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- 1. Astronomy in Bharat-varsha* *the ancient name of India
- 2. A presentation summarizing and based on the publication“Remarks on the astronomy of the Brahmins” by John Playfair (FRSE, FRS) Transactions of the Royal Society of Edinburgh, 1790
- 3. motivation
- 4. Modern day interpretations of ancient Bharat-Varsha (India) are oftendistorted by biases introduced by British colonizers, in line with thecolonial agenda.
- 5. Modern day interpretations of ancient Bharat-Varsha (India) are oftendistorted by biases introduced by British colonizers, in line with thecolonial agenda. These interpretations obscure/ignore the fundamental contributionsmade by Bharat-Varsha to science and technology, and the debt whichmodern civilization owes to the Indian civilization.
- 6. Modern day interpretations of ancient Bharat-Varsha (India) are oftendistorted by biases introduced by British colonizers, in line with thecolonial agenda. These interpretations obscure/ignore the fundamental contributionsmade by Bharat-Varsha to science and technology, and the debt whichmodern civilization owes to the Indian civilization. A more unbiased and reliable picture emerges from the records leftby early colonizers and scientists in the 18th century, by whom a carefulobservation of Indian society and traditions was undertaken, both forgathering technological know-how and for establishing political control.
- 7. Modern day interpretations of ancient Bharat-Varsha (India) are oftendistorted by biases introduced by British colonizers, in line with thecolonial agenda. These interpretations obscure/ignore the fundamental contributionsmade by Bharat-Varsha to science and technology, and the debt whichmodern civilization owes to the Indian civilization. A more unbiased and reliable picture emerges from the records leftby early colonizers and scientists in the 18th century, by whom a carefulobservation of Indian society and traditions was undertaken, both forgathering technological know-how and for establishing political control. A perusal of such records is necessary for dispelling stereotypicalnotions and myths regarding ancient Bharat-Varsha.
- 8. Modern day interpretations of ancient Bharat-Varsha (India) are oftendistorted by biases introduced by British colonizers, in line with thecolonial agenda. These interpretations obscure/ignore the fundamental contributionsmade by Bharat-Varsha to science and technology, and the debt whichmodern civilization owes to the Indian civilization. A more unbiased and reliable picture emerges from the records leftby early colonizers and scientists in the 18th century, by whom a carefulobservation of Indian society and traditions was undertaken, both forgathering technological know-how and for establishing political control. A perusal of such records is necessary for dispelling stereotypicalnotions and myths regarding ancient Bharat-Varsha. And hence, this discussion regarding the publication mentioned, ismeant to serve as a small step in this direction.
- 9. What this publication discusses
- 10. What this publication discussesThree sets of astronomical tables originating from India
- 11. What this publication discussesThree sets of astronomical tables originating from India (1) Brought from Siam in 1687 to Europe
- 12. What this publication discussesThree sets of astronomical tables originating from India (1) Brought from Siam in 1687 to Europe (2) Sent from Krishnapuram in about 1750 to Europe
- 13. What this publication discussesThree sets of astronomical tables originating from India (1) Brought from Siam in 1687 to Europe (2) Sent from Krishnapuram in about 1750 to Europe (3) Brought from Tiruvallur in 1772 from Europe
- 14. An example of one of the tables from Krishnapurampublished in the book “Traité de l’astronomie Indienne et orientale”, byM. Bailly, Paris, 1787.
- 15. “From the materials furnished by Monsieur Le Gentil andMonsieur Le Bailly, Mr. Playfair has gone even beyond thoseauthors, in establishing, by scientific proof, the originality of theHindoo astronomy, and its superior antiquity to any other that isknown.”-Quentin Craufurd, ‘Sketches chiefly relating the history,religion, learning, and manners, of the Hindoos’, Vol I, 1792.
- 16. some astronomical concepts
- 17. (1) Celestial Sphere
- 18. Celestial sphere- An imaginary sphere of arbitrarily large radius centered at theearth, useful for describing positions of heavenly objects observed from theearth.Celestial coordinates- Coordinates used for describing the position of aheavenly object on the celestial sphere.Celestial equator- Intersection of the equatorial plane of the earth with thecelestial sphere.Ecliptic- The circle on the celestial sphere in which the sun appears to revolvearound the earth in the course of a year. This motion is due to the orbital motionof the earth around the sun. The ecliptic plane and the celestial equatorial planeare tilted by about 23.50. This tilt is called obliquity of the ecliptic, and givesrise to the seasonal variations.Points of Equinox- The points where the ecliptic and the celestial equatorappear to intersect. This happens twice a year at diametrically opposite points ofthe celestial sphere: once during spring (spring/vernal equinox) and once duringautumn (autumnal equinox).
- 19. (2) Precession of the equinoxes The direction of the earth’s axis of rotation itself precesses (rotates) about a direction perpendicular to the ecliptic plane tracing out a cone with semi-angle 23.5o. A full precession is completed in about 26,000 yrs.
