet the science of astronomy originated with them and for this they must be revered like gods".,^[30] while the Mahabharata compliments them as "the all-knowing Yavanas" (sarvajnaa yavanaa), "The Yavanas, O king, are all-knowing; the Suras are particularly so. The mlecchas are wedded to the creations of their own fancy."^[31]
Indian astronomy reached China with the expansion of Buddhism during the Later Han dynasty (25–220 CE).^[32] Further translation of Indian works on astronomy was completed in China by the Three Kingdoms era (220–265 CE).^[32] However, the most detailed incorporation of Indian astronomy occurred only during the Tang Dynasty (618–907) when a number of Chinese scholars—such as Yi Xing— were versed both in Indian and Chinese astronomy.^[32] A system of Indian astronomy was recorded in China as Jiuzhi-li (718 CE), the author of which was an Indian by the name of Qutan Xida—a translation of Devanagari Gotama Siddha—the director of the Tang dynasty's national astronomical observatory.^[32]
Fragments of texts during this period indicate that Arabs adopted the sine function (inherited from Indian mathematics) instead of the chords of arc used in Hellenistic mathematics.^[33] Another Indian influence was an approximate formula used for timekeeping by Muslim astronomers.^[34] Through Islamic astronomy, Indian astronomy had an influence on European astronomy via Arabic translations. During the Latin translations of the 12th century, Muhammad al-Fazari's Great Sindhind, which was based on the Surya Siddhanta and the works of Brahmagupta, was translated into Latin in 1126 and was influential at the time.^[35]
In the 17th century, the Mughal Empire saw a synthesis between Islamic and Hindu astronomy, where Islamic observational instruments were combined with Hindu computational techniques. While there appears to have been little concern for planetary theory, Muslim and Hindu astronomers in India continued to make advances in observational astronomy and produced nearly a hundred Zij treatises. Humayun built a personal observatory near Delhi, while Jahangir and Shah Jahan were also intending to build observatories but were unable to do so. After the decline of the Mughal Empire, it was a Hindu king, Jai Singh II of Amber, who attempted to revive both the Islamic and Hindu traditions of astronomy which were stagnating in his time. In the early 18th century, he built several large observatories called Yantra Mandirs in order to rival Ulugh Beg's Samarkand observatory and in order to improve on the earlier Hindu computations in the Siddhantas and Islamic observations in Zij-i-Sultani. The instruments he used were influenced by Islamic astronomy, while the computational techniques were derived from Hindu astronomy.^[36][37]
Some scholars have suggested that knowledge of the results of the Kerala school of astronomy and mathematics may have been transmitted to Europe through the trade route from Kerala by traders and Jesuit missionaries.^[38] Kerala was in continuous contact with China and Arabia, and Europe. The existence of circumstantial evidence^[39] such as communication routes and a suitable chronology certainly make such a transmission a possibility. However, there is no direct evidence by way of relevant manuscripts that such a transmission took place.^[38]
In the early 18th century, Jai Singh II of Amber invited European Jesuit astronomers to one of his Yantra Mandir observatories, who had bought back the astronomical tables compiled by Philippe de La Hire in 1702. After examining La Hire's work, Jai Singh concluded that the observational techniques and instruments used in European astronomy were inferior to those used in India at the time. It is uncertain whether he was aware of the Copernican Revolution via the Jesuits.^[40] He did, however, employ the use of telescopes. In his Zij-i Muhammad Shahi, he states: "telescopes were constructed in my kingdom and using them a number of observations were carried out."^[41]
Following the arrival of the British East India Company in the 18th century, the Hindu and Islamic traditions were slowly displaced by European astronomy, though there were attempts at harmonizing these traditions. The Indian scholar Mir Muhammad Hussain had travelled to England in 1774 to study Western science and, on his return to India in 1777, he wrote a Persian treatise on astronomy. He wrote about the heliocentric model, and argued that there exists an infinite number of universes (awalim), each with their own planets and stars, and that this demonstrates the omnipotence of God, who is not confined to a single universe. Hussain's idea of a universe resembles the modern concept of a galaxy, thus his view corresponds to the modern view that the universe consists of billions of galaxies, each one consisting of billions of stars.^[42] The last known Zij treatise was the Zij-i Bahadurkhani, written in 1838 by the Indian astronomer Ghulam Hussain Jaunpuri (1760–1862) and printed in 1855, dedicated to Bahadur Khan. The treatise incorporated the heliocentric system into the Zij tradition

Hindu cosmology

In Hindu cosmology the universe is, according to Hindu tradition and Vedic cosmology, cyclically created and destroyed.

