Showing posts with label vedic astrology. Show all posts
Showing posts with label vedic astrology. Show all posts

Saturday, December 19, 2015

Ancient Indian Astrophysics and Time

"Temporal notions in Europe were overturned by an India rooted in eternity. The Bible had been the yardstick for measuring time, but the infinitely vast time cycles of India suggested that the world was much older than anything the Bible spoke of. It seem as if the Indian mind was better prepared for the chronological mutations of Darwinian evolution and astrophysics." 

He has commented on the wise division of life in India: "Here is a philosophy far removed from the grotesque refusal to grow old in the West, where wisdom has been replaced by cosmetic surgery and psychiatric help."

"The Indian tradition, on the other hand, is that men submit to nature and form part of it, there nature preserves its sacredness, lost in the West since the Industrial Revolution." He further states that the idea of feminism and ecology came from the 1968 movement, from the meeting between India and the West. He says: "There is hardly anything in European thought to predispose the West to reject virility, the respect for authority, the mastery over nature. India too has a warrior (khastriya) tradition of virility as exemplified in the Mahabharata, only it is secondary. First, comes the veneration of thousands of goddesses - for the Indians, India is above all Mother India. India's femininity and sexual ambiguity, is the very antithesis of Western virility. For example, when the British scaled earth's highest peak, the exploit was widely hailed as the "conquest of the Everest." It was not realized and is often not realized still, that the word "conquest" was totally out of place in the context of the peak which is considered an object of reverence by many.

"The Brahmins attached to knowledge and learning is what has helped the Indian civilization endure and allowed the arts to flourish. If comparisons have to be made, it may be said that the endurance of the Brahmins in India has kept her elite intact, whereas in neighboring China the anti-intellectualism of communist peasants has completely wiped out the intelligentsia of that country. The Brahmins kept knowledge and art alive in India, preserving not only their savant but also their popular forms. The Brahmin elite is perhaps egoistical and domineering, nonetheless it has preserved a sense of dignity and beauty that has disappeared from China where all that remains is vulgarity and crass ignorance."

"The more decentralized, diversified and ritualized a religion is the better it can withstand the onslaught of rationalist thought. Hinduism, derives its strength from the fact that it is not a single unified religion but the sum total of thousands of local faiths. Every village has its own cult, rooted in the local culture without any universalistic pretensions."

"India is a marvelous example of the art of living together at a time when Westerners are apprehensive about the future of their society."

"You cannot be a Hindu fundamentalist. It does not mean anything...The concept of fundamentalism does not exist in Hinduism." No one man embodies the spirit of universalism, it runs through the whole of India and there is a place for all religious groups and communities. The spiritual message of India is her capacity to let so many divergent practices coexist. The Enlightenment philosophers seemed to have grasped this profound originality...This the real message of India."

He says, "India has a strong cultural image in the west; unfortunately, it is not being commercially exploited." This should sink into the heads of those of us who are happy to be third-rate imitators of the US.

Sorman asserts that India is not a rogue state when he talks of the nuclear option. But there seem to be some Indians who are not so sure of their own country. He points out that "Nobody knows what is right. Each civilization...has its sense of the right. No one can impose his perception of right over others."

"Each Indian looks for God in his own way and worships one or several of the millions of deities who are the supposed reincarnation or expression of God, a Spirit or a Force. This has never led to a religious war. There have been communal clashes, but India has never had to face religious wars or crusades save those that were thrust on it from outside. The multiple revelation of the East has proved to be in many ways more advantageous than the single revelation of the West."

(source: The Genius of India - By Guy Sorman (Le Genie de l'Inde) Macmillan India Ltd. 2001. ISBN 0333 93600 0 p.195 , 122).

Friday, November 27, 2015

Hindu cosmology & Astronomy -Part 3

`Veda' means knowledge. And Yoga-
Patanjali Yoga Sutra 1:2
Yogas chitta vritti nirodhah
Yoga is the mastery of fluctuations of the mind.

For quite some time scholars believed that this knowledge amounted to no
more than speculations regarding the self; this is what we are still told in some schoolbook
accounts. New insights in archaeology, astronomy, history of science and Vedic scholarship
have shown that such a view is wrong. We now know that Vedic knowledge embraced physics,
mathematics, astronomy, logic, cognition and other disciplines. We find that Vedic science
is the earliest science that has come down to us.
Briefly, the Vedic texts present a tripartite and recursive world view. The universe is
viewed as three regions of earth, space, and sky with the corresponding entities of Agni,
Indra, and Vishve Devah (all gods).
Vedic Rishi and old education institutes alse read modern science but name was different.
These were Vedic science-
logic (nyaya) and physics (vaisheshika), cosmology (sankhya) and psychology
(yoga), and language (mimamsa) and reality (vedanta).
The Five Levels

In the Taittiriya Upanishad, the individual is represented in 5 levels that enclose the individual's self. These levels, shown in an ascending order, are:
The physical body (annamaya kosha)

Energy sheath (pranamaya kosha)

Mental sheath (manomaya kosha)

Intellect sheath (vijnanamaya kosha)

Emotion sheath (anandamaya kosha )

The emotion sheath, is innermost .
This is a recognition of the fact that eventually meaning is communicated by associations

The energy that underlies physical and mental processes is called prana.

Further description of above-
According to yogic theory & philosophy, a human being is comprised of 5 layers. These layers are called koshas, or sheath. Each layer is more subtle than the other.
The first is annamaya kosha, or literally mean ‘food sheath’ – it is the physical body: the bones, muscles, tissues, organs, bloods, etc. The grossest of the layers. It is made of the elements: earth, water, fire, air, and space. It is on this layer the gateway to the external world, the five receiving senses and the five action sense are located, so it is through this layer that one is experiencing life.
The second is pranamaya kosha, or the energy body, the prana layer. More subtle than the physical body, this layer not visible to the naked eye, but one can feel it. The chakras, or energy centers, are within this layer. Without prana, there is no life.
The third is manomaya kosha, the mind body. This is the mind that interacts with the inputs from the senses, carry out day to day operation of keeping oneself alive and well – eg if there’s a danger, move away – if there’s a reward, come closer. Manomaya kosha is full of emotions – a reaction to the input from the senses. It is key for survival.
The fourth is vijnanamaya kosha, sometimes called the higher mind. Also referred to as the ‘wisdom body’ – this is where awareness, insight, discernment, and consciousness located. Without awareness, one will be only reacting to whatever comes one’s way. With awareness, one can stop to only reacting and choose to response with intention.
The fifth is called anandamaya kosha, the bliss body. Sometimes also called the causal body. This is the innermost layer covering the essence – the soul, or spirit, or self, or atman. The unchanging eternal reality.
Using a computer as analogy, annamaya kosha is like the hardware. The receiving sense organs are keyboards, mouse, touchscreen, microphone. The action sense organs are the monitor, speaker, printer. Pranamaya kosha is like the electricity powering the computer – without plugging it into the electricity the computer can’t turn on. It’s the current that goes through the hardwares. Manomaya kosha is like the operating system – basic operation of the computer is controlled from here. Vijnanamaya kosha is like the more advanced software, with which the computer can interact in a more useful way, be productive, be of service. I can’t think yet of the parallel for anandamaya kosha in a computer… can you think of one? Although not yet complete, I think this computer analogy helps me understand more about the koshas.