- 20. ImplicationsDue to precession of the earth’s axis of rotation, every time the earthcompletes one revolution around the sun, the orientation of the earth’s axis ofrotation, with respect to the sun, would have changed slightly.This implies that the periodic change of the seasons occurs with a regularitythat is slightly different from the time taken by the earth to complete onerevolution around the sun, and this difference accumulates with time.This leads us to two definitions of the year:SIDEREAL YEAR and TROPICAL YEAR:
- 21. SIDEREAL YEAR:The time taken by the earth to complete one revolution around the sunwith respect to the fixed stars.
- 22. SIDEREAL YEAR:The time taken by the earth to complete one revolution around the sunwith respect to the fixed stars.TROPICAL YEAR:The time taken by the earth to return to the same cycle of seasons. Itcan also be defined as the time required by the sun to traverse aroundthe ecliptic from, say, the vernal equinox and back again to the vernalequinox, and thus returning back to the cycle of seasons.
- 23. The sidereal year is longer than the tropical year by about 20 minutes. Thismeans that the vernal equinox shifts slightly westwards as seen from theearth, with respect to the fixed stars, after each revolution of the sun along theecliptic. Earths precession was historically called precession of the equinoxesbecause the equinoxes move westward along the ecliptic relative to the fixedstars, opposite to the motion of the Sun along the ecliptic.
- 24. The tables
- 25. What they contain:Positions of the sun, moon and the planets on the celestialsphere calculated for different times, and the times of eclipses.Consequently, they give information on the ellipticity of theearth’s and the moon’s motion, precession of the equinoxes,and other details to a high level of precision.
- 26. Why they are special:
- 27. Why they are special: Offer solid evidence that astronomical observations werecarried out in Bharata-Varsha at least 5000 years ago, if notconsiderably earlier, and with no inputs from any of the latercivilizations.
- 28. Why they are special: Offer solid evidence that astronomical observations werecarried out in Bharata-Varsha at least 5000 years ago, if notconsiderably earlier, and with no inputs from any of the latercivilizations. Most of the predictions are in general agreement withcontemporary observations and theoretical calculations basedon the theory of gravitation.
- 29. Why they are special: Offer solid evidence that astronomical observations werecarried out in Bharata-Varsha at least 5000 years ago, if notconsiderably earlier, and with no inputs from any of the latercivilizations. Most of the predictions are in general agreement withcontemporary observations and theoretical calculations basedon the theory of gravitation. Since predicting the positions of heavenly objects is a taskinvolving considerable complexity, these tables offer atantalizing glimpse into the level of mathematical sophisticationachieved in Bharat-Varsha, and as such point to the existence ofan age of which almost every vestige has been lost.
- 30. Some terms…
- 31. Some terms…(1) Epoch: The time at which actual observations arecarried out, and which serve as the reference forcalculating the positions of heavenly objects at a futureinstant of time.
- 32. Some terms…(1) Epoch: The time at which actual observations arecarried out, and which serve as the reference forcalculating the positions of heavenly objects at a futureinstant of time.(2) Mean motion/position: This refers to position of aheavenly object in the celestial sphere at a given instant intime if its motion is subjected to no irregularities.
- 33. Some terms…(1) Epoch: The time at which actual observations arecarried out, and which serve as the reference forcalculating the positions of heavenly objects at a futureinstant of time.(2) Mean motion/position: This refers to position of aheavenly object in the celestial sphere at a given instant intime if its motion is subjected to no irregularities.(3) Correction: This refers to the correction, arising dueto irregularities, which must be added/subtracted to themean position of a heavenly object in order to obtain itstrue position at a given instant of time. The irregularitiesare caused by factors such as ellipticity of the orbits,precession of the equinoxes, or perturbing effects of otherplanets.
- 34. Thus the tables contain…
- 35. Thus the tables contain…The mean positions for the sun, moon and the planets atvarious times, the corrections that must be added to themean positions at the various times, and the rules foradding these corrections depending on the time one wantsthe position of a heavenly object.
- 36. The tables from Siam
- 37. The tables from SiamOriginally meant for the location of Benares, as deduced by the Frenchastronomer Cassini.
- 38. The tables from SiamOriginally meant for the location of Benares, as deduced by the Frenchastronomer Cassini.Supposed epoch of the tables: 21st March, year 638, as deduced byCassini.
- 39. The tables from SiamOriginally meant for the location of Benares, as deduced by the Frenchastronomer Cassini.Supposed epoch of the tables: 21st March, year 638, as deduced byCassini.Sidereal year according to the tables: 365d, 6h, 12’, 36” *Tropical year according to the tablesϯ: 365d, 5h, 50’, 41” ϯϯ* d = days, h = hours, ( ’ ) = minutes, ( ” )=seconds.ϯ Thus the equinoxes precess at a rate of once every 24,000 years, which is slightly more thanthe current rate of once every 26,000 years.ϯϯThe duration of the sidereal and tropical years is nearly the same in all the other tables, andhence the rate of the precession of the equinoxes is about once in 24,000 years.
