Guest guest Posted January 28, 2009 Report Share Posted January 28, 2009 Dear All, An excellent site by James Q. Jacobs: http://jqjacobs.net/ I have just invited him to this group. An excellent article by him is given below.Love and regards,Sreenadh============================================================ The Àryabhatiya of Àryabhata: The oldest exact astronomical constant? © 1998 by James Q. Jacobs In the work The Àryabhatiya of Àryabhata, An Ancient Indian Work on Mathematics and Astronomy, translated by William Eugene Clark, Professor of Sanskrit at Harvard University (The University of Chicago Press, Chicago, Illinois. 1930), I found the following to be written: "In a yuga the revolutions of the Sun are 4,320,000, of the Moon 57,753,336, of the Earth eastward 1,582,237,500, of Saturn 146,564, of Jupiter 364,224, of Mars 2,296,824 . . . " (page 9). As can be seen from the Clarke's translation Àryabhata wrote that 1,582,237,500 rotations of the Earth equal 57,753,336 lunar orbits. (These same two numbers are also presented by G. R. Kay in his appendices, where they are attributed to Àryabhata and Pusíla.) This is an extremely accurate ratio for two fundamental cosmic motions (1,582,237,500 / 57,753,336 = 27.3964693572). Given Jan. 1, 2000 astronomical constants and given the present day formulas to temporally adjust the astronomical constants, I calculated that Àryabhata's ratio was exact for 1604 BC.* The resulting data is presented in Table 1. The temporal variation formulas used can be obtained from my Astronomy Formulas page. The date AD 500 is the approximate epoch in which Àryabhata wrote. Àryabhata was born in 476 in Patna, India and died in 550. His Àryabhatiya was probably written in A.D 498. His sources remain obscure. Table 1. Comparison of The Àryabhatiya of Àryabhata and Astronomic values. Astronomy Constants AD 2000.0 AD 500 1604 BC Rotations per solar orbit 366.25636031 366.2563589 366.25635656 Days per solar orbit 365.25636031 365.2563589 365.25635656 Days per lunar orbit 27.32166120 27.3216638 27.32166801 Rotations per lunar orbit 27.39646289 27.39646514 27.39646936 While the majority of the ratios presented by Àryabhata are not equally precise, it is difficult to believe that the earth rotations to lunar orbits ratio, given such very large numbers, could be so precise by coincidence. The odds of that being the case are astronomical. This is particularly so given that the data derives from an era when it was more exactive than today. If it derived from an ancient Vedic source, it was even more exactive when it originated. Additionally, lunar orbit and earth rotation are two of the three actual fundamental cosmic motions, rather than the apparent day/night or lunar phase cycles. According to G. R. Kay, Àryabhata and the Paulisa Siddanta present the values below for the lunar periods. Kay's table of durations of sidereal and synodic months also quotes another ancient Indian authority of the era, Paulisa Siddanta. Obviously the accuracy of the ancient Indian astronomical data is not just coincidence. Note that the lunar orbit period of 27.321668 is accurate for the same epoch as the lunar orbit to earth rotations ratio quoted above. This is supportive of the suggestion that the information derives from an accurate ancient source. Table 2. Comparison of astronomic periods and historical sources. Lunar orbit Lunar synodic AD 2000.0 27.32166156 29.53058888 AD 498 27.3216638 29.530591 Àryabhata 27.321668 29.530582 Paulisa Siddanta 27.321673 29.530587 1604 BC 27.321668 29.530595 Àryabhata wrote the Àryabhatiya in four chapters. The first chapter presents the astronomical constants and sine tables. Chapter II is mathematics required for computation. Chapter III discusses time and the longitudes of the planets. Chapter IV includes rules of trigonometry and rules for eclipse computations. Àryabhata's work in effect started a new school of astronomy in South India. Àryabhata is the first known astronomer to have initiated a continuous counting of solar days, designating each day with a number. This 'count of days' is termed the 'ahargana.' His epoch began at the beginning of the Mahayuga. To avoid excessively large numbers, later