Description

The Hindu cosmology and timeline is the closest to modern scientific timelines and even more which might indicate that the Big Bang is not the beginning of everything but just the start of the present cycle preceded by an infinite number of universes and to be followed by another infinite number of universes. It also includes an infinite number of universes at one given time.
The Rig Veda questions the origin of the cosmos in: "Neither being (sat) nor non-being was as yet. What was concealed? And where? And in whose protection?…Who really knows? Who can declare it? Whence was it born, and whence came this creation? The devas were born later than this world's creation, so who knows from where it came into existence? None can know from where creation has arisen, and whether he has or has not produced it. He who surveys it in the highest heavens, he alone knows-or perhaps does not know." (Rig Veda 10. 129)
The Rig Veda's view of the cosmos also sees one true divine principle self-projecting as the divine word, Vaak, 'birthing' the cosmos that we know, from the monistic Hiranyagarbha or Golden Womb. The Hiranyagarbha is alternatively viewed as Brahma, the creator who was in turn created by God, or as God (Brahman) himself. The universe is considered to constantly expand since creation and disappear into a thin haze after billions of years.^{[citation needed]} An alternate view is that the universe begins to contract after reaching its maximum expansion limits until it disappears into a fraction of a millimeter.^{[citation needed]} The creation begins anew after billions of years (Solar years) of non-existence.
The puranic view asserts that the universe is created, destroyed, and re-created in an eternally repetitive series of cycles. In Hindu cosmology, a universe endures for about 4,320,000,000 years (one day of Brahma, the creator or kalpa) and is then destroyed by fire or water elements. At this point, Brahma rests for one night, just as long as the day. This process, named pralaya (literally especial dissolution in Sanskrit, commonly translated as Cataclysm), repeats for 100 Brahma years (311 Trillion, 40 Billion Human Years) that represents Brahma's lifespan. Brahma is regarded as a manifestation of Brahman as the creator.
We are currently^[when?] believed to be in the 51st year of the present Brahma and so about 156 trillion years have elapsed since He was born as Brahma. After Brahma's "death", it is necessary that another 100 Brahma years (311 Trillion, 40 Billion Years) pass until a new Brahma is born and the whole creation begins anew. This process is repeated again and again, forever.
Brahma's day is divided in one thousand cycles (Maha Yuga, or the Great Year). Maha Yuga, during which life, including the human race appears and then disappears, has 71 divisions, each made of 14 Manvantara (1000) years. Each Maha Yuga lasts for 4,320,000 years. Manvantara is Manu's cycle, the one who gives birth and governs the human race.
Each Maha Yuga consists of a series of four shorter yugas, or ages. The yugas get progressively worse from a moral point of view as one proceeds from one yuga to another. As a result, each yuga is of shorter duration than the age that preceded it. The current Kali Yuga (Iron Age) began at midnight 17 February / 18 February in 3102 BC in the proleptic Julian calendar.
Space and time are considered to be maya (illusion). What looks like 100 years in the cosmos of Brahma could be thousands of years in other worlds, millions of years in some other worlds and 311 trillion and 40 billion years for our solar system and earth. The life span of Lord Brahma, the creator, is 100 'Brahma-Years'. One day in the life of Brahma is called a Kalpa or 4.32 billion years.^[1][2] Every Kalpa creates 14 Manus one after the other, who in turn manifest and regulate this world. Thus, there are fourteen generations of Manu in each Kalpa. Each Manu’s life (Manvantara) consists of 71 Chaturyugas (quartets of Yugas or eras).^[3] Each Chaturyuga is composed of four eras or Yugas: Satya, Treta, Dwapara and Kali.^[3]
The span of the Satya Yuga is 1,728,000 human years, Treta Yuga is 1,296,000 human years long, the Dwapara Yuga 864,000 human years and the Kali Yuga 432,000 human years.^[4] When Manu perishes at the end of his life, Brahma creates the next Manu and the cycle continues until all fourteen Manus and the Universe perish by the end of Bramha's day. When 'night' falls, Brahma goes to sleep for a period of 4.32 billion years, which is a period of time equal one day (of Brahma) and the lives of fourteen Manus. The next 'morning', Brahma creates fourteen additional Manus in sequence just as he has done on the previous 'day'. The cycle goes on for 100 'divine years' at the end of which Brahma perishes and is regenerated. Bramha's entire life equals 311 trillion, 40 billion years. Once Bramha dies there is an equal period of unmanifestation for 311 trillion, 40 billion years, until the next Bramha is created.
The present period is the Kali Yuga or last era in one of the 71 Chaturyugis (set of four Yugas/eras) in the life one of the fourteen Manus. The current Manu is said to be the seventh Manu and his name is Vaivasvat.^[5]
According to Aryabhata, the Kali Yuga began in 3102 BC, at the end of the Dvapara Yuga that was marked by the disappearance of Vishnu's Krishna avatar. Aryabhata's date is widely repeated in modern Hinduism.
The beginning of the new Yuga (era) is known as "Yugadi/Ugadi", and is celebrated every year on the first day (Paadyami) of the first month (Chaitramu) of the 12-month annual cycle. But this is a disambiguation for beginning of new year in lunisolar calendar followed by most Hindus. The Ugadi of 1999 begins the year 1921 of the Shalivahana era (5101 Kali Yuga, 1999 AD). The end of the Kali Yuga is 426,899 years from 1921.^[6]
Overview of Yugas:

1. Satya Yuga (Krita Yuga):- 1,728,000 Human years
2. Treta Yuga:- 1,296,000 Human years
3. Dwapara Yuga:- 864,000 Human years
4. Kali Yuga:- 432,000 Human years (5,111 years have passed; 426,889 years remain). Kaliyuga started in 3102 B.C.; CE 2009 corresponds to Kaliyuga year 5,111

Further elaborations from the Vedic texts

Rig Veda

The Nasadiya Sukta of the Rig Veda describes the origin of the universe. The Rig Veda's view of the cosmos also sees one true divine principle self-projecting as the divine word, Vaak, 'birthing' the cosmos that we know, from the monistic Hiranyagarbha or Golden Egg.^[7] The Hiranyagarbha is alternatively viewed as Brahma, the creator who was in turn created by God, or as God (Brahman) Himself.^{[citation needed]} The Universe is preserved by Vishnu (The God of Preservation) and destroyed by Shiva (The God of Destruction). These three constitute the holy trinity (Trimurti) of the Hindu religion. Once the Universe has been destroyed by Shiva, Brahma starts the creation once again. This creation-destruction cycle repeats itself almost endlessly as described in the section above on Brahma, Manu and the Yugas.

The Puranas

The later Puranic view asserts that the Universe is created, destroyed, and re-created in an eternally repetitive series of cycles. In Hindu cosmology, a universe endures for about 4,320,000,000 years—one day/Kalpa of Brahma, the creator) and is then destroyed by fire or water elements. At this point, Brahma rests for one night, just as long as the day. This process, named Pralaya (Cataclysm), repeats for 100 Brahma years (311 trillion, 40 billion human years) that represents Brahma's lifespan. Brahma is the creator but not necessarily regarded as God in Hinduism because there are said to be many creations. Instead, he is regarded as a creation of the Supreme God or Brahman.
We are currently believed^{[citation needed]} to be in the 51st year of the present Brahma's life and so about 158.7 trillion years have elapsed since the birth of Brahma. After Brahma's "death", it is necessary that another 100 Brahma years pass until he is reborn and the whole creation begins anew. This process is repeated again and again, forever.
Brahma's day is divided in one thousand cycles (Maha Yuga, or the Great Year). Maha Yuga, during which life, including the human race appears and then disappears, made of 14 Manvantarahas each has 71 divisions. Each Maha Yuga lasts for 4,320,000 years. Manvantara is Manu's cycle, the one who gives birth and governs the human race.
Each Maha Yuga consists of a series of four shorter yugas, or ages as described earlier. The degree of happiness, prosperity and righteousness progressively decays as one proceeds from one yuga to another. Each yuga is of shorter duration than the age that preceded it. The current Kali Yuga (Iron Age) began at midnight 17 February / 18 February in 3102 BC in the proleptic Julian calendar.
Only some Puranas describe a universe that is cyclical or oscillating and infinite in time. The universe is described as a cosmic egg that cycles between expansion and total collapse. It expanded from a concentrated form — a point called a Bindu. The universe, as a living entity, is bound to the perpetual cycle of birth, death, and rebirth.
The Padma Purana discusses about the number of different types of life-forms in the universe. According to the Padma Purana, there are 8,400,000 life-form species, 900,000 of which are aquatic ones; 2,000,000 are trees and plants; 1,100,000 are small living species, insects and reptiles; 1,000,000 are birds; 3,000,000 are beasts and 400,000 are human species. ^[8]

Multiverse in Hinduism

The concept of multiverses is mentioned many times in Hindu Puranic literature, such as in the Bhagavata Purana:
Every universe is covered by seven layers — earth, water, fire, air, sky, the total energy and false ego — each ten times greater than the previous one. There are innumerable universes besides this one, and although they are unlimitedly large, they move about like atoms in You. Therefore You are called unlimited (Bhagavata Purana 6.16.37)
Lord Śiva said: "My dear son, I, Lord Brahmā and the other devas, who move within this universe under the misconception of our greatness, cannot exhibit any power to compete with the Supreme Personality of Godhead, for innumerable universes and their inhabitants come into existence and are annihilated by the simple direction of the Lord" (Bhagavata Purana 9.4.56)
After separating the different universes, the gigantic universal form of the Lord, which came out of the causal ocean, the place of appearance for the first puruṣa-avatāra, entered into each of the separate universes, desiring to lie on the created transcendental water (Bhagavata Purana 2.10.10)
The number of universes seems to be uncountable, immeasurable, or incalculable according to the Puranic literature:
Even though over a period of time I might count all the atoms of the universe, I could not count all of My opulences which I manifest within innumerable universes (Bhagavata Purana 11.16.39)
Analogies to describe multiple universes also exist in the Puranic literature:
What am I, a small creature measuring seven spans of my own hand? I am enclosed in a potlike universe composed of material nature, the total material energy, false ego, ether, air, water and earth. And what is Your glory? Unlimited universes pass through the pores of Your body just as particles of dust pass through the openings of a screened window (Bhagavata Purana 10.14.11)
Because You are unlimited, neither the lords of heaven nor even You Yourself can ever reach the end of Your glories. The countless universes, each enveloped in its shell, are compelled by the wheel of time to wander within You, like particles of dust blowing about in the sky. The śrutis, following their method of eliminating everything separate from the Supreme, become successful by revealing You as their final conclusion (Bhagavata Purana 10.87.41)
The layers or elements covering the universes are each ten times thicker than the one before, and all the universes clustered together appear like atoms in a huge combination (Bhagavata Purana 3.11.41)