- 40. The tables from SiamOriginally meant for the location of Benares, as deduced by the Frenchastronomer Cassini.Supposed epoch of the tables: 21st March, year 638, as deduced byCassini.Sidereal year according to the tables: 365d, 6h, 12’, 36” *Tropical year according to the tablesϯ: 365d, 5h, 50’, 41” ϯϯ“This determination of the length of the year is but 1’, 53” greater thanthat of De La Caille, which is a degree of accuracy beyond what is to befound in the more ancient tables of our astronomy.” *** d = days, h = hours, ( ’ ) = minutes, ( ” )=seconds.ϯ Thus the equinoxes precess at a rate of once every 24,000 years, which is slightly more thanthe current rate of once every 26,000 years.ϯϯThe duration of the sidereal and tropical years is nearly the same in all the other tables, andhence the rate of the precession of the equinoxes is about once in 24,000 years.**Statements within quotes, unless otherwise stated, should be understood as being directlyquoted from the article.
- 41. The tables from SiamOn the motion of the moon - IAccording to the Siamese (and presumably other) tables, themoon completes 235 revolutions with respect to the line joiningthe earth and the sun* in a period of about 19 years. Thediscovery of this so-called Metonic cycle is attributed to theGreek astronomer Meton, even though Indian astronomy seemsto have been independently well aware of this fact.* i.e., 235 lunar months.
- 42. The tables from SiamOn the motion of the moon - IIAccording to these tables, the apogee* of the moon was in the beginningof the moveable Zodiac 621 days after the epoch. This matches withcontemporary records to within a degree.And from this point, the apogee of the moon is supposed to make anentire revolution in the heavens in the space of 3232 days. This differsfrom contemporary records only by 11h, 14’, 31”.“and if it be considered that the apogee is an ideal point in the heavenswhich even the eyes of an astronomer cannot directly perceive, to havediscovered its true motion, so nearly, argues no small correctness ofobservation.”* The apogee is the point where the moon is farthest from the earth. The motion isslowest at the apogee.
- 43. The tables from Krishnapuram
- 44. The tables from KrishnapuramEpoch: Supposed to be 10th March, 1491, but as we shall see,probably much older.
- 45. The tables from KrishnapuramEpoch: Supposed to be 10th March, 1491, but as we shall see,probably much older.“The places which they assign at that time (epoch) to the sunand moon agree very well with the calculations made from thetables of Mayer * and De La Caille.**”* Tobias Mayer (1723-1762), German astronomer famous for his tables of the moon.** Abbé Nicolas Louis de Lacaille (1713-1762), French astronomer.
- 46. The tables from KrishnapuramEpoch: Supposed to be 10th March, 1491, but as we shall see,probably much older.“The places which they assign at that time (epoch) to the sunand moon agree very well with the calculations made from thetables of Mayer * and De La Caille.**”Equationϯ of the sun’s center: 2o, 10’, 30” ‡Equation of the moon’s center: 5o, 2’, 47”* Tobias Mayer (1723-1762), German astronomer famous for his tables of the moon.** Abbé Nicolas Louis de Lacaille (1713-1762), French astronomer.ϯThe equation of the center is, roughly speaking, a measure of the ellipticity of the orbit and ismeasured in units of the angle.‡ The angle is measured in units of degrees (o), minutes (’) and seconds (”) . One degree equalssixty minutes and one minute equals sixty seconds.
- 47. The tables from Tiruvallur
- 48. Epoch:
- 49. Epoch:3102 B.C.
- 50. Epoch: 3102 B.C.Commencement of the Kali Yuga
- 51. THE QUESTION:
- 52. GENUINE?
- 53. OR
- 54. FAKE?
- 55. The tables of Tiruvallur“We must, therefore, enquire, whether this epoch is real or fictitious, thatis, whether it has been determined by actual observation, or has beencalculated from the modern epochs of the other tables. For it maynaturally be supposed, that the Brahmins, having made observations inlater times, or having borrowed from the astronomical knowledge ofother nations…have only calculated what they pretend that theirancestors observed.”
- 56. The tables of Tiruvallur“In doing this, however, the Brahmins must have furnished us withmeans, almost infallible, of detecting their imposture. It is only forastronomy, in its most perfect state, to go back to the distance of forty-six centuries, and to ascertain the situation of the heavenly bodies at soremote a period. The modern astronomy of Europe…could not venture onso difficult a task, were it not assisted by the theory of gravitation, andhad not the integral calculus…been able, at last, to determine thedisturbances in our system, which arise from the action of the planets onone another.”
- 57. The tables of Tiruvallur“Unless the corrections for these disturbances be taken into account, anysystem of astronomical tables, however accurate at the time of itsformation, and however diligently copied from the heavens, will be foundless exact for every instant, either before or after that time, and willcontinually diverge more and more from the truth, both for future andpast ages.”
- 58. The tables of Tiruvallur“…it may (therefore) be established as a maxim, that, if there be given asystem of astronomical tables, founded on observations of an unknowndate (epoch), that date may be found, by taking the time when the tablesrepresent the celestial motions most exactly.”“Here, therefore, we have a criterion, by which we are to judge of thepretensions of the Indian astronomy to so great antiquity.”
- 59. The tables of TiruvallurThe location of Aldebaran in 3102 B.C.