astronomers changed the beginning of the epoch to the Kali era, commencing at midnight of 17-18 February of 3102 B.C. The Àryabhatiya is a summary of Hindu mathematics up to his time, including astronomy, spherical trigonometry, arithmetic, algebra and plane trigonometry. Some of his formulas are correct, others not. The first appearance of the sine of an angle appears in the work of Àryabhata. He gave tables of half chords (sine tables). To the best of my knowledge, Àryabhata's ratio represents the earliest known recorded astronomic ratio with such incredible accuracy. It surprises me that this fact has gone unnoticed to this date (to the best of my knowledge). I suspect that this oversight is due to our present day emphasis on days and years, rather than rotations and orbits. Few readers today would recognize the ratio of rotations of the earth per lunar orbit. Other author's have commented on the accuracy of ancient Indian astronomy, though typically the ratios were assessed in relation to the duration of the Mahayuga (4,320,000 years). It does not surprise me that such an accurate astronomic ratio may have been known to other cultures in earlier eras. Àryabhata wrote that the apparent motion of the heavens was due to the axial rotation of our planet. Àryabhata taught that the earth is a sphere and rotates on its axis, and that eclipses resulted from the shadows of the moon and earth. Àryabhata's innovations were opposed by Hindu teachers. His teachings were not in accordance with the religious views of his era. Àryabhata wrote, according to Clarke, "In a yuga the revolutions of the Sun are 4,320,000, of the Moon 57,753,336, of the Earth eastward 1,582,237,500, . . ." Given Àryabhata's value of 27.321668 days per lunar orbit period, the 57,753,336 lunar orbits represent 4,320,027.33 solar orbits (in AD 500), not 4,320,000. Why? Perhaps because the numbers are divisible by 60 and 6. The ancient Indians employed base 60 math. I have no certain answer for this question. Perhaps religious dogma had an influence in this matter. The accuracy of the ratios presented should be considered valid, even though they do not match the exact time intervals considered significant in Hindu cosmology. This inaccuracy poses a question regarding the planetary numbers. Should they be compared to the 4,320,000 years number or to the rotations and lunar orbits numbers? Table 3. Comparison of the astronomical numbers presented by the ancient Indian sources. The Surya Siddanta is dated to approximately AD 1100. Àryabhata Surya Siddanta Years in Cycle 4,320,000 4,320,000 Rotations 1,582,237,500 1,582,237,828 Days 1,577,917,500 1,577,917,828 Lunar Orbits 57,753,336 57,753,336 Kay notes 57,753,339 lunar orbits rather than 57,753,336 per Clarke. Synodic Months 53,433,336 53,433,336 Mercury 17,937,920 17,937,060 Venus 7,022,388 7,022,376 Mars 2,296,824 2,296,832 Jupiter 364,224 364,220 Saturn 146,564 146,568 * This date result is dependent on the accuracy of the obliquity of the ecliptic formula used. Modern, temporal-change-of-obliquity formulas merit closer analysis before reliance on their precision when date-reaching mechanisms are employed. SOME QUESTIONS: At this rewriting, Jan. 1, 2001, I still await some answers to the questions posed below. This may be indicative of the answers. To date I have found no indication of older accurate astronomical constants or published indications of modern writers noticing the accuracy of the data discovered in the Indian sources. Do you know of any source previously noticing and publishing the accuracy of Àryabhata's ratio? Do you know of any older record reflecting such an accurate astronomic ratio? From India? In Sanskrit? From other parts of the world? Do you know of any astronomic record reflecting such an accurate astronomic ratio prior to the last two centuries? When did modern astronomers first arrive at an astronomic ratio of comparable accuracy? The WWW is interactive. You can contribute to this niche of knowledge. If you can comment on or answer any of the questions posed please e-mail me your data: Contact. If your contribution is used to update this material, you will be credited. I do not read Sanskrit. If