The Structure of the Mind
The Sankhya system takes the mind as consisting of ¯ve components: manas, ahankara,
chitta(MEMORY BANK) buddhi, and atman. Again these categories parallel those of Figure ABOVE.
This mental complex surrounds the innermost aspect of consciousness which is called
atman, the self, brahman, or jiva.

In his famous paper on the origin of mathematics, Seidenberg (1978) concluded: Old-
Babylonia [1700 BC] got the theorem of Pythagoras from India.
Barend van Nooten (1993) has shown that binary numbers were known at the time of
Pingala's Chhandahshastra. Pingala, who lived around the early Frst century B.C.E., used
binary numbers to calssify Vedic Mantras.

The Puranas speak of countless universes, time  owing at different rates for different observers and so on.
Advanced Ancient Indian Science-
The Mahabharata speaks of an embryo being divided into one hundred parts each becoming, after maturation in a separate pot, a healthy baby; this is how the Kaurava brothers are born. There is also mention of an embryo, conceived in one womb, being transferred to the womb of another woman from where it is born; the transferred embryo is Balarama and this is how he is a brother to Krishna although he was born to Rohini and not to Devaki.

There is an ancient mention of space travellers wearing airtight suits in the epic Mahabharata which may be classi¯ed as an early form of science ¯ction. According to the well-known Sanskritist J.A.B. van Buitenen, in the accounts in Book 3 called The Razing of Saubha" and The War of the Yakshas":
the aerial city is nothing but an armed camp with fame-throwers and thundering cannon, no doubt a spaceship. The name of the demons is also revealing: they were Niv¹atakavacas, clad in airtight armor," which can hardly be anything but space suits. (van Buitenen, 1975, page 202)
Universes de¯ned recursively are described in the famous episode of Indra and the ants
in Brahmavaivarta Purana. Here Vishnu, in the guise of a boy, explains to Indra that
the ants he sees walking on the ground have all been Indras in their own solar systems in
different times! These Fights of imagination are to be traced to more than a straightforward
generalization of the motions of the planets into a cyclic universe.


Aryabhata is the author of the first of the later siddhantas called Aryabhatiyam which
sketches his mathematical, planetary, and cosmic theories. This book is divided into four
chapters: (i) the astronomical constants and the sine table, (ii) mathematics required for
computations, (iii) division of time and rules for computing the longitudes of planets using
eccentrics and epicycles, (iv) the armillary sphere, rules relating to problems of trigonometry
and the computation of eclipses.
The parameters of Aryabhatiyam have, as their origin, the commencement of Kaliyuga
on Friday, 18th February, 3102 B.C.E. He wrote another book where the epoch is a bit
Aryabhata took the earth to spin on its axis; this idea appears to have been his innovation.
He also considered the heavenly motions to go through a cycle of 4.32 billion years; here he
went with an older tradition, but he introduced a new scheme of subdivisions within this
great cycle. According to the historian Hugh Thurston, \Not only did Aryabhata believe
that the earth rotates, but there are glimmerings in his system (and other similar systems)
of a possible underlying theory in which the earth (and the planets) orbits the sun, rather
than the sun orbiting the earth. The evidence is that the basic planetary periods are relative
to the sun."

That Aryabhata was aware of the relativity of motion is clear from this passage in his
book,Just as a man in a boat sees the trees on the bank move in the opposite direction, so
an observer on the equator sees the stationary stars as moving precisely toward the west."

Varahamihira (died 587) lived in Ujjain and he wrote three important books: Panchasiddhan-
tika, Brihat Samhita, and Brihat Jataka. The ¯rst is a summary of  five early astronomical
systems including the Surya Siddhanta. (Incidently, the modern Surya Siddhanta is different
in many details from this ancient one.) Another system described by him, the Paitamaha
Siddhanta, appears to have many similarities with the ancient Vedanga Jyotisha of Lagadha.
Brihat Samhita is a compilataion of an assortment of topics that provides interesting
details of the beliefs of those times. Brihat Jataka is a book on astrology which appears to
be considerably influenced by Greek astrology.

Brahmagupta of Bhilamala in Rajasthan, who was born in 598, wrote his masterpiece,
Brahmasphuta Siddhanta, in 628. His school, which was a rival to that of Aryabhata, has
been very influential in western and northern India. Brahmagupta's work was translated into
Arabic in 771 or 773 at Baghdad and it became famous in the Arabic world as Sindhind.
One of Brahmagupta's chief contributions is the solution of a certain second order inde-
terminate equation which is of great significance in number theory.
Another of his books, the Khandakhadyaka, remained a popular handbook for astronomical computations for centuries.
Bhaskara (born 1114), who was from the Karnataka region, was an outstanding mathemati-
cian and astronomer. Amongst his mathematical contributions is the concept of di®erentials.
He was the author of Siddhanta Shiromani, a book in four parts: (i) Lilavati on arithmetic,
(ii) Bijaganita on algebra, (iii) Ganitadhyaya, (iv) Goladhyaya on astronomy. He epicyclic-
eccentric theories of planetary motions are more developed than in the earlier siddhantas.
Subsequent to Bhaskara we see a °ourishing tradition of mathematics and astronomy
in Kerala which saw itself as a successor to the school of Aryabhata.

Madhava (c. 1340-1425) developed a procedure to determine the positions of the moon every
36 minutes. He also provided methods to estimate the motions of the planets. He gave power
series expansions for trigonometric functions, and for pi correct to eleven decimal places.
Nilakantha Somayaji
Nilakantha (c. 1444-1545) was a very prolific scholar who wrote several works on astronomy.
It appears that Nilakantha found the correct formulation for the equation of the center of
the planets and his model must be considered a true heliocentric model of the solar system.
He also improved upon the power series techniques of Madhava.

The methods developed by the Kerala mathematicians were far ahead of the European

mathematics of the day.
7 Concepts of space, time, and matter
Yoga-Vasishtha (YV) is an ancient Indian text, over 29,000 verses long, traditionally attributed to Valmiki, author of the epic Ramayana- Of which some random translations are given here from
book done by Venkatesananda (1984).