- 60. The tables of Tiruvallur The location of Aldebaran in 3102 B.C.Aldebaran
- 61. The tables of Tiruvallur The location of Aldebaran in 3102 B.C. According to the tables from TiruvallurAldebaran
- 62. The tables of Tiruvallur The location of Aldebaran in 3102 B.C. According to the tables from Tiruvallur 40’ minutes before the vernal equinox in 3102 B.C.Aldebaran
- 63. The tables of Tiruvallur The location of Aldebaran in 3102 B.C.Aldebaran
- 64. The tables of Tiruvallur The location of Aldebaran in 3102 B.C. According to contemporary calculationsAldebaran
- 65. The tables of Tiruvallur The location of Aldebaran in 3102 B.C. According to contemporary calculations 1) If the rate of precession of equinoxes is assumed constant, it was 1o, 32’ before the vernal equinox in 3102 B.C., based on observations made in 1750.Aldebaran
- 66. The tables of Tiruvallur The location of Aldebaran in 3102 B.C. According to contemporary calculations 1) If the rate of precession of equinoxes is assumed constant, it was 1o, 32’ before the vernal equinox in 3102 B.C., based on observations made in 1750. 2) But the rate of precession of the equinoxes is itself variable, as discovered by La Grange, and “this result is to beAldebaran corrected…by the addition of 1o, 45’, 22” to the longitude of Aldebaran, which gives the longitude of that star 13’ from the vernal equinox, at the time of the Calyougham (Kali-yugam), agreeing, within 53’, with the determination of the Indian astronomy.”
- 67. The tables of Tiruvallur The location of Aldebaran in 3102 B.C.“This agreement is the more remarkable, that the Brahmins, by their ownrules for computing the motion of the fixed stars, could not haveassigned this place to Aldebaran for the beginning of the Calyougham,had they calculated it from a modern observation. For as they make themotion of the fixed stars too great by more than 3” annually,* if they hadcalculated backward from 1491, they would have placed the fixed starsless advanced by 4o or 5o, at their ancient epoch, than they have actuallydone.”*i.e., the rate of precession of equinoxes is faster than the observed rate of once every 26,000years in Indian astronomy.
- 68. The tables of Tiruvallur The location of Aldebaran in 3102 B.C.“This agreement is the more remarkable, that the Brahmins, by their ownrules for computing the motion of the fixed stars, could not haveassigned this place to Aldebaran for the beginning of the Calyougham,had they calculated it from a modern observation. For as they make themotion of the fixed stars too great by more than 3” annually,* if they hadcalculated backward from 1491, they would have placed the fixed starsless advanced by 4o or 5o, at their ancient epoch, than they have actuallydone.”“This argument carries with it a great deal of force, and even were it theonly one we had to produce, it would render it, in a high degree,probable, that the Indian Zodiac was as old as the Calyougham.”*i.e., the rate of precession of equinoxes is faster than the observed rate of once every 26,000years in Indian astronomy.
- 69. The tables of TiruvallurThe location of the Sun in 3102 B.C.
- 70. The tables of TiruvallurThe location of the Sun in 3102 B.C. According to the tables from Tiruvallur
- 71. The tables of TiruvallurThe location of the Sun in 3102 B.C. According to the tables from Tiruvallur 10s, 3o, 38’, 13” (Mean position)
- 72. The tables of TiruvallurThe location of the Sun in 3102 B.C.According to contemporary calculations
- 73. The tables of Tiruvallur The location of the Sun in 3102 B.C. According to contemporary calculations1) Assuming a uniform rate of precession of the equinoxes,it was, calculating back from later observations, at 10s, 1o,5’, 57”.
- 74. The tables of Tiruvallur The location of the Sun in 3102 B.C. According to contemporary calculations1) Assuming a uniform rate of precession of the equinoxes,it was, calculating back from later observations, at 10s, 1o,5’, 57”.2) After adding the correction by La Grange due to thevariation in the rate of precession, it is 10s, 2o, 51’, 19”.
- 75. The tables of Tiruvallur The location of the Sun in 3102 B.C. According to contemporary calculations1) Assuming a uniform rate of precession of the equinoxes,it was, calculating back from later observations, at 10s, 1o,5’, 57”.2) After adding the correction by La Grange due to thevariation in the rate of precession, it is 10s, 2o, 51’, 19”.“…not more than 47’ from the radical place in the tables ofTirvalore. This agreement is near enough to afford a strongproof of the reality of the ancient epoch…”
- 76. The tables of TiruvallurThe location of the Moon in 3102 B.C.
- 77. The tables of TiruvallurThe location of the Moon in 3102 B.C. According to the tables from Tiruvallur
- 78. The tables of TiruvallurThe location of the Moon in 3102 B.C. According to the tables from Tiruvallur 10s, 6o, 38’ (Mean position)
- 79. The tables of TiruvallurThe location of the Moon in 3102 B.C.According to contemporary calculations
- 80. The tables of Tiruvallur The location of the Moon in 3102 B.C. According to contemporary calculations1) Assuming a constant rate of motion for the moon, itsmean place, calculated by Mayer’s tables, is 10s, 0o, 51’,16”.