you do, and you have read the original works, your contributions will be especially appreciated. FURTHER COMMENTS 2007.08.22. In response to the questions above, I have received few replies in nearly a decade now. Today I received an interesting observation from Clive Ross. In part, Mr. Ross wrote: Earth years 1,582,237,500/365.256336 = 4,331,855.04 years. Now we know that nobody recorded planet motion for 4,331,855.04 years, therefore the number is significant.it is relevant to something. Evaluating: Jupiter orbits the Sun in 4332.5 days .compare to the number of Earth days chosen by the author when converted to Earth years. 4,331,855.04. 1000 times the days for Jupiter to orbit the Sun.! BIBLIOGRAPHY Clark, William Eugene, The Àryabhatiya of Àryabhata, An Ancient Indian Work on Mathematics and Astronomy, The University of Chicago Press, Chicago, Illinois. 1930. Kay, G. R., Hindu Astronomy, Ancient Science of the Hindus, Cosmo Publications, New Dehli. India, 1981. Pingree, David, Jyotihsastra, Astral and Mathematical Literature, Otto Harrassowitz, Weisbaden, 1981. Sastri, Pundit Bapu Deva, and Lancelot Wilkinson, The Surya Siddhánta, or An Ancient System of Hindu Astronomy, Philo Press, Amsterdam, 1974. Sen, S. N., and K. S. Shukla, History of Astronomy in India, Indian National Science Academy, New Dehli, 1985. ============================================================ Quote Link to comment Share on other sites More sharing options...
Guest guest Posted January 28, 2009 Report Share Posted January 28, 2009 Dear Sreenadhji, Thank you for posting such an excellent article. However, if you permit me to say, I differ on the date of Aryabhatta. Aryabhatta was born in 1325 BCE ie. about 12 centuries before Varahamihira, who was born in 124 BCE. Regards, Sunil K. Bhattacharjya--- On Wed, 1/28/09, Sreenadh <sreesog wrote: Sreenadh <sreesog An excellent site by James Q. Jacobs Date: Wednesday, January 28, 2009, 5:14 AM Dear All, An excellent site by James Q. Jacobs: http://jqjacobs. net/ I have just invited him to this group. An excellent article by him is given below.Love and regards,Sreenadh============ ========= ========= ========= ========= ========= === The Àryabhatiya of Àryabhata: The oldest exact astronomical constant? © 1998 by James Q. Jacobs In the work The Àryabhatiya of Àryabhata, An Ancient Indian Work on Mathematics and Astronomy, translated by William Eugene Clark, Professor of Sanskrit at Harvard University (The University of Chicago Press, Chicago, Illinois. 1930), I found the following to be written: "In a yuga the revolutions of the Sun are 4,320,000, of the Moon 57,753,336, of the Earth eastward 1,582,237,500, of Saturn 146,564, of Jupiter 364,224, of Mars 2,296,824 . . . " (page 9).As can be seen from the Clarke's translation Àryabhata wrote that 1,582,237,500 rotations of the Earth equal 57,753,336 lunar orbits. (These same two numbers are also presented by G. R. Kay in his appendices, where they are attributed to Àryabhata and Pusíla.) This is an extremely accurate ratio for two fundamental cosmic motions (1,582,237,500 / 57,753,336 = 27.3964693572). Given Jan. 1, 2000 astronomical constants and given the present day formulas to temporally adjust the astronomical constants, I calculated that Àryabhata's ratio was exact for 1604 BC.* The resulting data is presented in Table 1. The temporal variation formulas used can be obtained from my Astronomy Formulas page. The date AD 500 is the approximate epoch in which Àryabhata wrote. Àryabhata was born in 476 in Patna, India and died in 550. His Àryabhatiya was probably written in A.D 498. His sources remain obscure. Table 1. Comparison of The Àryabhatiya of Àryabhata and Astronomic values. Astronomy Constants AD 2000.0 AD 500 1604 BC Rotations per solar orbit 366.25636031 366.2563589 366.25635656 Days per solar orbit 365.25636031 365.2563589 365.25635656 Days per lunar orbit 27.32166120 27.3216638 27.32166801 Rotations per lunar orbit 27.39646289 27.39646514 27.39646936 While the majority of the ratios presented by Àryabhata are not equally precise, it is difficult to believe that the earth rotations to lunar orbits ratio, given such very large numbers, could be so