² Time cannot be analyzed... Time uses two balls known as the sun and the moon for

its pastime. [16]
² The world is like a potter's wheel: the wheel looks as if it stands still, though it revolves

at a terrific speed. [18]
² Just as space does not have a fixed span, time does not have a fixed span either. Just

as the world and its creation are mere appearances, a moment and an epoch are also

imaginary. [55]
² Infinite consciousness held in itself the notion of a unit of time equal to one-millionth

of the twinkling of an eye: and from this evolved the time-scale right up to an epoch

consisting of several revolutions of the four ages, which is the life-span of one cosmic

creation. Infinite consciousness itself is uninvolved in these, for it is devoid of rising

and setting (which are essential to all time-scales), and it devoid of a beginning, middle

and end. [72]
² There are three types of space|the psychological space, the physical space and the

in¯nite space of consciousness. [52]
The in¯nite space of individed consciousness is that which exists in all, inside and

outside... The ¯nite space of divided consciousness is that which created divisions of

time, which pervades all beings... The physical space is that in which the elements

exist. The latter two are not independent of the ¯rst. [96]
² Other universes. On the slopes of a far-distant mountain range there is a solid rock

within which I dwell. The world within this rock is just like yours: it has its own

inhabitants, ...the sun and the moon and all the rest of it. I have been in it for

countless aeons. [402]
² The entire universe is contained in a subatomic partice, and the three worlds exist

within one strand of hair. [404]
² In every atom there are worlds within worlds. [55]

² (There are) countless universes, diverse in composition and space-time structure... In

every one of them there are continents and mountains, villages and cities inhabited by

people who have their time-space and life-span. [401-2]
² Direct experience alone is the basis for all proofs... That substratum is the experiencing

intelligence which itself becomes the experiencer, the act of experiencing, and the

experience. [36]
² Everyone has two bodies, the one physical and the other mental. The physical body

is insentient and seeks its own destruction; the mind is ¯nite but orderly. [124]
² I have carefully investigated, I have observed everything from the tips of my toes to the

top of my head, and I have not found anything of which I could say, `This I am.' Who

is `I'? I am the all-pervading consciousness which is itself not an object of knowledge or

knowing and is free from self-hood. I am that which is indivisible, which has no name,

which does not undergo change, which is beyond all concepts of unity and diversity,

which is beyond measure. [214]
² I remember that once upon a time there was nothing on this earth, neither trees and

plants, nor even mountains. For a period of eleven thousand years the earth was

covered by lava. In those days there was neither day nor night below the polar region:

for in the rest of the earth neither the sun nor the moon shone. Only one half of the

polar region was illumined.

Then demons ruled the earth. They were deluded, powerful and prosperous, and the

earth was their playground.

Apart from the polar region the rest of the earth was covered with water. And then

for a very long time the whole earth was covered with forests, except the polar region.

Then there arose great mountains, but without any human inhabitants. For a period

of ten thousand years the earth was covered with the corpses of the demons. [280]
² The same in¯nite self conceives within itself the duality of oneself and the other. [39]

² Thought is mind, there is no distinction between the two. [41]

² The body can neither enjoy nor su®er. It is the mind alone that experiences. [109-110]

² The mind has no body, no support and no form; yet by this mind is everything con-

sumed in this world. This is indeed a great mystery. He who says that he is destroyed

by the mind which has no substantiality at all, says in e®ect that his head was smashed

by the lotus petal... The hero who is able to destroy a real enemy standing in front of

him is himself destroyed by this mind which is [non-material].
² The intelligence which is other than self-knowledge is what constitutes the mind. [175]

² The absolute alone exists now and for ever. When one thinks of it as a void, it is

because of the feeling one has that it is not void; when one thinks of it as not-void, it

is because there is a feeling that it is void. [46]
² All fundamental elements continued to act on one another|as experiencer and experience|

and the entire creation came into being like ripples on the surface of the ocean. And,

they are interwoven and mixed up so e®ectively that they cannot be extricated from

one another till the cosmic dissolution. [48]

² The entire universe is forever the same as the consciousness that dwells in every atom.

² The ¯ve elements are the seed fo which the world is the tree; and the eternal conscious-

ness if the seed of the elements. [48]
² Cosmic consciousness alone exists now and ever; in it are no worlds, no created beings.

That consciousness re°ected in itself appears to be creation. [49]
² This consciousness is not knowable: when it wishes to become the knowable, it is known

as the universe. Mind, intellect, egotism, the ¯ve great elements, and the world|all

these innumerable names and forms are all consciousness alone. [50]
² The world exists because consciousness is, and the world is the body of consciousness.

There is no division, no di®erence, no distinction. Hence the universe can be said

to be both real and unreal: real because of the reality of consciousness which is its

own reality, and unreal because the universe does not exist as universe, independent of
consciousness. [50]

² Consciousness is pure, eternal and in¯nite: it does not arise nor cease to be. It is ever

there in the moving and unmoving creatures, in the sky, on the mountain and in ¯re

and air. [67]
² Millions of universes appear in the in¯nite consciousness like specks of dust in a beam
of light. In one small atom all the three worlds appear to be, with all their components

like space, time, action, substance, day and night. [120]
² The universe exists in in¯nte consciousness. In¯nite consciousness is unmanifest,

though omnipresent, even as space, though existing everywhere, is manifest. [141]
² The manifestation of the omnipotence of in¯nite consciousness enters into an alliance

with time, space and causation. Thence arise in¯nite names and forms. [145]
² The Lord who is in¯nite consciousness is the silent but alert witness of this cosmic

dance. He is not di®erent from the dancer (the cosmic natural order) and the dance

(the happenings). [296]

Might then one accept the claim of Srinivasa Ramanujan that his theorems were revealed to him in his dreams by the goddess Namagiri? This claim, so persistently made by Ramanujan, has generally been dismissed by his biographers (see, for example, Kanigel, 1991). Were Ramanujan's astonishing discoveries instrumented by the autonomously creative potential of consciousness, represented by him by the image of Namagiri? If that be the case then the marvellous imagination shown in Yoga-Vasishtha and other Indian texts becomes easier to comprehend.

Is nature and animals, human all are molecule- Yes partly with consciousness.
ET (1)ET (2)ET (3)ET (4)ET (6)

ET (5)
ET (7)
ET (8)


13.7 BYASeconds after Bang13.2 BYA4.4 BYA4.1 BYA3.9 BYA45 MYA150,000 Year Ago

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Thursday, November 26, 2015

Hindu Cosmology -Part 2

Hindu Cosmology upholds the idea that creation is timeless, having no beginning in time. Each creation is preceded by dissolution and each dissolution is followed by creation. The whole cosmos exists in two states - the unmanifested or undifferentiated state and the manifested or differentiated state. This has been going on eternally. There are many universes - all follow the same rhythm, creation and dissolution (the systole and diastole of the cosmic heart). According to the Bhagavad Gita this srishti (creation) and pralaya (dissolution) recur at a period of 1,000 mahayuga or 4.32 billion years or 4,320 million years:
For a thousand ages lasts One day of Brahma, And for a thousand ages one such night;
This knowing, men will know (what is meant by) day and night.
At the day's dawning all things manifest; Spring forth from the Unmanifest;
And then at nightfall they dissolve again, In (that same mystery) surnamed "Unmanifest."