- 81. The tables of Tiruvallur The location of the Moon in 3102 B.C. According to contemporary calculations1) Assuming a constant rate of motion for the moon, itsmean place, calculated by Mayer’s tables, is 10s, 0o, 51’,16”.2) “But, according to the same astronomer, the moon issubject to a small, but uniform acceleration…the real meanplace of the moon, at the astronomical epoch of theCalyougham…is therefore 10s, 6o, 37’ .”
- 82. The tables of Tiruvallur The location of the Moon in 3102 B.C. According to contemporary calculations1) Assuming a constant rate of motion for the moon, itsmean place, calculated by Mayer’s tables, is 10s, 0o, 51’,16”.2) “But, according to the same astronomer, the moon issubject to a small, but uniform acceleration…the real meanplace of the moon, at the astronomical epoch of theCalyougham…is therefore 10s, 6o, 37’ .”“…a degree of accuracy that nothing but actual observationcould have produced.”
- 83. On the acceleration of the moon
- 84. On the acceleration of the moon(according to data from Mayer’s tables)
- 85. On the acceleration of the moon (according to data from Mayer’s tables) “But, according to the same astronomer, the moon is subject toa small, but uniform acceleration, such, that her angular motion,in any one age, is 9” greater than in the preceding, which in aninterval of 4801 years, must have amounted to 5o, 45’, 44”.
- 86. On the acceleration of the moon(according to the theory of gravity)
- 87. On the acceleration of the moon (according to the theory of gravity)“…that acceleration…is a phenomenon, which M. De La Place* has, withgreat ability, deduced from the principle of universal gravitation, andshown to be necessarily connected with the changes in the eccentricityof the earth’s orbit, discovered by M. De La Grange; so that theacceleration of the moon is indirectly produced by the action of theplanets, which alternately increasing and diminishing the saideccentricity, subjects the moon to different degrees of that force bywhich the sun disturbs the time of her revolution around the earth. It istherefore a periodical inequality, by which the moon’s motion in thecourse of ages, will be as much retarded as accelerated; but its changesare so slow, that her motion has been constantly accelerated, even for alonger period than that to which the observations of India extend.”* Pierre-Simon, marquis de Laplace (1749-1827), French astronomer and mathematician.
- 88. On the acceleration of the moon(according to the tables of Krishnapuram)
- 89. On the acceleration of the moon (according to the tables of Krishnapuram)“The moon’s motion in 4383 years, 94 days, taken from those ofChrisnabouram, is 3o, 2’, 10” less than in the tables of Tirvalore,from which it is reasonable to conclude, with M. Bailly, that theformer are, in reality, more ancient than the latter…and hence also,the tables of Chrisnabouram make the moon’s motion less thanMayer’s, by the above mentioned interval, by 5o, 44’, 14”, whichtherefore is, according to them, the quantity of the acceleration.” The angular motion of the moon predicted by the tables ofKrishnapuram for 4383 years, 94 days from the commencement ofthe Kali Yuga, is 5o, 44’, 14”. The tables thus capture the subtle effects of the gravitationalforce exerted by other planets on the motion of the moon. Antiquity of the Krishnapuram tables is probably even older thanthose from Tiruvallur.
- 90. “…observations made in India, when all Europe was barbarous oruninhabited, and investigations into the most subtle effects ofgravitation made in Europe, near five thousand years afterwards…thus come in mutual support of one another.”
- 91. On the antiquity of the tables
- 92. On the antiquity of the tablesWhy it is highly probable that the tables go back to 1200 years before the commencement of the Kali-Yuga
- 93. On the antiquity of the tables Why it is highly probable that the tables go back to 1200 years before the commencement of the Kali-Yuga The values of three independent quantities, calculated back for thebeginning of the Kali-Yuga (3102 B.C.), using the theory of gravitationand contemporary astronomical tables, show a slight mismatchcompared to the values assigned to them in the Indian tables.
- 94. On the antiquity of the tables Why it is highly probable that the tables go back to 1200 years before the commencement of the Kali-Yuga The values of three independent quantities, calculated back for thebeginning of the Kali-Yuga (3102 B.C.), using the theory of gravitationand contemporary astronomical tables, show a slight mismatchcompared to the values assigned to them in the Indian tables. However, the same three quantities show a very good agreementwith the Indian tables when calculated back to 1200 years before thecommencement of the Kali-Yuga.