Hindu calendar

Hindu calendar is a collective name for most of the lunar calendars used in India since ancient times. Since ancient times it has undergone many changes in the process of regionalization and today there are several regional Indian Hindu calendars. It has also been standardized as Indian national calendar. Nepali calendar, Bengali calendar, Malayalam calendar, Tamil calendar, Telugu calendar, Kannada calendar etc. are some prominent regional Hindu calendars.^[1] The common feature of all regional Hindu calendars is that the names of the twelve months are the same (because the names are based in Sanskrit) though the spelling and pronunciation have come to vary slightly from region to region over thousands of years. The month which starts the year also varies from region to region.
Most of the Hindu calendars are inherited from a system first enunciated in Vedāṅga Jyotiṣa's of Lagadha, a late BCE adjunct to the Veda-s, standardized in the Sūrya Siddhānta (3rd century CE) and subsequently reformed by astronomers such as Āryabhaṭṭa (499 CE), Varāhamihira (6th c. CE), and Bhāskara II (12^th c. CE). Differences and regional variations abound in these computations, but the following is a general overview of Hindu lunisolar calendar.

Day

In the Hindu calendar, the day starts with local sunrise. It is allotted five "properties" or "limbs", called aṅga-s. They are:

1. the Tithi (one of 30 divisions of a synodic month) active at sunrise
2. the Vāsara (ancient nomeclature), vāra (modern nomeclature), like in ravi-vāra, somā-vāra, etc. or weekday
3. the Nakṣatra (one of 27 divisions of the celestial ecliptic) in which the moon resides at sunrise
4. the Yoga (one of 27 divisions based on the ecliptic longitude of the sun and moon) active at sunrise time
5. the Karaṇa (divisions based on tithis) active at sunrise.

Together 5 limbs or properties are labelled under as the pañcāṅga-s (Sanskrit: pañca = five). An explanation of the terms follows.

Vāsara

Vāsara refers to the weekdays and the names of the week in many western cultures bear striking similarities with the Vāsara:

No.	Sanskrit name of the day (Day begins at sunrise)	Tamil name	English & Latin names of the approximate day (Day begins at 00:00Hrs)	Celestial object
1	Ravi vāsara रविवासर	ஞாயிறு	Sunday/dies Solis	Ravi = Sun
2	Soma vāsara सोमवासर	திங்கள்	Monday/dies Lunae	Soma = Moon
3	Maṅgala vāsara मंगलवासर	செவ்வாய்	Tuesday/dies Martis	Maṅgala = Mars
4	Budha vāsara बुधवासर	புதன்	Wednesday/dies Mercurii	Budha = Mercury
5	Guru vāsara गुरुवासर or Bruhaspati vāsara बृहस्पतिवासरः	வியாழன்	Thursday/dies Iovis	Deva-Guru Bṛhaspati = Jupiter
6	Śukra vāsara शुक्रवासर	வெள்ளி்	Friday/dies Veneris	Śukra = Venus
7	Śani vāsara शनिवासर	சனி	Saturday/dies Saturnis	Śani = Saturn

The term -vāsara is often realized as vāra or vaar in Sanskrit-derived languages. There are many variations of the names in the regional languages, mostly using alternate names of the celestial bodies involved.

