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History of Astronomy — Ancient India

Contents

• Hindu Flood Legends
• Indus-Saraswati Civilization
• Vedic Names
• Post-Vedic Sanskrit Texts
• Greek and Roman Chroniclers of India
• Hindu Cosmos
• The Hindu Nakshatras and Arabian Manazil
• Ancient Hindu Astronomers
• The Hindu Calendar

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Indus-Saraswati Civilization. In the 1800s, orientalist Max Müller, referring to the word "arya" (noble, lofty) in the Rig Veda, formed the notion of an ancient Aryan race. He guessed that these Aryans had entered India from the north around 1,200 BCE when he thought they composed the Rig Veda, but it was only a theory. Unfortunately, his theory became considered undipsutable fact after his death.

From 1873, archaeologists have uncovered traces of an ancient, well-organized civilization along the banks of the Indus and Saraswati Rivers. Today these sites are located across modern-day Afghanistan, Pakistan, and India. The "Aryan invasion" theory of the 1800s and 1900s (which we know today to be incorrect) explained that invading Aryan tribes must have invaded and replaced Harappan culture with Aryan culture. Yet Harappan seals depict meditating figures in yogic positions that might even represent Shiva, the Hindu god of the Himalayas and of ascetics. With new evidence discussed below, archaeologists now know that Hindus were living in India for a very long time, thousands of years before the Common Era.

The first of these discovered cities were the Mohenjo-Daro and Harappa communities, dating back possibly as early as 3,000 BCE. The main Harappan Period generally is dated from 2,600 to 1,900 BCE.

Measuring devices have been found in Mohenjo-Daro and other areas showing a base 10 counting system, unlike neighboring Sumerians but like Egyptians and later Indians. Weights have also been found in multiples of 2: 1, 2, 4, 8, etc., which is how Egyptians performed multiplication but again is culturally distinct from Sumeria. The standard weight at Harappa was 0.856 grams. Weight cubes existed in 1, 2, 4, 8, and 16 times this weight (16 times 0.856 grams is 13.7 grams, or a little over half an ounce). Larger weights of 137 grams and 1370 grams show increases by factors of 10.

The most common object found on Mohenjo-Daro seals is the unicorn, which later apeared in Greek and Roman art, and which Greek authors mentioned as living in India (such as Pliny in his "Natural History").

Seals have also been found in Mohenjo-Daro with the swastika, ancient symbol of the Sun and representing power and good fortune. The name comes from the Sanskrit "su" (good) + "asti" (to be) + "ka" (diminuitive suffix). This same symbol is a religious symbol among Hindus and Buddhists today. At one time, the swastika spread as far as ancient Troy, where it was called "tetraskelion" or "gammadion." The swastika was also used by Sumerians, but not by the later Babylonians.

The Harappan communities also buried their dead in wooden coffins, as was done by their contemporaries in the Middle East.

The significance of these shared mythical unicorn and other symbols, religious symbols like the swastika, and burial traditions among geographically diverse cultures shows communication and probably the sharing of many beliefs. If these cultures exchanged religious symbols and meanings, we could expect them to have also exchanged scientific ideas.

In the 1930s and 1940s, Adolf Hitler's Nazi Party used the swastika as the symbol of a supposed Aryan Race that invaded India from Europe. Today we know this migration from Europe could not have occurred, as much of Europe was covered with glaciers in the early days of Mesopotamia.

Today, more people believe that there was no "Aryan invasion" in India, and in fact the ancestral land of the composers of India's Vedas was India itself. Vedic India seems to have developed a culture and science distinct from neighboring Mesopotamia, though archaeological finds show that these cultures traded grain and goods.

In 1974, 101 years after the first discovery of Harappan civilization, French archaeologist Jean-François Jarrige was digging at the base of a pass through the hills of Baluchistan, Pakistan at a location along the Bolan River, called Mehrgarh. He unearthed a city that had been occupied continuously from 6,800 BCE to about 2,000 BCE. This unbroken occupation has made the site invaluable in tracing cultural developments in the area.

Early Mehrgarh dwellers were Neolithic until around 5,500 BCE, when pottery began to appear. From the beginning, dwellings were aligned with the four cardinal directions (North, East, South, West). For the first thousand years, corpses were buried in the fetal position surrounded with personal possessions and food. This clearly shows a religious belief in an afterlife, as in ancient Egypt. Bodies were buried with their heads towards the East and feet towards the West.