The Rig Veda describes the origin of the universe as:
"Then was not non-existence nor existence: there was no realm of air, no sky beyond it. What covered in, and where? and what gave shelter? Was water there, unfathomed depth of water? 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. Darkness there was at first concealed in darkness this. All was indiscriminated chaos. All that existed then was void and form less: by the great power of Warmth was born that Unit. Thereafter 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. 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. Who verily knows and who can here declare it, whence it was born and whence comes this creation? The devas are later than this world's production. Who knows then whence it first came into being? 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" - (Rig Veda 10.129.1-7)

Structure of the universe

The Yugas

  • Satya or Krta (1,728,000 years): Satya means "truth"; the age is also known as Krta, "action," i.e., the age in which the people did unquestioningly what their benevolent elders told them.
  • Treta (1,296,000 years): Treta means "three," the third age, counting backwards from the present: also the age in which the feelings and forces of good are as three parts, and those of evil as one; also the age in which people were specially "protected," trayate, by their elders.
  • Dva-para (864,000 years): Dva-para means "two-sided," hence doubt also.
  • Kali (432,000 years) which rotates in succession. Kali means "discord," "struggle".
And all of these add to 4,320,000 years. Now, these four yugas, taken together, constitute one Mahayuga. One thousand Mahayugas are one day of Brahma. Brahma's one day is one Kalpa. So one day of Brahma will be 432 crores or 4,320 million years or 4.32 billion years. A similar expanse of time will make His one night, and that is another Kalpa. Our wildest imagination staggers in conceiving Brahma's life-span. This is the expansive view of time. No other culture had this unique vision of the infinity of time as well as the infinity of space.
vedic mathematics 

Friday, April 24, 2015

Ancient Indian ASTROLOGY and effect of Sun on earth

puranicAncient Indian wisdom is a treasure trove of science. In fact, most of the claims made by ancient India (related to astrology, yoga, ayurveda) have been validated by Modern Science today. For example, this physics journal from USA in 1998 was astonished to find that ancient India knew the speed of light, down to the last digit of accuracy!!

Not only that new scientist acknodge that Solar does influence mind of all living in earth. Heard about Full moon and many unusual activites.
The radiation patterns of the Sun not only affects at individual level but might affect at society level as well. Extensive studies and historical evidences have shown the correlation between historical activity and moments of maxima of solar activity.
For example, this webpage from National University of Singapore gives more insight into the concepts of maxima-minima of solar activity (sunspots & sunflares) and their effect on humans
Carlini Research Institute, based in Canada, is involved in intensive study of the effect of solar activity on human psychology and has been publishing papers depicting the influence of solar activity on our lives.
Following is an interesting revelation from a science magazine which claims: “Solar activity affects every single aspect of human life
A recent study published in the popular science journal NewScientist claims that solar activity affects physical & mental state of humans.

Sunday, April 5, 2015

Aryabhata,Zero, Bhaskara

Aryabhata wrote many books on mathematics, astronomy etc but most of them are lost today.His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times. The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines.Arabic translation of Aryabhata’s work is Al ntf or Al-nanf and it claims that it is a translation of Aryabhatiya like other Ancient Indian texts -translated mostly by Persian scholars during golden age and advent of Islam.

Place Value System and ZERO

The place-value system, first seen in the 3rd-century Bakhshali Manuscript, was clearly in place in his work. While he did not use a symbol for zero, the French mathematician Georges Ifrah explains that knowledge of zero was implicit in Aryabhata’s place-value system as a place holder for the powers of ten with null coefficients.However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic form.

Approximation of π

Aryabhata worked on the approximation for pi (π), and may have come to the conclusion that is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes :

caturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.||

Translation : “Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached.”

This calculates to 3.1416 close to the actual value Pi (3.14159).Aryabhata used the word āsanna (approaching / approximating), to mean that not only is this an approximation but that the value is incommensurable (or irrational).This is quite a sophisticated insight, because the irrationality of pi(π) was proved only in 1761 by Johann Heinrich Lambert.After Aryabhatiya was translated into Arabic (during 820 CE) this approximation was mentioned in Al-Khwarizmi‘s book on algebra.

Contributions in Trigonometry


In Ganitapada 6, Aryabhata gives the area of a triangle as :

tribhujasya phalashariram samadalakoti bhujardhasamvargah ||

Translation : “for a triangle, the result of a perpendicular with the half-side is the area.”

Aryabhata discussed the concept of sine in his work by the name of ardha-jya, which literally means “half-chord (half-wave)“. For simplicity, people started calling it jya.When Arabic writers translated his works from Sanskrit into Arabic, they referred it as "jiba".However, in Arabic writings, vowels are omitted, and it was abbreviated as jb.
Later writers substituted it with "jaib", meaning “pocket” or “fold (in a garment)“.Later in the 12th century, when Gherardo of Cremona translated these writings from Arabic into Latin, he replaced the Arabic "jaib" with its Latin counterpart, sinus, which means “cove” or “bay“; thence comes the English SINE.Alphabetic code has been used by him to define a set of increments. If we use Aryabhata’s table and calculate the value of sin(30) (corresponding to hasjha) which is 1719/3438 = 0.5; the value is correct. His alphabetic code is commonly known as the Aryabhata cipher