precise by coincidence. The odds of that being the case are astronomical. This is particularly so given that the data derives from an era when it was more exactive than today. If it derived from an ancient Vedic source, it was even more exactive when it originated. Additionally, lunar orbit and earth rotation are two of the three actual fundamental cosmic motions, rather than the apparent day/night or lunar phase cycles. According to G. R. Kay, Àryabhata and the Paulisa Siddanta present the values below for the lunar periods. Kay's table of durations of sidereal and synodic months also quotes another ancient Indian authority of the era, Paulisa Siddanta. Obviously the accuracy of the ancient Indian astronomical data is not just coincidence. Note that the lunar orbit period of 27.321668 is accurate for the same epoch as the lunar orbit to earth rotations ratio quoted above. This is supportive of the suggestion that the information derives from an accurate ancient source. Table 2. Comparison of astronomic periods and historical sources. Lunar orbit Lunar synodic AD 2000.0 27.32166156 29.53058888 AD 498 27.3216638 29.530591 Àryabhata 27.321668 29.530582 Paulisa Siddanta 27.321673 29.530587 1604 BC 27.321668 29.530595 Àryabhata wrote the Àryabhatiya in four chapters. The first chapter presents the astronomical constants and sine tables. Chapter II is mathematics required for computation. Chapter III discusses time and the longitudes of the planets. Chapter IV includes rules of trigonometry and rules for eclipse computations. Àryabhata's work in effect started a new school of astronomy in South India. Àryabhata is the first known astronomer to have initiated a continuous counting of solar days, designating each day with a number. This 'count of days' is termed the 'ahargana.' His epoch began at the beginning of the Mahayuga. To avoid excessively large numbers, later astronomers changed the beginning of the epoch to the Kali era, commencing at midnight of 17-18 February of 3102 B.C. The Àryabhatiya is a summary of Hindu mathematics up to his time, including astronomy, spherical trigonometry, arithmetic, algebra and plane trigonometry. Some of his formulas are correct, others not. The first appearance of the sine of an angle appears in the work of Àryabhata. He gave tables of half chords (sine tables). To the best of my knowledge, Àryabhata's ratio represents the earliest known recorded astronomic ratio with such incredible accuracy. It surprises me that this fact has gone unnoticed to this date (to the best of my knowledge). I suspect that this oversight is due to our present day emphasis on days and years, rather than rotations and orbits. Few readers today would recognize the ratio of rotations of the earth per lunar orbit. Other author's have commented on the accuracy of ancient Indian astronomy, though typically the ratios were assessed in relation to the duration of the Mahayuga (4,320,000 years). It does not surprise me that such an accurate astronomic ratio may have been known to other cultures in earlier eras. Àryabhata wrote that the apparent motion of the heavens was due to the axial rotation of our planet. Àryabhata taught that the earth is a sphere and rotates on its axis, and that eclipses resulted from the shadows of the moon and earth. Àryabhata's innovations were opposed by Hindu teachers. His teachings were not in accordance with the religious views of his era. Àryabhata wrote, according to Clarke, "In a yuga the revolutions of the Sun are 4,320,000, of the Moon 57,753,336, of the Earth eastward 1,582,237,500, . . ." Given Àryabhata's value of 27.321668 days per lunar orbit period, the 57,753,336 lunar orbits represent 4,320,027.33 solar orbits (in AD 500), not 4,320,000. Why? Perhaps because the numbers are divisible by 60 and 6. The ancient Indians employed base 60 math. I have no certain answer for this question. Perhaps religious dogma had an influence in this matter. The accuracy of the ratios presented should be considered valid, even though they do not match the exact time intervals considered significant in Hindu cosmology. This inaccuracy poses a question regarding the planetary numbers. Should they be compared to