Although several hundred miles inland, Mehrgarh inhabitants used seashells as beads and for other purposes, showing a maritime affiliation.

Scholars are now trying to decipher the scripts and seals used at these locations. Some have claimed to successfully show the scripts are based on a Sanskrit-like language. There are seals that some believe deptic the Sun, Moon, and constellations such as the Pleiades. However, no one interpretation has been accepted as authoritative.

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Vedic Names. The Vedas are the oldest surviving Hindu scriptures. There are four vedas: Rig Veda, Yajur Veda, Sama Veda, and Atharva Veda. Of these, the Rig Veda is the oldest and the Atharva Veda the most recent (although the later parts of the Rig Veda mention the Yajur and Sama Vedas, for example RV 10.90.9).

Of the books of the Rig Veda, Book 1 is recognized as the oldest. The first mention of Saraswati, as a goddess and flodding river, appears in RV 1.3:

10. Wealthy in spoil, enriched with hymns, may bright Saraswati desire,
With eager love, our sacrifice.
11. Inciter of all pleasant songs, inspirer of all gracious thought,
Saraswati, accept our rite!
12. Saraswati, the mighty flood, — she with her light illuminates,
She brightens every pious thought.

The glacial melt of the Himalayas fed the Saraswati with her fresh water. By around 8,000 BCE, the flow of glacial meltwater was so great that the Saraswati flowed to the sea. A couple of thousand years later, the Saraswati was still mighty, but no longer ran to the ocean.

By about 3,000 BCE, this flow began to decrease. The Saraswati is thought to have dried up around 2,000 BCE. This timeline correlates with Harappan villages being abandoned about 1,900 BCE (with the assumption that they were Vedic communities). This chronology provides the latest possible dates for the Rig Veda. Had the Rig Veda been composed any later, the Saraswati would not have been described as a mighty river.

The mighty Saraswati is mentioned throughout the Rig Veda, which thus must have been composed long ago. Hindus have always said that India is their ancestral home. Recent archaeological and geological discoveries are proving this to be true.

Seven celestial bodies were known since Vedic times to move faster than the background of the stars: the Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn.

At some point, knowledge also developed of the nodes of all the planets (see the citation of Arybhata I below, under Ancient Indian Astronomers). The nodes are those points where a planet or the Moon crosses the ecliptic (the Earth's orbital plane around the Sun) going north or south of the ecliptic. The North Node is the point where a planet or Moon crosses from south of the ecliptic to north of the ecliptic. The South Node is the point where a planet or Moon crosses from north of the ecliptic to south of the ecliptic.

When the Moon crosses the ecliptic at the same time the Sun is visible, there will be an eclipse. Knowledge of the Moon's Nodes is reasonable evidence of an understanding of eclipses in ancient cultures. The Vedas have a special name for the Moon's North Node (Rahu) and the Moon's South Node (Ketu). Vedic Indians therefore probably possessed knowledge of the nature of eclipses.

The Vedic names of the Navagraha (nine (nava) planets (graha)) are:

Hindu texts speak of Pravaha, a celestial wind, being the force that moves that planets.

Sunspots seem to be mentoined as early as the Upanishads, unless the reference is to Mercury and Venus transiting the Sun. For example, Chandogyopanishad 3.3.3 says:

It flowed forth; it settled by the side of the Sun.
Verily, it is that appears as the black form in the Sun.

The Sun's eye keeps revolving;
On it depends all the worlds.

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Post-Vedic Sanskrit Texts. The Vedas date back thousands of years. We do not know exactly how old they are. A much later work, the Mahabharata (and the Bhagavad Gita that it contains) can be approximately dated.

The Bhagavad Gita tells of how Sri Krishna established the capitol of his kingdom in Dwarka. The Gita relates that after his death, Krishna's follower, Arjuna, brought Krishna's relatives away from Dwarka. At that point, the city became submerged by the rising ocean.

In the 1981, the submerged city of Dwarka was discovered off the coast of the modern-day Indian state of Gujarat. Pottery and other artifacts in this submerged city have been dated using carbon dating, thermo-luminescence dating, and other techniques. These methods date Dwarka as approximately 3,500 years old.