Saturday, February 7, 2015

Ancient Vedic astrology and cosmology

Astronomy-1: Newton told by bhaskaracharya before gravity theory

Eye of the Veda astronomy said, because the behavior of the entire srishtiyon period and period of planetary motion occurs. So since ancient times has been part of winged astronomy. In the Rigveda, shatpath brahrin chandramas, saurmas, Star, etc. grathon stool mass, season change, uttarayan, period of dakshinayan, akashchakra, the glory of the Sun, in terms of the measurement of Kalpa quotes are found. For the Sage used direct observation. Says the blind Sage dirghatmas, to study the Sun, Sage gritsmad the womb of the moon about the results. In chapter chalisven of the 18th Sept yajurved spells were told that due to the Moon's Lucent rays Sun. Instruments using Astro is to inspect the system.
Aryabhatta time today in more than 1,500 years ago was that the Observatory(Observatory) pataliputra using aryabhatta extracted many conclusions.
Bhaskaracharya theory says in the case of yantradhyay Shiromani treatise "CAL"knowledge of micro sections is not possible without instruments. So now I tell aboutinstruments. They nadivlay equipment, individual equipment, instruments, tools, instruments, plummeted cycle cone arc, describe turya, Panel etc.
Direct observation and kalganna of unmistakable planetary and 6000 years old history:-Mr dharampal has "Indian Science and Technology in the Eighteenth Century called" book is written. It is one of the eminent khagolgya John foreplay article "Remarks on the Astronomy of the brahmins" (published from 1790) is given. This article proves that more than 6,000 years ago in India and had knowledge of the astronomical calculations were used in the world here. The essence of that in his article in 1667 m. law. Labatt, which were in the Siamese Embassy, Bring your come back when an almanac. India sent two missionaries, a calendar, was from South India and one from Varanasi. Another Almanac m. d. Sent by lisle, who was from South India to narsapur. The ephemeris when that time came, the French mathematicians don't understand he sent to John foreplay Which were the Royal astronomer. The focus of another bizarre thing when he came to foreplay that was given in the ephemeris Siamese yamottar line-the meridian (the imaginary point in the sky from the high line) 180-15 ". In the West, and is not located on the Siamese. Surprise that it gets from the meridian of Banaras. This means that the Hindustan Siamese is the origin of the Almanac. Secondly, he writes, "a surprising is that all mentions of an sanvat Almanac that they consider the start of caughley. And the day of the commencement of the nakshatras caughley was, Describe your ephemeris calculate from there and in that period. The planetary positions at the time was what it explains. So it seems to be the big bizarre thing. Since the start of the 3,000-year-old ISA provided caughley thing.
(1) brahrinon count will be developed and the flawless and unmistakable pattern in the universe and the planets to draw brahrin from karnibhut terms of gravity were familiar.
(2) observe the sky brahrinon have scientific manner.

Conclusion end foreplay foreplay says two things
(1) it is proven that in the year 3000 BC from years ago India was astronomy, anddescribed the position of the Sun at kaliyugarambh and was based on the actualinspection Chandra.
(2) it is a neutral foreign analysis gives us some inspiration. Mr. dharampal has its corresponding written in the book that the then british Army General of Bengal, who later became a member of the British Parliament, wrote an article in 1777 by Sir Robertbarker Bramins observatory at Banaras (Varanasi Observatory) are highlighted. In1772, he inspected the Observatory. At that time it was freaked out because there wasno use for a long time. After the Observatory was the instrument and instrument left,he studied closely by Mr. barker. Their inspection was an important point in mind that these tools were designed almost 400 years ago.
Some previews of ancient astronomy
(1) the speed of light:-knowledge of what our ancestors did to the speed of light? The above questions are a time Governor of Gujarat, Shri k. Shah Mysore UniversityPhysics Professor Pro. L. Shivayya asked. Mr. shivayya were both Sanskrit and scienceWiz. He immediately replied, "ya know."Evidence, he explained that the first system is the Rigveda richaen-
Psycho-not yoऽdhvan: vasva: atk satra suro ishe i.e. were able to mind like fleet arealone on the path the Sun late. (1-71-9)
("Tarnirvishvadarshato jyotikridsi Sun vishvamabhasirochnam" sarvasundar o Sun, and light the explosive and donor and jagat are supposed to unfold. (1.50.9)
Dve dve yojnanan sahasre dveshte f yojne. Akin nimishardhen cameramannamoऽstute..
That is half the light margakraman of the 2202 nimesh Yojana you greet. There are 1Yojana-9 miles 160 yards, namely 1 Yojana-9.11 miles 1 day night-810000 seminishesh so 1 seconds-9.41 semi nimesh thus 2202 x 9.11-20060.22 20060.22 x 9.41-semi nimesh per mile and 188766.67 miles per second. Modern expert

!! Astronomy-2: reconstructed by astrophysicist aryabhatta!!
Lilavati asks his father that father, I see around the Earth is flat, then why do you saythat the Earth is round. Then bhaskaracharya says daughter, what we see is not alwaysthe same truths. You pull a large circle, then look at his perimeter hundredths, you'll see it in a straight line. But in fact he is not, the curve. Similarly, large parts of the Earth's sphere we see, he is flat. In fact the Earth is round.
Samo typically syatparidhe: shatansh:
Earth nitran Earth taniyan f. Narashch tatprishthagtasya tasya pratibhatyat: samevkutsna SA || 13 ||
Sherman goladhyay-bhuvnakosh principle
The Earth is not static: in the 15th century is the notion that by the time of galileanEarth imposes his round steady and Sun, but today was 1,500 years ago byaryabhatta, land moves its axis, its details are as follows-
Anulomgatinaunsth: pashyatyachlam vilomang yadvat. Achlani bhani tadvat even pashchimgani lankayam ||
Aryabhattiya golpad-9
Namely the boat trip on the edges that shy in the direction against the rock, tree andsees the same fixed star Lanka scrabbled towards from East to West directly can be seen. Similarly, prithudak owner, who wrote the doctrine of vrahmagupt vrahmasphut gloss, is used to refer to an aryabhatta Arya-
I daivisikau revavrityavritya prati sthiro panjar: geo. Udyastamyau sampadyatinakshtragrahanam ||
Namely, the star system is stable and roam the Earth at a speed of nakshatras and their daily planets will rise and sunset. In his treatise called the dashgitika episode aryabhattiya written in clear-aryabhatta prane naitiklambhu: namely a vitality revolves a Earth in Arts (a day are 21600 lives) sunrise-sunset-land round due to being rekhantar diverse cities in different places at different times are Sunrise and sunset. Itwas known by aryabhatta, he writes-
Udyo yo sostamay lankayan:
Saviturev siddhapure.
Madhyahno yavkotyan syat romak vishyeऽrdharatra: ||
(Aryabhattiya golpad-13)
I.e. When is sunrise at sunset in Sri Lanka gets siddhapur. Yavkoti is in the Meridian and romak midnight. Lunar-solar eclipse-aryabhatta said Rahu Ketu reason but Earth and Lunar Eclipse is due to shadow. Namely, the Earth's shadow when the Moon is at the Lunar Eclipse. Similarly, when the Earth comes between the Sun and Lunar, solar eclipse happens. Various planets the distance of the planets from the Sun by aryabhatta-diverse told about. He resembles today's measurement is. Nowadays the Earth Distance from Sun (15 million KMS). It AU (Astronomical unit) is called. This ratio is based on the following list is created.
Vrahmand expands-
The immensity of the vrahmand also had experience by our ancestors. Nowadays the immensity of the vrahmand unit of measure to use for light years. A second is run at a speed of 3 million kilometers. A year shy of the speed as the distance light will decide itis called light years. This scale of modern science tells us that our fabulos that Milki called way, the length of one million light years and width is ten thousand light years. At the top of this fabulos androulla called fabulos this fabulos 20 million 20,000 light years away and there are millions of sky gangaen in vrahmand.
Shrimadbhagvat King ask, vrahmand mahamuni is tested shukdeo inter vyap of what?Interpretation refers to the expansion of the vrahmand in shukdeo inter-
Our ten times older than him who vrahmand cover-up is matted. Each cover uptenfold and seven cover I know. Including all it looks like nuclear and vrahmand that there are millions of vrahmand, he is the cause of all causes.‘
It seems to be some inexplicable thing IQ-c. But we generate everything from a powerwhich was the God-driven names a name of infinite rank vrahmand hero's. This namewhere vrahmandon tells infinity, the sensation of having this analysis is also scientific.Thus this overview, we can say that time calculations and astronomy is bright in Indiaof tradition. In previous centuries it was something blocking the stream c. Inspire him again today to pursue the anterior are giving today's generation of Acharya.
खगोल विज्ञान-१ : न्यूटन से पहले भास्कराचार्य ने बताया था गुरुत्वाकर्षण का सिद्धान्त