Nakṣatra

The ecliptic is divided into 27 Nakṣatra-s, which are variously called lunar houses or asterisms. These reflect the moon's cycle against the fixed stars, 27 days and 7¾ hours, the fractional part being compensated by an intercalary 28^th nakṣatra titled Abhijit. Nakṣatra's computation appears to have been well known at the time of the Ṛgveda (2^nd–1^st millennium BCE).
The ecliptic is divided into the nakṣatras eastwards starting from a reference point which is traditionally a point on the ecliptic directly opposite the star Spica called Citrā in Sanskrit. (Other slightly different definitions exist.) It is called Meṣādi - "start of Aries"; this is when the equinox — where the ecliptic meets the equator — was in Aries (today it is in Pisces, 28 degrees before Aries starts). The difference between Meṣādi and the present equinox is known as Ayanāṃśa - denoting by how much of a fraction of degrees & minutes the ecliptic has progressed from its fixed (sidereal) position. Given the 25,800 year cycle for the precession of the equinoxes, the equinox was directly opposite Spica in 285 CE, around the date of the Sūrya Siddhānta.^[2][3]
The nakṣatra-s with their corresponding regions of sky are given below, following Basham.^[4] As always, there are many versions with minor differences. The names on the right-hand column give roughly the correspondence of the nakṣatra-s to modern names of stars. Note that nakṣatras are (in this context) not just single stars but are segments on the ecliptic characterised by one or more stars. Hence there are more than one star mentioned for each nakṣatra.

#	Sanskrit	Malayalam name മലയാളം	Tamil name தமிழ்	Telugu name తెలుగు	Kannada name ಕನ್ನಡ	Western star name
1	Aśvinī अश्विनी	Ashvati അശ്വതി	Aswini அஸ்வினி	Ashwini అశ్విని	Ashwini ಅಶ್ವಿನಿ	β and γ Arietis
2	Bharaṇī भरणी	Bharaṇi ഭരണി	Baraṇi பரணி	Bharani భరణి	Bharaṇi ಭರಣಿ	35, 39, and 41 Arietis
3	Kṛttikā कृत्तिका	Kārttika കാർത്തിക	Kārthikai கார்த்திகை	Krittika కృత్తిక	Kruthike ಕೃತಿಕೆ	Pleiades
4	Rohiṇī रोहिणी	Rōhiṇi രോഹിണി	Rōhiṇi ரோகிணி	Rohini రోహిణి	Rohini ರೋಹಿಣಿ	Aldebaran
5	Mṛgaśiras म्रृगशीर्षा	Makayiram മകയിരം	Mirugasīridam மிருகசீரிடம்	Mrugashīra మృగశిర	Mrugashīra ಮೃಗಶಿರ	λ, φ Orionis
6	Ārdrā आद्रा	Ātira or Tiruvātira ആതിര (തിരുവാതിര)	Thiruvādhirai திருவாதிரை	Arudra ఆరుద్ర	Aridra ಆರಿದ್ರ	Betelgeuse
7	Punarvasu पुनर्वसु	Puṇartam പുണർതം	Punarpoosam புனர்பூசம்	Punarvasu పునర్వసు	Punarvasu ಪುನರ್ವಸು	Castor and Pollux
8	Puṣya पुष्य	Pūyam പൂയം	Poosam பூசம்	Pushyami పుష్యమి	Pushya ಪುಷ್ಯ	γ, δ and θ Cancri
9	Aśleṣā आश्ळेषा / आश्लेषा	Āyilyam ആയില്യം	Ayilyam ஆயில்யம்	Āshleshā ఆశ్లేష	Aslesha ಆಶ್ಲೇಷ	δ, ε, η, ρ, and σ Hydrae
10	Maghā मघा	Makam മകം	Magam மகம்	Makha మఖ	Makha ಮಖ	Regulus
11	Pūrva or Pūrva Phalguṇī पूर्व फाल्गुनी	Pūram പൂരം	Pooram பூரம்	Pūrva Phalgunī/Pubba పూర్వా ఫల్గుణి / పుబ్బ	Pubba ಪುಬ್ಬ	δ and θ Leonis
12	Uttara or Uttara Phalguṇī उत्तर फाल्गुनी	Utram ഉത്രം	Uthiram உத்திரம்	Uttara Phalgunī/Uttara ఉత్తర ఫల్గుణి / ఉత్తర	Utthara ಉತ್ತರ	Denebola
13	Hasta हस्त	Attam അത്തം	Astham அஸ்தம்	Hasta హస్త	Hastha ಹಸ್ತ	α, β, γ, δ and ε Corvi
14	Citrā चित्रा	Chittira (Chitra) ചിത്തിര (ചിത്ര)	Chithirai சித்திரை	Chitta చిత్త	Chittha ಚಿತ್ತ	Spica
15	Svāti स्वाति	Chōti ചോതി	Swathi சுவாதி	Swati స్వాతి	Swathi ಸ್ವಾತಿ	Arcturus
16	Viśākha विशाखा	Vishākham വിശാഖം	Visakam விசாகம்	Vishākhā విశాఖ	Vishakhe ವಿಶಾಖೆ	α, β, γ and ι Librae
17	Anurādhā अनुराधा	Anizham അനിഴം	Anusham அனுஷம்	Anurādhā అనూరాధ	Anuradha ಅನುರಾಧ	β, δ and π Scorpionis
18	Jyeṣṭha ज्येष्ठा	Kēṭṭa (Trikkēṭṭa) കേട്ട (തൃക്കേട്ട)	Kettai கேட்டை	Jyeshtha జ్యేష్ఠ	Jyesta ಜ್ಯೇಷ್ಠ	α, σ, and τ Scorpionis
19	Mūla मूल/मूळ	Mūlam മൂലം	Mūlam மூலம்	Mūla మూల	Moola ಮೂಲ	ε, ζ, η, θ, ι, κ, λ, μ and ν Scorpionis
20	Pūrvāṣāḍha पूर्वाषाढा	Pūrāṭam പൂരാടം	Pūradam பூராடம்	Pūrva Ashādhā పూర్వాషాఢ	Poorvashada ಪೂರ್ವಾಷಾಢ	δ and ε Sagittarii
21	Uttarāṣāḍha उत्तराषाढा	Utrāṭam ഉത്രാടം	Uthirādam உத்திராடம்	Uttara Ashādhā ఉత్తరాషాఢ	Uttharashada ಉತ್ತರಾಷಾಢ	ζ and σ Sagittarii
22	Śravaṇa श्रवण	Tiruvōnam ഓണം (തിരുവോണം)	Tiruvōnam திருவோணம்	Shravanam శ్రవణం	Shravana ಶ್ರವಣ	α, β and γ Aquilae
23	Śraviṣṭhā or Dhaniṣṭha श्रविष्ठा or धनिष्ठा	Aviṭṭam അവിട്ടം	Aviṭṭam அவிட்டம்	Dhanishta ధనిష్ఠ	Dhanishta ಧನಿಷ್ಠ	α to δ Delphinus
24	Śatabhiṣak or Śatatārakā शतभिषक् / शततारका	Chatayam ചതയം	Sadayam சதயம்	Shatabhishām శతభిషం	shathabhisha ಶತಭಿಷ	γ Aquarii
25	Pūrva Bhādrapadā पूर्वभाद्रपदा / पूर्वप्रोष्ठपदा	Pūruruṭṭāti പൂരുരുട്ടാതി	Pūraṭṭādhi பூரட்டாதி	Pūrva Bhādra పూర్వాభాద్ర	poorvabadhra ಪೂರ್ವಾ ಭಾದ್ರ	α and β Pegasi
26	Uttara Bhādrapadā उत्तरभाद्रपदा / उत्तरप्रोष्ठपदा	Uttṛṭṭāti ഉത്രട്ടാതി	Uttṛṭṭādhi உத்திரட்டாதி	Uttara Bhādra ఉత్తరాభాద్ర	Uttharabadhra ಉತ್ತರಾ ಭಾದ್ರ	γ Pegasi and α Andromedae
27	Revatī रेवती	Rēvati രേവതി	Rēvathi ரேவதி	Rēvati రేవతి	Revati ರೇವತಿ	ζ Piscium