Other ancient Hindu texts maintain that the present age ("yuga," or world cycle) began on midnight between February 17 and 18 in 3102 BCE (in the proleptic Julian calendar), and so many Hindus believe this is the date for the Mahabharata. Some have speculated that there are ruins further offshore at Dwarka that have not yet been explored dating back to that time. Today there is no evidence to prove or disprove this conjecture.

The Vedas have a more complex grammatical structure than the Mahabharata, making their language far older.

The Mahabharata, contains numerous references to cosmology. For example, Mahabharata 3.43.30 describes the stars:

The luminous stars, though really very large, appear small, and twinkle like lamps on account of their great distance.

Manu is the Hindu legendary father of mankind, mentioned in the Rig Veda. He codified laws and described the yugas (world cycles) in his Manu Smriti. Chapter 1 contains these verses (text in parentheses was added in Buhler's standard translation in 1886):

64. Eighteen nimeshas (twinklings of the eye, are one kashtha), thirty kashthas one kala, thirty kalas one muhurta, and as many (muhurtas) one day and night.
65. The sun divides days and nights, both human and divine, the night (being intended) for the repose of created beings and the day for exertion.
66. A month is a day and a night of the manes, but the division is according to fortnights. The dark (fortnight) is their day for active exertion, the bright (fortnight) their night for sleep.
67. A year is a day and a night of the gods; their division is (as follows): the half year during which the sun progresses to the north will be the day, that during which it goes southwards the night.
68. But hear now the brief (description of) the duration of a night and a day of Brahman and of the several ages (of the world, yuga) according to their order.
69. They declare that the Krita age (consists of) four thousand years (of the gods); the twilight preceding it consists of as many hundreds, and the twilight following it of the same number.
70. In the other three ages with their twilights preceding and following, the thousands and hundreds are diminished by one (in each).
71. These twelve thousand (years) which thus have been just mentioned as the total of four (human) ages, are called one age of the gods.
72. But know that the sum of one thousand ages of the gods (makes) one day of Brahman, and that his night has the same length.
73. Those (only, who) know that the holy day of Brahman, indeed, ends after (the completion of) one thousand ages (of the gods) and that his night lasts as long, (are really) men acquainted with (the length of) days and nights.
...
79. The before-mentioned age of the gods, (or) twelve thousand (of their years), being multiplied by seventy-one, (constitutes what) is here named the period of a Manu (Manvantara).
80. The Manvantaras, the creations and destructions (of the world, are) numberless; sporting, as it were, Brahman repeats this again and again.
81. In the Krita age Dharma is four-footed and entire, and (so is) Truth; nor does any gain accrue to men by unrighteousness.
82. In the other (three ages), by reason of (unjust) gains (agama), Dharma is deprived successively of one foot, and through (the prevalence of) theft, falsehood, and fraud the merit (gained by men) is diminished by one fourth (in each).
83. (Men are) free from disease, accomplish all their aims, and live four hundred years in the Krita age, but in the Treta and (in each of) the succeeding (ages) their life is lessened by one quarter.
84. The life of mortals, mentioned in the Veda, the desired results of sacrificial rites and the (supernatural) power of embodied (spirits) are fruits proportioned among men according to (the character of) the age.
85. One set of duties (is prescribed) for men in the Krita age, different ones in the Treta and in the Dvapara, and (again) another (set) in the Kali, in a proportion as (those) ages decrease in length.
86. In the Krita age the chief (virtue) is declared to be (the performance of) austerities, in the Treta (divine) knowledge, in the Dvapara (the performance of) sacrifices, in the Kali liberality alone.

The common interpretation today is that Manu described the lengths of the ages in years of the gods, each of which is 360 of our years. The dawn and twilight of each age are a tenth of the time of the age. Literally, he describes the ages, with their dawn and twilight periods, as Krita (4800 years), Treta (3600 years), Dwapara (2400 years), and Kali (1200 years). He also describes a day and a night of the gods being the length of a solar year, with the day being the time the Sun moves North and the night being the time the Sun moves South. This is a little longer than the 360 days that chroniclers use today. The following durations result from these interpretations:

Some believe that the shorter cycle refers to the precession of the equinoxes, which lasts approximately 26,000 years. The Surya Siddhanta and other astronomical texts use the longer cycles of 360 human years in a year of the gods.