खगोल विज्ञान को वेद का नेत्र कहा गया, क्योंकि सम्पूर्ण सृष्टियों में होने वाले व्यवहार का निर्धारण काल से होता है और काल का ज्ञान ग्रहीय गति से होता है। अत: प्राचीन काल से खगोल विज्ञान वेदांग का हिस्सा रहा है। ऋग्वेद, शतपथ ब्राहृण आदि ग्रथों में नक्षत्र, चान्द्रमास, सौरमास, मल मास, ऋतु परिवर्तन, उत्तरायन, दक्षिणायन, आकाशचक्र, सूर्य की महिमा, कल्प का माप आदि के संदर्भ में अनेक उद्धरण मिलते हैं। इस हेतु ऋषि प्रत्यक्ष अवलोकन करते थे। कहते हैं, ऋषि दीर्घतमस् सूर्य का अध्ययन करने में ही अंधे हुए, ऋषि गृत्स्मद ने चन्द्रमा के गर्भ पर होने वाले परिणामों के बारे में बताया। यजुर्वेद के 18वें अध्याय के चालीसवें मंत्र में यह बताया गया है कि सूर्य किरणों के कारण चन्द्रमा प्रकाशमान है। यंत्रों का उपयोग कर खगोल का निरीक्षण करने की पद्धति रही है।
आर्यभट्ट के समय आज से 1500 से अधिक वर्ष पूर्व पाटलीपुत्र में वेधशाला (Observatory) थी, जिसका प्रयोग कर आर्यभट्ट ने कई निष्कर्ष निकाले।
भास्कराचार्य सिद्धान्त शिरोमणि ग्रंथ के यंत्राध्याय प्रकरण में कहते हैं, "काल" के सूक्ष्म खण्डों का ज्ञान यंत्रों के बिना संभव नहीं है। इसलिए अब मैं यंत्रों के बारे में कहता हूं। वे नाड़ीवलय यंत्र, यष्टि यंत्र, घटी यंत्र, चक्र यंत्र, शंकु यंत्र, चाप, तुर्य, फलक आदि का वर्णन करते हैं।
प्रत्यक्ष निरीक्षण एवं अचूक ग्रहीय व कालगणना का 6000 वर्ष से अधिक पुराना इतिहास :- श्री धर्मपाल ने "Indian Science and Technology in the Eighteenth Century" नामक पुस्तक लिखी है। उसमें प्रख्यात खगोलज्ञ जॉन प्लेफेयर का एक लेख "Remarks on the Astronomy of the brahmins" (1790 से प्रकाशित) दिया है। यह लेख सिद्ध करता है कि 6000 से अधिक वर्ष पूर्व में भारत में खगोल का ज्ञान था और यहां की गणनाएं दुनिया में प्रयुक्त होती थीं। उनके लेख का सार यह है कि सन् 1667 में एम.लॉ. लाबेट, जो स्याम के दूतावास में थे, जब वापस आये तो अपने साथ एक पंचांग लाए। दो पंचांग मिशनरियों ने भारत से भेजे, जो एक दक्षिण भारत से था और एक वाराणसी से। एक और पंचांग एम.डी. लिस्ले ने भेजा, जो दक्षिण भारत के नरसापुर से था। वह पंचांग जब उस समय के फ्रेंच गणितज्ञों की समझ में न आया तो उन्होंने वह जॉन प्लेफेयर के पास भेज दिया, जो उस समय रॉयल एस्ट्रोनोमर थे। उन्होंने जब एक और विचित्र बात प्लेफेयर के ध्यान में आई कि स्याम के पंचांग में दी गई यामोत्तर रेखा-दी मेरिडियन (आकाश में उच्च काल्पनिक बिन्दु से निकलती रेखा) 180-15"। पश्चिम में है और स्याम इस पर स्थित नहीं है। आश्चर्य कि यह बनारस के मेरिडियन से मिलती है। इसका अर्थ है कि स्याम के पंचांग का मूल हिन्दुस्तान है। दूसरी बात वह लिखता है, "एक आश्चर्य की बात यह है कि सभी पंचांग एक संवत् का उल्लेख करते हैं, जिसे वे कलियुग का प्रारंभ मानते हैं। और कलियुग के प्रारंभ के दिन जो नक्षत्रों की स्थिति थी, उसका वर्णन अपने पंचांग में करते हैं तथा वहीं से काल की गणना करते हैं। उस समय ग्रहों की क्या स्थिति थी, यह बताते हैं। तो यह बड़ी विचित्र बात लगती है। क्योंकि कलियुग का प्रारंभ यानि ईसा से 3000 वर्ष पुरानी बात।
(1) ब्राहृणों ने गिनती की निर्दोष और अचूक पद्धति विकसित की होगी तथा ब्रह्मांड में दूर और पास के ग्रहों को आकर्षित करने के लिए कारणीभूत गुरुत्वाकर्षण के नियम से ब्राहृण परिचित थे।
(2) ब्राहृणों ने आकाश का निरीक्षण वैज्ञानिक ढंग से किया।