the 4,320,000 years number or to the rotations and lunar orbits numbers? Table 3. Comparison of the astronomical numbers presented by the ancient Indian sources. The Surya Siddanta is dated to approximately AD 1100. Àryabhata Surya Siddanta Years in Cycle 4,320,000 4,320,000 Rotations 1,582,237,500 1,582,237,828 Days 1,577,917,500 1,577,917,828 Lunar Orbits 57,753,336 57,753,336 Kay notes 57,753,339 lunar orbits rather than 57,753,336 per Clarke. Synodic Months 53,433,336 53,433,336 Mercury 17,937,920 17,937,060 Venus 7,022,388 7,022,376 Mars 2,296,824 2,296,832 Jupiter 364,224 364,220 Saturn 146,564 146,568 * This date result is dependent on the accuracy of the obliquity of the ecliptic formula used. Modern, temporal-change- of-obliquity formulas merit closer analysis before reliance on their precision when date-reaching mechanisms are employed. SOME QUESTIONS: At this rewriting, Jan. 1, 2001, I still await some answers to the questions posed below. This may be indicative of the answers. To date I have found no indication of older accurate astronomical constants or published indications of modern writers noticing the accuracy of the data discovered in the Indian sources. Do you know of any source previously noticing and publishing the accuracy of Àryabhata's ratio? Do you know of any older record reflecting such an accurate astronomic ratio? From India? In Sanskrit? From other parts of the world? Do you know of any astronomic record reflecting such an accurate astronomic ratio prior to the last two centuries? When did modern astronomers first arrive at an astronomic ratio of comparable accuracy? The WWW is interactive. You can contribute to this niche of knowledge. If you can comment on or answer any of the questions posed please e-mail me your data: Contact. If your contribution is used to update this material, you will be credited. I do not read Sanskrit. If you do, and you have read the original works, your contributions will be especially appreciated. FURTHER COMMENTS 2007.08.22. In response to the questions above, I have received few replies in nearly a decade now. Today I received an interesting observation from Clive Ross. In part, Mr. Ross wrote: Earth years 1,582,237,500/ 365.256336 = 4,331,855.04 years. Now we know that nobody recorded planet motion for 4,331,855.04 years, therefore the number is significant. it is relevant to something. Evaluating: Jupiter orbits the Sun in 4332.5 days .compare to the number of Earth days chosen by the author when converted to Earth years. 4,331,855.04. 1000 times the days for Jupiter to orbit the Sun.! BIBLIOGRAPHY Clark, William Eugene, The Àryabhatiya of Àryabhata, An Ancient Indian Work on Mathematics and Astronomy, The University of Chicago Press, Chicago, Illinois. 1930. Kay, G. R., Hindu Astronomy, Ancient Science of the Hindus, Cosmo Publications, New Dehli. India, 1981. Pingree, David, Jyotihsastra, Astral and Mathematical Literature, Otto Harrassowitz, Weisbaden, 1981. Sastri, Pundit Bapu Deva, and Lancelot Wilkinson, The Surya Siddhánta, or An Ancient System of Hindu Astronomy, Philo Press, Amsterdam, 1974. Sen, S. N., and K. S. Shukla, History of Astronomy in India, Indian National Science Academy, New Dehli, 1985. ============ ========= ========= ========= ========= ========= === Quote Link to comment Share on other sites More sharing options...
Guest guest Posted January 29, 2009 Report Share Posted January 29, 2009 Sunil Bhattacharjya ... wrote: > > ... I differ on the date of Aryabhatta. > Aryabhatta was born in 1325 BCE ... I would be interested in a source of this information. Most writers state around AD 500, albeit I have not sourced their original sources or assumptions. Quote Link to comment Share on other sites More sharing options...