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Greek and Roman Chroniclers of India. Pliny (23-79 CE), in his Natural History 6.21, tells us of India that:

It was opened up to our knowledge not only by the arms of Alexander the Great and of the kings who succeeded him, Seleucus and Antiochus, as well as by their admiral Patrokles who sailed round even into the Hyrcanian and Caspian seas, but also by certain Greek authors, who resided with Indian kings, such as Megasthenes, and Dionysius who was sent by Philadelphus, and have thus informed us of the power and resources of the Indian nations. However, there is no room for a careful examination of their statements, they are so diverse and incredible. The companions of Alexander the Great have written that in that tract of India, which he subdued, there were 5000 towns, none less than Cos — that its nations were nine in number — that India was the third part of all the world, and that the multitude of its inhabitants was past reckoning. For this there was probably a good reason, since the Indians almost alone among the nations have never emigrated from their own borders. Their kings from Father Bacchus down to Alexander the Great are reckoned at 153 over a space of 6451 years and three months.

Third Century Roman Gaius Julius Solinus, in his Of the Wonders of the World, 53 makes similar statements:

The Father [Bacchus] was the first who invaded India, and was the first of all who triumphed over the vanquished Indians. From him to Alexander the Great 6451 years are reckoned with 3 months additional, the calculation being made by counting the kings who reigned in the intermediate period, to the number of 153.... But those who live near the sea have no kings. The Pandaean nation is governed by females, and their first queen is said to have been the daughter of Hercules. The city Nysa is assigned to this region, as is also the mountain sacred to Jupiter, Meros by name, in a cave on which the ancient Indians affirm Father Bacchus was nourished; while the name has given rise to the well known fantastic story that Bacchus was born from the thigh of his father.

The second century Macedonian Polyaenus, in Strategemata I.1.1-3, relates how Dionysos named the mountain Meros mentioned above by Solinus:

Dionysos, in the course of his Indian campaign, seeing that his army could not endure the fiery heat of the air, took forcible possession of the three-peaked mountain of India. Of these peaks, one is called Korasibie, another Kondaske, but to the third he himself gave the name of Meros, in remembrance of his birth. Thereon were many fountains of water sweet to drink, game in great plenty, tree-fruits in unsparing profusion, and snows which gave new vigour to the frame.

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Hindu Cosmos. In addition to developing very exact astronomical methods, ancient Hindus also expressed deep thoughts about the cosmos and the nature of our existence. Perhaps the most celebrated explanation of the infinite Brahman (God) and his creation is this Sanskrit verse, which appears at the beginning of Ishopanishad (Isha Upanishad) and elsewhere:

Purnamadah purnamidam
Purnat purnamudachyate
Purnasya purnamadaya
Purnamevavashishyate.

The most famous mantra (invocation) is the Gayatri Mantra, which dates back to the Rig Veda. This mantra is so important it is also called Vedamatri (the Mother of the Vedas). Vedic priests then and today recite this invocation to the Sun as the giver of life and intelligence. The metre is the 24-syllable Gayatri metre; hence the name of this verse, the Gayatri Mantra (Rig Veda, 3.62.10):

[Om, bhur, bhuvah, swaha]
Tat savitur varenyam
Bhargo devasya dhimahi
Dhiyo yo nah prachodayat.

The Rig Veda bestows upon the Sun the title "Lord of the Universe", in RV 8.59.2:

The One Sun is the Lord of the Universe.
One Dawn, it lights up all this.

The Rig Veda 10.90 (Yajur Veda 31) contains a story of the Creation. RV 10.90.14-15 (YV 31.12-13) mentions the Earth, Moon, and Sun:

12. The Moon was gendered from his mind, and from his eyes the Sun had birth;
Vayu and Prana from his ear, and from his mouth was Agni born
13. Forth from his navel came mid-air; the sky was fashioned from his head;
Earth from his feet, and from his ear the Quarters, Thus they formed the worlds.

On the origin of the Universe, the Rig Veda, Book 10 Hymn 72 contains this remarkable description of gods producing "with blast and smelting, like a smith," with an overseeing Productive Power creating the Earth out of "a thickening cloud of dust" and speaks of Surya (the Sun) being born from a sea:

1. Let us with tuneful skill proclaim these generations of the Gods,
That one may see them when these hymns are chanted in a future age.
2. These Brahmanaspati produced with blast and smelting, like a smith,
Existence, in an earlier age of Gods, from Non-existence sprang.
3. Existence, in the earliest age of Gods, from Non-existence sprang.
Thereafter were the regions born. This sprang from the Productive Power.
4. Earth sprang from the Productive Power; the regions from earth were born.
Daksha [Power personified] was born of Aditi [the Infinite], and Aditi was Daksha's Child.
5. For Aditi, O Daksha, she who is thy Daughter, was brought forth.
After her were the blessed Gods born sharers of immortal life.
6. When ye, O Gods, in yonder deep close-clasping one another stood,
Thence, as of dancers, from your feet a thickening cloud of dust arose.
7. When, O ye Gods, like Yatis, ye caused all existing things to grow,
Then ye brought Surya forward who was lying hidden in the sea.
8. Eight are the Sons of Aditi who from her body sprang to life.
With seven she went to meet the Gods: she cast Martanda [the Sun] far away.
9. So with her Seven Sons Aditi went forth to meet the earlier age.
She brought Martanda thitherward to spring to life and die again.

The Rig Veda 10.129.1-7 speaks more on the the creation of the Universe:

1. Then was not non-existent nor existent:
there was no realm of air, no sky beyond it.
What covered in, and where? and what gave shelter?
What water there, unfathomed depth of water?
2. Death was not then, nor was there aught immortal:
no sign was there, the day's and night's divider.
That One Thing, breathless, breathed by its own nature:
apart from it was nothing whatsoever.
3. Darkness there was: at first concealed in darkness
this All was indiscriminated chaos.
All that existed then was void and formless:
by the great power of Warmth was born that Unit.
4. Therefore rose Desire in the beginning,
Desire, the primal seed and germ of Spirit
Sages who searched with their heart's thought
discovered the existent's kinship in the non-existent.
5. Transversely was their severing line extended:
what was above it then, and what below it?
There were begetters, there were mighty forces,
free action here and energy up yonder.
6. Who verily knows and who can here declare it,
whence it was born and whence comes this creation?
The Gods are later than this world's production.
Who knows then whence it first came into being?
7. He, the first origin of this creation,
whether he formed it all or did not form it.
Whose eye controls this world in highest heaven,
he verily knows it, or perhaps he knows not.

The Rig Veda continues to describe that in the beginning there was darkness, then water was created, then the Sun, Moon, sky, and Earth. Rig Veda 10.190.1-3:

1. Truth and truthfulness were born from intense penance.
Hence was darkness born and thence the watery ocean.
2. From the watery ocean was born the year,
ordaining days and nights, the controller of every living moment.
3. The Creator then created, in due order, the Sun, the Moon,
the sky, the earth and the regions of the air and light.

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The Hindu Nakshatras and Arabian Manazil. Ancient Hindus divided the stars into 28 or 27 nakshatras (asterisms), to mark the approximately 27 or 28 sidereal days in a Lunar Month. The word nakshatra could originate from the Rig-Vedic Sanskrit nak, meaning "night," and shatra, meaning "altogether, always") or from na (name of Moon) and kshetra (place, mansion). Originally, Hindus divided the ecliptic into 28 nakshatras. Arabian astronomers later used 28 Manazil-Al-Kamar, "Mansions of the Moon." These divisions are shown in the following table. The Chinese adopted a division they called hsiu that was similar to the nakshatras, but these divisions had unequal lengths and so are not listed below.

The sidereal lunar month (the time it takes the Moon to return to the same position among the stars) is closer to 27 days than 28 days (about 27.322 days). At some point, Hindu astronomers began skipping the Abhijit nakshatra and using a division of 27 nakshatras, though even today both 27 and 28 nakshatra systems are in use.

Each nakshatra in the 27-sign division is 360°/27 = 13°20'. Each nakshatra had its principal star. Hindu astronomers also used the 12-sign Zodiac. Using the 12-sign Zodiac and the 28-sign (and later 27-sign) nakshatra division helped them to track celestial bodies under the time scales of both the Sun and the Moon.

A nakshatra is further divided into four equal padas, each being 3°20'. (Pada in Sanskrit means "legs," as in the four legs of a quadrupedal animal, or "a quarter" or "quadrant.") The number of padas in the ecliptic with twenty-seven nakshatras amounts to four times twenty-seven, or 108 padas. The number 108 appears often in Hindu and Buddhist philosophy. The significance of this number might have influenced dropping one of the original nakshatras, or the change could simply have been because the sidereal lunar month is closer to 27 days than to 28 days. The change could also have been made because the "draconic month," during which the Moon's nodes (the "dragons") revolve, is also closer to 27 days (about 27.21 days).