- 95. On the antiquity of the tables Why it is highly probable that the tables go back to 1200 years before the commencement of the Kali-Yuga The values of three independent quantities, calculated back for thebeginning of the Kali-Yuga (3102 B.C.), using the theory of gravitationand contemporary astronomical tables, show a slight mismatchcompared to the values assigned to them in the Indian tables. However, the same three quantities show a very good agreementwith the Indian tables when calculated back to 1200 years before thecommencement of the Kali-Yuga. The three quantities are:
- 96. On the antiquity of the tables Why it is highly probable that the tables go back to 1200 years before the commencement of the Kali-Yuga The values of three independent quantities, calculated back for thebeginning of the Kali-Yuga (3102 B.C.), using the theory of gravitationand contemporary astronomical tables, show a slight mismatchcompared to the values assigned to them in the Indian tables. However, the same three quantities show a very good agreementwith the Indian tables when calculated back to 1200 years before thecommencement of the Kali-Yuga. The three quantities are: 1) The length of the tropical year,
- 97. On the antiquity of the tables Why it is highly probable that the tables go back to 1200 years before the commencement of the Kali-Yuga The values of three independent quantities, calculated back for thebeginning of the Kali-Yuga (3102 B.C.), using the theory of gravitationand contemporary astronomical tables, show a slight mismatchcompared to the values assigned to them in the Indian tables. However, the same three quantities show a very good agreementwith the Indian tables when calculated back to 1200 years before thecommencement of the Kali-Yuga. The three quantities are: 1) The length of the tropical year, 2) The equation of the sun’s center, and
- 98. On the antiquity of the tables Why it is highly probable that the tables go back to 1200 years before the commencement of the Kali-Yuga The values of three independent quantities, calculated back for thebeginning of the Kali-Yuga (3102 B.C.), using the theory of gravitationand contemporary astronomical tables, show a slight mismatchcompared to the values assigned to them in the Indian tables. However, the same three quantities show a very good agreementwith the Indian tables when calculated back to 1200 years before thecommencement of the Kali-Yuga. The three quantities are: 1) The length of the tropical year, 2) The equation of the sun’s center, and 3) The obliquity of the ecliptic.
- 99. On the antiquity of the tablesThe length of the tropical year
- 100. On the antiquity of the tables The length of the tropical year 365d, 5h, 50’, 35”, according to the tables from Tiruvallur.
- 101. On the antiquity of the tables The length of the tropical year 365d, 5h, 50’, 35”, according to the tables from Tiruvallur. 1’, 46” longer than contemporary records.
- 102. On the antiquity of the tables The length of the tropical year 365d, 5h, 50’, 35”, according to the tables from Tiruvallur. 1’, 46” longer than contemporary records. But, “the tropical year was in reality longer at that time than it is at present,”as it is affected by the precession of the equinoxes and is subjected to slow andunequal alternations of diminution and increase.
- 103. On the antiquity of the tables The length of the tropical year 365d, 5h, 50’, 35”, according to the tables from Tiruvallur. 1’, 46” longer than contemporary records. But, “the tropical year was in reality longer at that time than it is at present,”as it is affected by the precession of the equinoxes and is subjected to slow andunequal alternations of diminution and increase. “If we suppose these observations to have been made in that period of 2400years, immediately preceding the Calyougham,…we shall find, that, at the middleof this period, or 1200 years before the beginning of the Calyougham, the lengthof the year was 365d, 5h, 50’, 41”, almost precisely as in the tables of Tirvalore.”
- 104. On the antiquity of the tables The length of the tropical year 365d, 5h, 50’, 35”, according to the tables from Tiruvallur. 1’, 46” longer than contemporary records. But, “the tropical year was in reality longer at that time than it is at present,”as it is affected by the precession of the equinoxes and is subjected to slow andunequal alternations of diminution and increase. “If we suppose these observations to have been made in that period of 2400years, immediately preceding the Calyougham,…we shall find, that, at the middleof this period, or 1200 years before the beginning of the Calyougham, the lengthof the year was 365d, 5h, 50’, 41”, almost precisely as in the tables of Tirvalore.” “And hence it is natural to conclude, that this determination of the solar year isas ancient as the year 1200 before the Calyougham, or 4300 before the Christianera.”
- 105. On the antiquity of the tablesThe equation of the sun’s center
- 106. On the antiquity of the tables The equation of the sun’s center Fixed in the tables at 2o, 10’, 32”.
- 107. On the antiquity of the tables The equation of the sun’s center Fixed in the tables at 2o, 10’, 32”. Present value according to contemporary records: 1o, 551/₂’ , i.e., 15’ less thanin the Indian tables.
- 108. On the antiquity of the tables The equation of the sun’s center Fixed in the tables at 2o, 10’, 32”. Present value according to contemporary records: 1o, 551/₂’ , i.e., 15’ less thanin the Indian tables. But as shown by La Grange, the sun’s equation has been diminishing for manyages. In 3102 B.C., it was therefore 2o, 6’, 281/₂”, i.e., only 4’ less than in theIndian tables.
- 109. On the antiquity of the tables The equation of the sun’s center Fixed in the tables at 2o, 10’, 32”. Present value according to contemporary records: 1o, 551/₂’ , i.e., 15’ less thanin the Indian tables. But as shown by La Grange, the sun’s equation has been diminishing for manyages. In 3102 B.C., it was therefore 2o, 6’, 281/₂”, i.e., only 4’ less than in theIndian tables. But if calculated for 1200 years before the commencement of the Kali-Yuga,the agreement is still more exact.
- 110. On the antiquity of the tables The equation of the sun’s center Fixed in the tables at 2o, 10’, 32”. Present value according to contemporary records: 1o, 551/₂’ , i.e., 15’ less thanin the Indian tables. But as shown by La Grange, the sun’s equation has been diminishing for manyages. In 3102 B.C., it was therefore 2o, 6’, 281/₂”, i.e., only 4’ less than in theIndian tables. But if calculated for 1200 years before the commencement of the Kali-Yuga,the agreement is still more exact. “1200 years before the commencement of that period (Kali-Yuga)…it appears,by computing from M. De La Grange’s formula, that the equation of the sun’scenter was actually 2o, 8’, 16”, so that if the Indian astronomy be as old as thatperiod, its error with respect to this equation is but of 2’. ”
- 111. On the antiquity of the tablesObliquity of the ecliptic
- 112. On the antiquity of the tables Obliquity of the ecliptic The Indian tables take the obliquity of the ecliptic to be 24o. But contemporaryEuropean records in the year 1700 take it to be 23o, 28’, 41”.