Guest guest Posted January 29, 2009 Report Share Posted January 29, 2009 Dear James Jacobs ji, and Sunil Bhattacharjya ji, * Most of the historians date Aryabhata around AD 498 * Chandra Hari has argued by providing many supporting evidences that the calculations provided in Aryabhateeya is based on the Ancient work Surya Siddhanta and the observations made on the year AD. 522. * Sunil Bhattacharjya ji states that "Aryabhatta was born in 1325 BCE". But I don't know what he has to say about the clear statement about the year AD 498 in his text etc. * James Q. Jacobs ji states that "I calculated that Àryabhata's ratio was (Rotations per lunar orbit) exact for 1604 BC." I am NOT qualified enough in astronomy to comment on the observations of James Q. Jacobs ji, Chandra Hari ji or Sunil Bhattacharjya ji. But I know taht - * Aryabhata lived in Kerala (since the circumference of earth provided by Aryabhata matches to the latitude of Kerala only, and also because such a basic argument is true for all the anceint astronomers like Ptolamy, Brahmagupta etc who gave or calculated 2 circumpherance to earth each - one based on their native place and the other based on equator). * I know that Aryabhata was a Jain (from internal reference to 'Utsarpini-Apasarpini Sushama-Dushma' Jain yuga system provided in Aryabhateeya) and that ancient non-vedic Agama knowledge spread from Gujrat (Western cost of India) and Orissa (Eastern cost of India) to Kerala mainly through the Jains. * I know that the Aryabhateeya is a text written based on and continuing the tradition of ancient Surya siddhanta (This text is unavailable today. The two available modified surya siddhantas are - 1) The version of Surya Siddhanta provided by Mihira in Pancha siddhantika of AD 525; 2) The version of Surya Siddhanta provided by an unknown scholar based on the year AD 522, modified around AD 1000) * The source of information for Aryabhata could be - 1) The unavailable ancient Surya Siddhanta text that might be older than we currently believe; 2) It could be the knowledge propagated from some cultures like Sinddhu Sarasvati civilization; 3) It could be the knowledge propagated from some ancient cultures like Crete, Minoan, Assyrian, Babylonian, Polynesian, Mayan or some other civilization - since Kerala was a hub of merchant communication through sea in that ancient past of AD 500. It is not only regarding the ancient astronomical info provided in texts like Aryabhateeya and Surya Siddhanta I am wonder struck about; but also regarding the info provided in astrological quotes available from texts like Skanda Hora, Brihat Prajapatya, Sounaka Hora, Kousika Hora etc as well. I failed to track the source (location and tradition) of these texts till date, especially stunned by the fact that they are all in Sanskrit. They don't seem to have much connection with the Vedic tropical astronomical tradition. I don't know whether they were in any way connected to Sindhu Sarasvati tradition or not (that is the only choice I can think of...with the available evidence, but I could be made completely off the mark by some new archeological discovery about some non-vedic tradition that too used Sanskrit or so from the ancient past)... The only thing I am sure about is that there is too much mysterious information available with mysterious origin and a stunning hallow of knowledge connected with them... It seems that we know nothing about the origins...... To Jacobs ji: If you want any Sanskrit quote of Aryabhata or available Surya Siddhanta with meaning - I can provide you the same. If you want the papers of Chandrahari related to Aryabhata they are available in the file section of the group and you can directly communicate to Chandrahari as well since he is a member of this group. To Sunil Bhattacharjya ji: I am not for an argumentation regarding the date of Aryabhata etc - I am not an expert on such subjects. My personal opinion is still in favor of the date around AD 498 and the argument that the calculations are most possibly based on AD 522 observations. But if encountered with solid evidence and arguments, I may change this opinion in future. Hope this information helps. Love and regards, Sreenadh , "James Q. Jacobs" <jqjacobs wrote:>> Sunil Bhattacharjya ... wrote:> >> > ... I differ on the date of Aryabhatta. > > Aryabhatta was born in 1325 BCE ...> > I would be interested in a source of this information. Most writers> state around AD 500, albeit I have not sourced their original sources> or assumptions.> Quote Link to comment Share on other sites More sharing options...
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