Ancient Hindus devised a scheme to track the lunar days. They refer to a lunar day as a "tithi," with 15 tithis assigned to the bright half of the lunar month ("shukla paksha"), when the Moon is waxing, and 15 tithis assigned to the dark half of the lunar month ("krishna paksha"), when the Moon is waning. The tithi is a measure of the phase of the Moon, which is also a measure of the difference in longitude between the Sun and the Moon.

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Ancient Hindu Astronomers.

The Sanskrit word "jyotish" referred to the study of astronomy and astrology both; as in other cultures of the day, astronomy and astrology were considered inseperable. One of the oldest works on jyotish is the Vedanga-jyotisha, probably written by Lagadha. He most likely compiled techniques and observations from manuscripts that existed in his day.

The work that survives was probably rewritten by later astronomers around 400 BCE, judging from the work's clasical (post-Vedic) Sanskrit. However, this work contains an observation that the Winter Solstice occurred when the star Shravishtha (α Delphini) was on the horizon. This dates the original work around 1400 BCE, placing it in the late Vedic period.

The astronomical methods outlined in the Vedanga-jyotisha were thus in use in India for a long time, a thousand years before the fourth-century BCE invasion of Alexander the Great.

After the Vedanga-jyotisha, several important astronomical treatises were written following the invasion of Alexander the Great. These came to be called siddhantas, meaning "highest knowledge" or "culmination of knowledge." There are eighteen traditional siddhantas:

Around 505 CE, the famous Indian astronomer Varahamihira codified five of these siddhantas in his Panchasiddhantika ("five little siddhantas"). The five siddhantas thus codified were: Surya, Paitamaha, Vasishtha, Romaka, and Paulisha Siddhantas. Of these five, Varahamihira stated that the Surya Siddhanta was the most accurate, then the Paulisa and Romaka; he mentioned the Paitamaha and Vasishtha being inaccurate.

Varahamihira described the Earth as spherical and as being suspended in space in the Panchasiddhanta 13.1:

The spherical Earth, which is constituted of the five elements, stands poised in the region of space as if it is an iron ball held in position in a cage of magnets.

Varahamihira, like many other Hindu astronomers of his day, used as a reference meridian the city of Ujjain (the Avantika of the Upanishads and Puranas), located at 23°11' North Latitude and 75°47' East Longitude, at an elevation of 489 meters. Other Indian astronomers used Kanchipuram and the battlefield of the Bhagavad Gita, Kurukshetra, as zero meridians.

One popular reason for using Ujjain as the prime meridian was that it shared the same longitude as Lanka (now Sri Lanka). Bhaskara I, in his Laghubhaskariya 1.23, declares:

The line which pases though Lanka, Vatsyapura, Avanti [i.e., Ujjain], Sthaneshwara, and Meru (the abode of the gods) is the prime meridian.

Varahamihira correctly identified the time of noon being determined by longitude, and the length of a day being determined by latitude. For example in the Panchasiddhanta 13.17, he states:

The midday of Lanka is the same as that at Ujjain, which is north of Lanka on the same longitude. But their day-time durations are different, except when the Sun is on the equator.

The Surya Siddhanta that survives today could differ from the one that Varahamihira used. It has definitely been altered from its original form in some places; for example, it gives the longitude of Chitra (Spica) as exactly 180° in the sidereal zodiac, which does not correlate with other listed star positions.

The Surya Siddhanta version that has reached us discusses planetary mean motion, true motion, eclipses of the Sun and Moon, planetary heliacal rising and setting, time measurement, and other aspects of astronomical science. It also discusses precession of the equinoxes, and gives a figure of 54 arcseconds per year — close to the actual 50.2 arcseconds. However, it incorrectly considers this motion to oscillate back and forth like a pendulum. Older works possibly describe a circular precession movement.

Varahamihira wrote another astronomical text, his Brihat Samhita.

Countless Indian astronomers studied the work of Varahamihira and made their own observations. The most famous astronomers besides Varahamihira, who wrote treatises of their own, were: Aryabhata I (5th-6th century and Varahamihira's contemporary, born ca. 476 CE in Kerala, India); his student, Prabhakara (6th century); Bhaskara I (6th-7th century); Brahmagupta (6th-7th century); and Devacharya (circa 689 CE).