प्लेफेयर के निष्कर्ष अंत में प्लेफेयर दो बातें कहते हैं-
(1) यह सिद्ध होता है कि भारत वर्ष में एस्ट्रोनॉमी ईसा से 3000 वर्ष पूर्व से थी तथा कलियुगारम्भ पर सूर्य और चन्द्र की वर्णित स्थिति वास्तविक निरीक्षण पर आधारित थी।
(2) एक तटस्थ विदेशी का यह विश्लेषण हमें आगे कुछ करने की प्रेरणा देता है। श्री धर्मपाल ने अपनी इसी पुस्तक में लिखा है कि तत्कालीन बंगाल की ब्रिाटिश सेना के सेनापति, जो बाद में ब्रिटिश पार्लियामेंट के सदस्य बने, सर रॉबर्ट बारकर ने 1777 में लिखे एक लेख Bramins observatory at Banaras (बनारस की वेधशाला) पर प्रकाश डाला है। सन् 1772 में उन्होंने वेधशाला का निरीक्षण किया था। उस समय इसकी हालत खराब थी क्योंकि लंबे समय से उसका कोई उपयोग नहीं हुआ था। इसके बाद भी उस वेधशाला में जो यंत्र व साधन बचे थे , उनका श्री बारकर ने बारीकी से अध्ययन किया। उनके निरीक्षण में एक महत्वपूर्ण बात यह ध्यान में आई कि ये साधन लगभग 400 वर्ष पूर्व तैयार किए गए थे।
प्राचीन खगोल विज्ञान की कुछ झलकियां
(1) प्रकाश की गति :- क्या हमारे पूर्वजों को प्रकाश की गति का ज्ञान था? उपर्युक्त प्रश्न एक बार गुजरात के राज्यपाल रहे श्री के.के.शाह ने मैसूर विश्वविद्यालय के भौतिकी के प्राध्यापक प्रो. एल. शिवय्या से पूछा। श्री शिवय्या संस्कृत और विज्ञान दोनों के जानकार थे। उन्होंने तुरंत उत्तर दिया, "हां जानते थे।" प्रमाण में उन्होंने बताया कि ऋग्वेद के प्रथम मंडल में दो ऋचाएं है-
मनो न योऽध्वन: सद्य एत्येक: सत्रा सूरो वस्व ईशे अर्थात् मन की तरह शीघ्रगामी जो सूर्य स्वर्गीय पथ पर अकेले जाते हैं। ( 1-71-9)
("तरणिर्विश्वदर्शतो ज्योतिकृदसि सूर्य विश्वमाभासिरोचनम्" अर्थात् हे सूर्य, तुम तीव्रगामी एवं सर्वसुन्दर तथा प्रकाश के दाता और जगत् को प्रकाशित करने वाले हो। ( 1.50.9)
योजनानां सहस्रे द्वे द्वेशते द्वे च योजने। एकेन निमिषार्धेन क्रममाण नमोऽस्तुते।।
अर्थात् आधे निमेष में 2202 योजन का मार्गक्रमण करने वाले प्रकाश तुम्हें नमस्कार है। इसमें 1 योजन- 9 मील 160 गज अर्थात् 1 योजन- 9.11 मील 1 दिन रात में- 810000 अर्ध निषेष अत: 1 सेकेंड में - 9.41 अर्ध निमेष इस प्रकार 2202 x 9.11- 20060.22 मील प्रति अर्ध निमेष तथा 20060.22 x 9.41- 188766.67 मील प्रति सेकण्ड। आधुनिक विज्ञान को मान्य प्रकाश गति के यह अत्यधिक निकट है।
(2) गुरुत्वाकर्षण: "पिताजी, यह पृथ्वी, जिस पर हम निवास करते हैं, किस पर टिकी हुई है?" लीलावती ने शताब्दियों पूर्व यह प्रश्न अपने पिता भास्कराचार्य से पूछा था। इसके उत्तर में भास्कराचार्य ने कहा, "बाले लीलावती, कुछ लोग जो यह कहते हैं कि यह पृथ्वी शेषनाग, कछुआ या हाथी या अन्य किसी वस्तु पर आधारित है तो वे गलत कहते हैं। यदि यह मान भी लिया जाए कि यह किसी वस्तु पर टिकी हुई है तो भी प्रश्न बना रहता है कि वह वस्तु किस पर टिकी हुई है और इस प्रकार कारण का कारण और फिर उसका कारण... यह क्रम चलता रहा, तो न्याय शास्त्र में इसे अनवस्था दोष कहते हैं। लीलावती ने कहा फिर भी यह प्रश्न बना रहता है पिताजी कि पृथ्वी किस चीज पर टिकी है? तब भास्कराचार्य ने कहा,क्यों हम यह नहीं मान सकते कि पृथ्वी किसी भी वस्तु पर आधारित नहीं है।..... यदि हम यह कहें कि पृथ्वी अपने ही बल से टिकी है और इसे धारणात्मिका शक्ति कह दें तो क्या दोष है? इस पर लीलावती ने पूछा यह कैसे संभव है। तब भास्कराचार्य सिद्धान्त की बात कहते हैं कि वस्तुओं की शक्ति बड़ी विचित्र है।4
मरुच्लो भूरचला स्वभावतो यतो विचित्रावतवस्तु शक्त्य:।। सिद्धांत शिरोमणी गोलाध्याय-भुवनकोश (5)
आगे कहते हैं-
आकृष्टिशक्तिश्च मही तया यत् खस्थं
गुरुस्वाभिमुखं स्वशक्तत्या।
आकृष्यते तत्पततीव भाति समेसमन्तात् क्व पतत्वियं खे।। सिद्धांत शिरोमणी गोलाध्याय-भुवनकोश- (6)
अर्थात् पृथ्वी में आकर्षण शक्ति है। पृथ्वी अपनी आकर्षण शक्ति से भारी पदार्थों को अपनी ओर खींचती है और आकर्षण के कारण वह जमीन पर गिरते हैं। पर जब आकाश में समान ताकत चारों ओर से लगे, तो कोई कैसे गिरे? अर्थात् आकाश में ग्रह निरावलम्ब रहते हैं क्योंकि विविध ग्रहों की गुरुत्व शक्तियां संतुलन बनाए रखती हैं। आजकल हम कहते हैं कि न्यूटन ने ही सर्वप्रथम गुरुत्वाकर्षण की खोज की, परन्तु उसके 550 वर्ष पूर्व भास्कराचार्य ने यह बता दिया था।
!! खगोल विज्ञान-२ : आर्यभट्ट ने खंगाला खगोल !!
लीलावती अपने पिता से पूछती है कि पिताजी, मुझे तो पृथ्वी चारों ओर सपाट दिखाई देती है, फिर आप यह क्यों कहते हैं कि पृथ्वी गोल है। तब भास्कराचार्य कहते हैं कि पुत्री, जो हम देखते हैं वह सदा वैसा ही सत्य नहीं होता। तुम एक बड़ा वृत्त खींचो, फिर उसकी परिधि के सौवें भाग को देखो, तुम्हें वह सीधी रेखा में दिखाई देगा। पर वास्तव में वह वैसी नहीं होता, वक्र होता है। इसी प्रकार विशाल पृथ्वी के गोले के छोटे भाग को हम देखते हैं, वह सपाट नजर आता है। वास्तव में पृथ्वी गोल है।