Yoga

The Sanskrit word Yoga means "union," but in astronomical calculations it is used in the sense of "alignment." First one computes the angular distance along the ecliptic of each object, taking the ecliptic to start at Meṣa or Aries (Meṣādi, as defined above): this is called the longitude of that object. The longitude of the sun and the longitude of the moon are added, and normalized to a value ranging between 0° to 360° (if greater than 360, one subtracts 360). This sum is divided into 27 parts. Each part will now equal 800' (where ' is the symbol of the arcminute which means 1/60 of a degree). These parts are called the yogas. They are labeled:

1. Viṣkambha
2. Prīti
3. Āyuśmān
4. Saubhāgya
5. Śobhana
6. Atigaṇḍa
7. Sukarma
8. Dhṛti
9. Śūla
10. Gaṇḍa
11. Vṛddhi
12. Dhruva
13. Vyāghatā
14. Harṣaṇa
15. Vajra
16. Siddhi
17. Vyatipāta
18. Variyas
19. Parigha
20. Śiva
21. Siddha
22. Sādhya
23. Śubha
24. Śukla
25. Brahma
26. Māhendra
27. Vaidhṛti

Again, minor variations may exist. The yoga that is active during sunrise of a day is the prevailing yoga for the day.

Karaṇa

A karaṇa is half of a tithi. To be precise, a karaṇas is the time required for the angular distance between the sun and the moon to increase in steps of 6° starting from 0°. (Compare with the definition of a tithi above.)
Since the tithis are 30 in number, and since 1 tithi = 2 karaṇa, therefore one would logically expect there to be 60 karaṇa-s. But there are only 11 such karaṇa which fill up those slots to accommodate for those '30 tithi'-s. There are actually 4 "fixed" (sthira) karaṇa-s and 7 "repeating" (cara) karaṇa.
The 4 "fixed" karaṇa-s are:

1. Śakuni
2. Catuṣpāda
3. Nāga
4. Kiṃtughna

The 7 "repeating" karaṇa-s are:

1. Vava or Bava
2. Valava or Bālava
3. Kaulava
4. Taitila or Taitula
5. Gara or Garaja
6. Vaṇija
7. Viṣṭi (Bhadra)

• Now the first half of the 1^st tithi (of Śukla Pakṣa) is always Kiṃtughna karaṇa. Hence this karaṇa' is "fixed".
• Next, the 7-repeating karaṇa-s repeat eight times to cover the next 56 half-tithis. Thus these are the "repeating" (cara) karaṇa-s.
• The 3 remaining half-tithi-s take the remaining "fixed" karaṇa-s in order. Thus these are also "fixed" (sthira).
• Thus one gets 60 karaṇa-s from those 11 preset karaṇa-s.