Aryabhata I studied astronomy at the ancient observatory in Khagol and the University at Nalanda. He added many original ideas to the established wisdom of his day. He described the heliocentric Solar System, demonstrated why the Earth was a sphere (from the Earth's shadow on the Moon), explained methods for calculating and correcting eclipse predictions, stated that the Moon's light was actually reflected sunlight, and codified much of the knowlege of trigonometric laws. His Aryabhatiya (composed in 499 CE) was studied by famous Arabian astronomers such as al-Biruni and al-Khwarizmi, and spread from Arabia to Europe when translated into Latin in the 13th century.

By the time of Aryabhata I, knowledge of the planets' and Moon's nodes. For example, in Aryabhatiya 4.1-3, he writes:

1. One half of the ecliptic, running from the beginning of the sign Aries to the end of the sign Virgo, lies obliquely inclined northwards. The remaining half running from the beginning of the sign Libra to the end of the sign Pisces, lies southwards. 2. The Nodes of the star-planets [Mercury, Venus, Mars, Jupiter, and Saturn] and of the Moon incessantly move on the ecliptic. So also does the Sun. From the Sun, at a distance of half a circle, moves theron the shadow of the Earth. 3. The Moon moves to the north and to the south of the ecliptic from its Nodes. So also do the planets Mars, Jupiter, and Saturn. Similarly also the motion of the shighroccas of Mercury and Venus.

Aryabhata I knew that the Earth revolved during the course of a day, but Bhaskara I did not believe this was true. The 8th-9th Century Prithudaka Swami, in his commentary on the Brahmasphuta-Siddhanta, Goladipika 30, wrote:

The Earth's rotation had been accepted by Aryabhata also, vide his words 'The Earth rotates through one arcsecond per one prana' (Aryabhatiya 1.6). On account of adverse criticism by people, Bhaskara I and others explained the verse to give it a different meaning.

Beneath the asterisms [Nakshatras] lie Saturn, Jupiter, Mars, the Sun, Venus, Mercury, and the Moon; and beneath them all lies the Earth like the hitching peg in the midst of space.

39. Beyond the Moon are orbiting higher and higher: Mercury, Venus, the Sun, Mars, Jupiter and Saturn, and beyond that there are fixed stars. All the planets move in their own individual orbita at a constant speed. 40. Just as the spokes of the oil-press wheel are close to one another near the navel, and the space between one another increases as the rim is approached, so the linear extension of the rashi [zodiac sign] increases as the orbits are situated higher and higher. 41. Situated near-most, the Moon goes round in the shortest time, its orbit being the shortest. But Saturn situated farther-most, in its longest orbit, cannot move so fast, that is moves slowet.

Devacharya (6th-7th Century) is notable as the first astronomer to describe a method for calculating the precession of the equinoxes; Varahamihira knew of precession, but was not certain of its rate. Aryabhata I and Brahmagupta do not mention precession, while Bhaskara I did not believe in it.

Like Ptolemy, Hindu astronomers used epicycles (small circular motions within the larger circular orbit around the Earth) to describe the motion of the planets in a geocentric Solar System. One method of epicycles ("manda" in Sanskrit) was given in the Surya Siddhanta. The 15th Century Nilakantha Somayaji, in Siddhantadarpana 4.18.1.19-21, explains the operation of epicycles:

19. The circles along which the planets take place, move on the epicycle of the equation of the center with the velocity of the higher apses. In the case of the Sun and the Moon it has its center at the center of the Earth-sphere. 20. For the other [planets] the center moves on the epicycle of the equation of conjunction, with the mean velocity of the Sun. The center of their fast ("shighra") epicycle is the center of the globe itself and these are not oblique to the ecliptic. 21. In the case of Mercury and Venus, their own orbits are stated to be the same as their shighra epicycles. In the case of these, the increase and decrease of the manda epicycles alone are according to the hypotenuse.

With the invasion of the Moghuls, astronomy in India stagnated for some time. In an effort to try to revive India's past glory in astronomy, Raja Jai Singh (1686-1743) sought to build new observatories. One impetus was to improve the tables used for calendrical calculations. Those tables were composed by Ulugh Beg (1394-1449 CE), the Mongolian ruler of Samarkand in modern-day Uzbekistan and builder of the greatest astronomical observatory of his day in 1424.