- 113. On the antiquity of the tables Obliquity of the ecliptic The Indian tables take the obliquity of the ecliptic to be 24o. But contemporaryEuropean records in the year 1700 take it to be 23o, 28’, 41”. But the obliquity itself, like the rate of precession of equinoxes, and theequation of the sun’s center, slowly varies with time due to perturbing effects ofthe other planets.
- 114. On the antiquity of the tables Obliquity of the ecliptic The Indian tables take the obliquity of the ecliptic to be 24o. But contemporaryEuropean records in the year 1700 take it to be 23o, 28’, 41”. But the obliquity itself, like the rate of precession of equinoxes, and theequation of the sun’s center, slowly varies with time due to perturbing effects ofthe other planets. Therefore, “M. De La Grange’s formula for the variation of the obliquity, gives22’, 32”, to be added to its obliquity in 1700, … , in order to have that which tookplace in the year 3102 before our era. This gives us 23o, 51’, 13”, which is 8’, 47”,short of the determination of the Indian astronomers.”
- 115. On the antiquity of the tables Obliquity of the ecliptic The Indian tables take the obliquity of the ecliptic to be 24o. But contemporaryEuropean records in the year 1700 take it to be 23o, 28’, 41”. But the obliquity itself, like the rate of precession of equinoxes, and theequation of the sun’s center, slowly varies with time due to perturbing effects ofthe other planets. Therefore, “M. De La Grange’s formula for the variation of the obliquity, gives22’, 32”, to be added to its obliquity in 1700, … , in order to have that which tookplace in the year 3102 before our era. This gives us 23o, 51’, 13”, which is 8’, 47”,short of the determination of the Indian astronomers.” If the obliquity is calculated for 1200 years before the Kali-Yuga set in, theagreement is still more exact.
- 116. On the antiquity of the tables Obliquity of the ecliptic The Indian tables take the obliquity of the ecliptic to be 24o. But contemporaryEuropean records in the year 1700 take it to be 23o, 28’, 41”. But the obliquity itself, like the rate of precession of equinoxes, and theequation of the sun’s center, slowly varies with time due to perturbing effects ofthe other planets. Therefore, “M. De La Grange’s formula for the variation of the obliquity, gives22’, 32”, to be added to its obliquity in 1700, … , in order to have that which tookplace in the year 3102 before our era. This gives us 23o, 51’, 13”, which is 8’, 47”,short of the determination of the Indian astronomers.” If the obliquity is calculated for 1200 years before the Kali-Yuga set in, theagreement is still more exact. “But if we suppose, … , that the observations on which this determination isfounded, were made 1200 years before the Calyougham, we shall find that theobliquity of the ecliptic was 23o, 53’, 45”, and that the error of the tables did notmuch exceed 2’. ”
- 117. On the antiquity of the tables Thus three entirely independent elements separately answer to belongto an age 1200 years before the Kali-Yuga set in, or about 6300 yearsfrom today. Too much to be a matter of chance! “This coincidence … cannot be the effect of chance…there is no otheralternative…but to acknowledge that the Indian astronomy is as ancientas one, or other of the periods above mentioned.”
- 118. On the planets
- 119. On the planets (1)The retrograde motion and the aphelion of Jupiter
- 120. On the planets (1)The retrograde motion and the aphelion of Jupiter (2) The equation of Saturn’s center
- 121. On the planets (1)The retrograde motion and the aphelion of Jupiter (2) The equation of Saturn’s center (3)The mutual interaction between Saturn and Jupiter
- 122. On the planets The retrograde motion and the aphelion of JupiterRetrograde motion: The apparent occasional motion of a planet opposite to thatusually observed, due to the projection of the planet’s motion on the celestialsphere.Aphelion: The point in aplanet’s orbit which is farthestfrom the sun. The motion isslowest at this point. Figure illustrating the retrograde motion of the planets
- 123. On the planetsThe retrograde motion and the aphelion of Jupiter
- 124. On the planets The retrograde motion and the aphelion of JupiterAccording to the Indian tables, Jupiter has a retrograde motion of 15o in 200,000years, and thus, calculating back from Jupiter’s position in 1491 as given in theKrishnapuram tables, its aphelion at the onset of Kali-Yuga was at 3s, 27o, 0’ fromthe equinox.
- 125. On the planets The retrograde motion and the aphelion of JupiterAccording to the Indian tables, Jupiter has a retrograde motion of 15o in 200,000years, and thus, calculating back from Jupiter’s position in 1491 as given in theKrishnapuram tables, its aphelion at the onset of Kali-Yuga was at 3s, 27o, 0’ fromthe equinox.Calculating back from contemporary European records gives for the aphelion ofJupiter in 3102 B.C. as 3s, 16o, 48’, 58”, “so that there would seem to be an error ofmore than 10o in the tables of the Brahmins.”