समो यत: स्यात्परिधे: शतांश:
पृथ्वी च पृथ्वी नितरां तनीयान्‌। नरश्च तत्पृष्ठगतस्य कुत्स्ना समेव तस्य प्रतिभात्यत: सा॥ १३ ॥
सिद्धांत शिरोमणी गोलाध्याय-भुवनकोश
पृथ्वी स्थिर नहीं है:-पश्चिम में १५वीं सदी में गैलीलियों के समय तक धारणा रही कि पृथ्वी स्थिर है तथा सूर्य उसका चक्कर लगाता है, परन्तु आज से १५०० वर्ष पहले हुए आर्यभट्ट, भूमि अपने अक्ष पर घूमती है, इसका विवरण निम्न प्रकार से देते हैं-
अनुलोमगतिनौंस्थ: पश्यत्यचलम्‌ विलोमंग यद्वत्‌। अचलानि भानि तद्वत्‌ सम पश्चिमगानि लंकायाम्‌॥
आर्यभट्टीय गोलपाद-९
अर्थात्‌ नाव में यात्रा करने वाला जिस प्रकार किनारे पर स्थिर रहने वाली चट्टान, पेड़ इत्यादि को विरुद्ध दिशा में भागते देखता है, उसी प्रकार अचल नक्षत्र लंका में सीधे पूर्व से पश्चिम की ओर सरकते देखे जा सकते हैं। इसी प्रकार पृथुदक्‌ स्वामी, जिन्होंने व्रह्मगुप्त के व्रह्मस्फुट सिद्धान्त पर भाष्य लिखा है, आर्यभट्ट की एक आर्या का उल्लेख किया है-
भ पंजर: स्थिरो भू रेवावृत्यावृत्य प्राति दैविसिकौ। उदयास्तमयौ संपादयति नक्षत्रग्रहाणाम्‌॥
अर्थात्‌ तारा मंडल स्थिर है और पृथ्वी अपनी दैनिक घूमने की गति से नक्षत्रों तथा ग्रहों का उदय और अस्त करती है। अपने ग्रंथ आर्यभट्टीय में आर्यभट्ट ने दशगीतिका नामक प्रकरण में स्पष्ट लिखा-प्राणे नैतिकलांभू: अर्थात्‌ एक प्राण समय में पृथ्वी एक कला घूमती है (एक दिन में २१६०० प्राण होते हैं) सूर्योदय-सूर्यास्त-भूमि गोलाकार होने के कारण विविध नगरों में रेखांतर होने के कारण अलग-अलग स्थानों में अलग-अलग समय पर सूर्योदय व सूर्यास्त होते हैं। इसे आर्यभट्ट ने ज्ञात कर लिया था, वे लिखते हैं-
उदयो यो लंकायां सोस्तमय:
सवितुरेव सिद्धपुरे।
मध्याह्नो यवकोट्यां रोमक विषयेऽर्धरात्र: स्यात्‌॥
(आर्यभट्टीय गोलपाद-१३)
अर्थात्‌ जब लंका में सूर्योदय होता है तब सिद्धपुर में सूर्यास्त हो जाता है। यवकोटि में मध्याह्न तथा रोमक प्रदेश में अर्धरात्रि होती है। चंद्र-सूर्यग्रहण- आर्यभट्ट ने कहा कि राहु केतु के कारण नहीं अपितु पृथ्वी व चंद्र की छाया के कारण ग्रहण होता है। अर्थात्‌ पृथ्वी की बड़ी छाया जब चन्द्रमा पर पड़ती है तो चन्द्र ग्रहण होता है। इसी प्रकार चन्द्र जब पृथ्वी और सूर्य के बीच आता है तो सूर्यग्रहण होता है। विभिन्न ग्रहों की दूरी- आर्यभट्ट ने सूर्य से विविध ग्रहों की दूरी के बारे में बताया है। वह आजकल के माप से मिलता-जुलता है। आजकल पृथ्वी से सूर्य की दूरी (15 करोड़ किलोमीटर) है। इसे AU ( Astronomical unit) कहा जाता है। इस अनुपात के आधार पर निम्न सूची बनती है।
व्रह्माण्ड का विस्तार-
व्रह्माण्ड की विशालता का भी हमारे पूर्वजों ने अनुभव किया था। आजकल व्रह्माण्ड की विशालता मापने हेतु प्रकाश वर्ष की इकाई का प्रयोग होता है। प्रकाश एक सेकेंड में ३ लाख किलोमीटर की गति से भागता है। इस गति से भागते हुए एक वर्ष में जितनी दूरी प्रकाश तय करेगा उसे प्रकाश वर्ष कहा जाता है। इस पैमाने से आधुनिक विज्ञान बताता है कि हमारी आकाश गंगा, जिसे Milki way ‌ कहा जाता है, की लम्बाई एक लाख प्रकाश वर्ष है तथा चौड़ाई दस हजार प्रकाश वर्ष है। इस आकाश गंगा के ऊपर स्थित एण्ड्रोला नामक आकाश गंगा इस आकाश गंगा से २० लाख २० हजार प्रकाश वर्ष दूर है और व्रह्माण्ड में ऐसी करोड़ों आकाश गंगाएं हैं।
श्रीमद्भागवत में राजा परीक्षित महामुनि शुकदेव से पूछते हैं, व्रह्माण्ड का व्याप क्या है? इसकी व्याख्या में शुकदेव व्रह्माण्ड के विस्तार का उल्लेख करते हैं-
‘हमारा जो व्रह्माण्ड है, उसे उससे दस गुने बड़े आवरण ने ढंका हुआ है। प्रत्येक ऊपर का आवरण दस गुना है और ऐसे सात आवरण मैं जानता हूं। इन सबके सहित यह समूचा व्रह्माण्ड जिसमें परमाणु के समान दिखाई देता है तथा जिसमें ऐसे करोड़ों व्रह्माण्ड हैं, वह समस्त कारणों का कारण है।‘
ये बात बुद्धि को कुछ अबोध्य-सी लगती है। पर हमारे यहां जिस एक शक्ति से सब कुछ उत्पन्न-संचालित माना गया, उस ईश्वर के अनेक नामों में एक नाम अनंत कोटि व्रह्माण्ड नायक बताया गया है। यह नाम जहां व्रह्मांडों की अनन्तता बताता है, वहीं इस विश्लेषण के वैज्ञानिक होने की अनुभूति भी कराता है। इस प्रकार इस संक्षिप्त अवलोकन से हम कह सकते हैं कि काल गणना और खगोल विज्ञान की भारत में उज्ज्वल परम्परा रही है। पिछली सदियों में यह धारा कुछ अवरुद्ध सी हो गई थी। आज पुन: उसे आगे बढ़ाने की प्रेरणा पूर्वकाल के आचार्य आज की पीढ़ी को दे रहे हैं।