Jai Singh built five observatories, known as Jantar Mantar, in Delhi (built in 1721-1724), Jaipur (his capital, built circa 1728-1734), Mathura and Ujjain (built circa 1723-1734), and Benares (completed circa 1737). He fashioned these observatories after the old design of a large circle, from which one could observe the 2160 divisions (360 degrees times 60 minutes/degree = 2160 arcminutes). He experimented with European telescopes, but found their mounts too unsteady to produce reliable observations.

Jai Singh worked under the patronage of the local ruler, Muhammad Shah. Using his observatories with instruments of his own design. He described these instruments in his work "Yantra Prakara," completed in 1729. He produced a corrected set of astronomical tables, Zij-i Muhammad Shahi ("The astronomical tables of Muhammad Shah"), from 1725-1735 CE.

In fact, these tables were the last of the era of producing "zij," or "astronomical tables," from the siddhantas. This zij-producing era began in 9th Century Bagdad, with the Arabic translation of Brahmagupta's works, finally ending with Jai Singh's tables of 1735.

Unfortunately, Jai Singh lived in the days when the Moghul empire was in decline and European invaders were making their way across India. Thus world events took priority over the leisurely pursuit of astronomical science, and his observatories fell into disuse. Today, however, his observatories in Delhi, Jaipur, Ujjain, and Benares still exist, as a reminder of India's millenia-long astronomical tradition.

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The Hindu Calendar. The Hindu calendar, like most ancient calendars, depends upon astronomical events to fix the dates of religious festivals. These events are largely related to the Sun and the Moon. A Hindu religious calendar is called a "panchang" (from "panch" five, indicating five parts). The five parts of a panchang are: tithi, wara, nakshatra, yoga, and karana.

Tithis and Nakshatras are described above, in the Nakshatra section.

Wara is the day of the week for each day:

1. Raviwara (Sunday), ruled by the Sun
2. Somawara (Monday), ruled by the Moon
3. Mangalwara (Tuesday), ruled by Mars
4. Budhawara (Wednesday), ruled by Mercury
5. Guruwara (Thursday), ruled by Jupiter
6. Shukrawara (Friday), ruled by Venus
7. Shaniwara (Saturday), ruled by Saturn

There are 27 yogas, each 13°20', just as there are 27 nakshatras. To determine the yoga, the longitude of the Moon and the Sun are added. The resulting longitude of 0-360° determines the yoga number, 1-27.

The last of the five parts of a panchang is the karana. A karana is a half of a tithi (lunar day).

Together these five parts of the panchang (nakshatra, tithi, wara, yoga, and karana) allow priests to determine the proper dates for festivals, and determine whether a day is auspicious or inauspicious.

Traditionally, Hindu priests set dates for festivals according to local calendars and customs. After Independence, India sought to unify these practices into a national calendar. One hurdle was the aforementioned ayanamsa, which is the difference between the sidereal zodiac and the tropical zodiac.

From the days of the Rig Veda, the Hindu calendar has always been based on the sidereal zodiac. However, priests differed as to the beginning (the First Point of Aries). Some held that Revati (ζ Piscium) was at 0° sidereal longitude; others believed that Revati was 10' before the First Point of Aries. Still others held that Chitra (Spica) had a sidereal longitude of exactly 180°.

None of the ancient Hindu astronomers knew of the proper motion of stars, whereby they move slightly in relation to each other over time. To truly fix the starting point of an historical calendar, one must know the date at which a specified longitude of a star was given. For Sanskrit texts, this can often only be guessed.

Having to adopt some convention, the Government of India chose the position of Chitra (Spica) in 1950 CE as exactly 180° sidereal longitude. Of course, no ancient Hindu calendar could have been based on the position of Spica in 1950, but it serves as a convention for government holidays. This compromise was proposed by N.C. Lahiri, and so this ayanamsa is referred to as the "Lahiri ayanamsa."

Today Hindu priests still follow calculations for panchangas using the various sidereal zodiacs mentioned above, set according to local time, but this is heavily influenced by the Indian Government's standard of the Lahiri ayanamsa.

Years are numbered in various conventions. One convention is the year of the Common Era (Christian Era). Another common starting date is the Saka Era (79 CE), when Persian tribes invaded northern India. Still another is years of the commonly accepted Kali Yuga date, midnight between 17 and 18 February 3102 BCE. Hence some modern calendars might give the year 2005 CE as "Year 5107 of Kali Yuga." That is based on the interpretation that Kali Yuga is 432,000 years (360 times 1200 years), rather than just 1200 years.

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