The karaṇa-s at sunrise of a particular day shall be the prevailing karaṇa-s for the whole day. Note. The day changes at every sunrise i.e. from Sunrise 1 to Sunrise 2 - is 1 Vedic day.

Months of the lunisolar calendar

When a new moon occurs before sunrise on a day, that day is said to be the first day of the lunar month. So it is evident that the end of the lunar month will coincide with a new moon. A lunar month has 29 or 30 days (according to the movement of the moon).
The tithi at sunrise of a day is the only label of the day. There is no running day number from the first day to the last day of the month. This has some unique results, as explained below:
Sometimes two successive days have the same tithi. In such a case, the latter is called an adhika tithi where adhika means "extra". Sometimes, one tithi may never touch a sunrise, and hence no day will be labeled by that tithi. It is then said to be a Tithi Kṣaya where Kṣaya means "loss".

Month names

There are 12 months in Hindu lunar Calendar:

1. Chaitra (चैत्र) Meṣa (Aries)^[5]
2. Vaiśākha (वैशाख) Vṛṣabha (Taurus)^[6]
3. Jyaiṣṭha (ज्येष्ठ) Mithuna (Gemini)^[7]
4. Āṣāḍha (आषाढ ) Karka (Cancer)^[7]
5. Śrāvaṇa (श्रावण) Siṃha (Leo)^[7]
6. Bhādrapada or Bhādra also Proṣṭhapada (भाद्रपद,भाद्र,प्रोष्ठपद) Kanyā (Virgo)^[7]
7. Āśvina in,sometimes Aśvayuja ( आश्विन,अश्वयुज) Tula (Libra)^[7]
8. Kārtika (कार्तिक) Vṛścika (Scorpio)^[7]
9. Agrahāyaṇa or, Mārgaśīrṣa (मार्गशीर्ष,अग्रहायण) Dhanus (Sagittarius)^[7]
10. Pauṣa (पौष) Makara (Capricorn)^[7]
11. Māgha (माघ) Kumbha (Aquarius)^[7]
12. Phālguna (फाल्गुन)Mīna (Pisces)^[7]

Determining which name a lunar month takes is somewhat indirect. It is based on the rāshi (Zodiac sign) into which the sun transits within a lunar month, i.e. before the new moon ending the month.
There are 12 rāśi names, there are twelve lunar month names. When the sun transits into the Meṣa rāśi in a lunar month, then the name of the lunar month is Caitra. When the sun transits into Vṛṣabha, then the lunar month is Vaiśākha. So on.
If the transits of the Sun through various constellations of the zodiac (Rāśi) are used, then we get Solar months, which do not shift with reference to the Gregorian calendar. The Solar months along with the corresponding Hindu seasons and Gregorian months are:

(Rāśi) Saura Māsa (solar months)	Ṛtu (season)	Tamil name	Gregorian Tropical months	Sidereal Vedic Zodiac
Meṣa	Vasanta (spring)	இளவேனில்	Mar-Apr	Aries
Vṛṣabha			Apr-May	Taurus
Mithuna	Grīṣma (summer)	முதுவேனில்	May-June	Gemini
Karkaṭa			June-July	Cancer
Siṃha	Varṣā (monsoon)	கார்	July-Aug	Leo
Kanyā			Aug-Sept	Virgo
Tulā	Śarad (Autumn)	கூதிர்	Sept-Oct	Libra
Vṛścik‌‌‌a			Oct-Nov	Scorpius
Dhanu	Hemanta (Winter)	முன்பனி	Nov-Dec	Sagittarius
Makara			Dec-Jan	Capricornus
Kumbha	Śiśira (Cold)	பின்பனி	Jan-Feb	Aquarius
Mīna			Feb-Mar	Pisces

The Sanskrit grammatical derivation of the lunar month names Caitra etc., is: the (lunar) month which has its central full moon occurring at or near the Citrā nakṣatra is called Caitra. Another example is let's say when Pūrṇimā occurs in or near Viśākha nakṣatra, this in turn results to the initiation of the lunar month titled Vaiśākha Māsa.
Similarly, for the nakṣatra-s Viśākha, Jyeṣṭhā, (Pūrva) Āṣāḍhā, Śravaṇa, Bhādrapadā, Aśvinī (old name Aśvayuj), Kṛttikā, Mṛgaśiras, Puṣya, Meghā and (Pūrva/Uttara) Phalguṇī the names Vaiśākha etc. at pūrṇimā, the other Lunar names are derived subsequently.
The lunar months are split into two Pakṣas of 15 days. The waxing paksha is called Śukla Pakṣa, light half, and the waning paksha the Kṛṣṇa Pakṣa, dark half. There are two different systems for making the lunar calendar:

• Amāvāsyanta or mukhya mana system – a month begins with a new moon and ends at new moon, mostly followed in the southern states
• Pūrṇimānta or gauna mana system – a month begins with a full moon and ends at full moon, followed more in the North.

p.s. Pūrṇimānta is also known as Śuklānta Māsa. And this system is recommended by Varāhamihira.

Extra months (Adhika Māsa)

When the sun does not at all transit into any rāśi but simply keeps moving within a rāśi in a lunar month (i.e. before a new moon), then that lunar month will be named according to the first upcoming transit. It will also take the epithet of adhika or "extra". For example, if a lunar month elapsed without a solar transit and the next transit is into Meṣa, then this month without transit is labeled Adhika Caitra Māsa. The next month will be labeled according to its transit as usual and will get the epithet nija ("original") or Śuddha ("unmixed"). [Note that an adhika māsa (month) is the first of two whereas an adhika tithi is the second of two.]
Extra Month, or adhika māsa (māsa = lunar month in this context) falls every 32.5 months. It is also known as puruśottama māsa, so as to give it a devotional name. Thus 12 Hindu mas (māsa) is equal to approximate 356 days, while solar year have 365 or 366 (in leap year) which create difference of 9 to 10 days, which is offset every 3rd year. No adhika māsa falls during Kārtika to Māgh.
A month long fair is celebrated in Machhegaun during adhika māsa. It is general belief that one can wash away all one's sins by taking a bath in the Machhenarayan's pond.

Lost months (Kṣaya Māsa)

If the sun transits into two rāshis within a lunar month, then the month will have to be labeled by both transits and will take the epithet kṣaya or "loss". There is considered to be a "loss" because in this case, there is only one month labeled by both transits. If the sun had transited into only one raashi in a lunar month as is usual, there would have been two separate months labeled by the two transits in question.
For example, if the sun transits into Meṣa and Vṛṣabha in a lunar month, then it will be called Caitra-Vaiśākha kṣaya-māsa. There will be no separate months labeled Caitra and Vaiśākha.
A Kṣaya-Māsa occurs very rarely. Known gaps between occurrence of Kṣaya-Māsas are 19 and 141 years. The last was in 1983. January 15 through February 12 were Pauṣa-Māgha kṣaya-māsa. February 13 onwards was (Adhika) Phālguna.
Special Case:
If there is no solar transit in one lunar month but there are two transits in the next lunar month,

• the first month will be labelled by the first transit of the second month and take the epithet Adhika and
• the next month will be labelled by both its transits as is usual for a Kṣaya-Māsa

This is a very very rare occurrence. The last was in 1315. October 8 to November 5 were Kārtika Adhika-Māsa. November 6 to December 5 were Kārtika-Mārgaśīrṣa Kṣaya-Māsa. December 6 onwards was Pauṣa.

Religious observances in case of extra and lost months

Among normal months, adhika months, and kshaya months, the earlier are considered "better" for religious purposes. That means, if a festival should fall on the 10th tithi of the Āshvayuja month (this is called Vijayadashamī) and there are two Āśvayuja (Āśvina)' months caused by the existence of an adhika Āśvayuja, the first adhika month will not see the festival, and the festival will be observed only in the second nija month. However, if the second month is āshvayuja kshaya then the festival will be observed in the first adhika month itself.
When two months are rolled into one in the case of a kshaya māsa, the festivals of both months will also be rolled into this Kṣaya Māsa'. For example, the festival of Mahāshivarātri which is to be observed on the fourteenth tithi of the Māgha Kṛṣṇa-Pakṣa was, in 1983, observed on the corresponding tithi of Pauṣa-Māgha Kṣaya Kṛṣṇa-Pakṣa, since in that year, Pauṣa and Māgha were rolled into one, as mentioned above. When two months are rolled into one in the case of a Kṣaya Māsa, the festivals of both months will also be rolled into this kṣaya māsa.

Vaiṣṇava calendar

Main article: Gaurabda

Month	Predominating Deity-name of month
Agrahāyaṇa	Keśava
Pauṣa	Nārāyaṇa
Maghā	Mādhāva
Phālguna	Govinda
Caitra	Viṣṇu
Vaiśākha	Madhusudana
Jyeṣṭha	Trivikrama
Āṣāḍha	Vāmana
Śrāvaṇa	Śrīdhara
Bhādrapada	Hṛṣīkeśa
Āśvina	Padmanābha
Kārtika	Dāmodara

Om Tat Sat

                                                        

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