- 126. On the planets The retrograde motion and the aphelion of JupiterAccording to the Indian tables, Jupiter has a retrograde motion of 15o in 200,000years, and thus, calculating back from Jupiter’s position in 1491 as given in theKrishnapuram tables, its aphelion at the onset of Kali-Yuga was at 3s, 27o, 0’ fromthe equinox.Calculating back from contemporary European records gives for the aphelion ofJupiter in 3102 B.C. as 3s, 16o, 48’, 58”, “so that there would seem to be an error ofmore than 10o in the tables of the Brahmins.”But Jupiter’s orbit is subject to great disturbances from the action of Saturn, whichthe above calculation ignores. Including these disturbances (by making use of aformula due to La Grange), gives for the aphelion of Jupiter at the beginning of Kali-Yuga (3102 B.C.), as 3s, 26o, 50’, 40”, “which is but 10’, 40” different from thetables of Krishnapuram.”
- 127. On the planetsThe equation of Saturn’s center
- 128. On the planets The equation of Saturn’s center“The equation of Saturn’s center is an instance of the same kind. Thatequation, at present, is according to M. De La Lande, 6o, 23’ 19”; andhence, by means of one of the formulas above mentioned, M. Baillycalculates, that, 3102 years before Christ, it was 7o, 41’, 22”. The tablesof the Brahmins make it 7o, 39’, 44”, which is less only by 1’, 38”, thanthe preceding equation…”
- 129. On the planetsThe mutual interaction between Saturn and Jupiter
- 130. On the planets The mutual interaction between Saturn and Jupiter“Since the publication of M. Bailly’s work*, two other instances of an exactagreement, between the elements of these tables, and the conclusionsdeduced from the theory of gravity, have been observed, andcommunicated to him by M. De La Place, in a letter, inserted in theJournal des Savans.”*Traité de l’astronomie Indienne et orientale”, M. Bailly, Paris, 1787.
- 131. On the planets The mutual interaction between Saturn and Jupiter“Since the publication of M. Bailly’s work*, two other instances of an exactagreement, between the elements of these tables, and the conclusionsdeduced from the theory of gravity, have been observed, andcommunicated to him by M. De La Place, in a letter, inserted in theJournal des Savans.”“M. De La Place has discovered, that there are inequalities belonging toboth these planets (Saturn and Jupiter), arising from their mutual actionon one another, which have long periods, one of them no less than 877years; so that the mean motion must appear different, if it be determinedfrom observations made in different parts of those periods.”*Traité de l’astronomie Indienne et orientale”, M. Bailly, Paris, 1787.
- 132. On the planets The mutual interaction between Saturn and JupiterSays M. De La Place (as quoted in the article by Playfair):
- 133. On the planets The mutual interaction between Saturn and JupiterSays M. De La Place (as quoted in the article by Playfair):“Now I find, by my theory, that at the Indian epoch of 3102 years beforeChrist, the apparent and annual mean motion of Saturn was 12o, 13’, 14”,and the Indian tables make it 12o, 13’, 13”. ”
- 134. On the planets The mutual interaction between Saturn and JupiterSays M. De La Place (as quoted in the article by Playfair):“Now I find, by my theory, that at the Indian epoch of 3102 years beforeChrist, the apparent and annual mean motion of Saturn was 12o, 13’, 14”,and the Indian tables make it 12o, 13’, 13”. ”“In like manner, I find, that the annual and apparent mean motion ofJupiter at that epoch was 30o, 20’, 42”, precisely as in the Indianastronomy.”
- 135. General conclusions
- 136. General conclusions Astronomy in Bharat-Varsha goes back to at least 6300 years ago, andits development had no influence from any other systems of astronomyanywhere else in the world.“It is …certain that the astronomy of the Brahmins is neither derived fromthat of the Greeks, the Arabians, the Persians or the Tartars.”
- 137. General conclusions The principles underlying the rules for calculating the positions ofheavenly objects implies a high level mathematical sophistication, andmuch of the geometry attributed to the Greeks has originated in India.
- 138. General conclusions This is certainly true of the theorem attributed to Pythagoras,* for themethod of calculating the duration of a lunar or solar eclipse according tothe Indian tables is based on this theorem.“These operations (for finding the duration of eclipses) are all founded ona very distinct conception of what happens in the case of an eclipse, andon the knowledge of this theorem, that, in a right angled triangle, thesquare of the hypotenuse is equal to the squares of the other two sides. Itis curious to find the theorem of Pythagoras in India, where, for aught weknow, it may have been discovered, and from whence that philosophermay have derived some of the solid, as well as the visionary speculations,with which he delighted to instruct or amuse his disciples.”*The earliest mention of this theorem is to be found in the Sulbasutras credited to Bodhayana(c. 800 B.C.), but it is clear from these astronomical tables that the knowledge of this theoremwas prevalent since much earlier.
- 139. General conclusions Regarding Pythagoras, it is interesting to note the followingremarks from another article:“we know that he (Pythagoras) went to India to be instructed; but thecapacity of the learner determines his degree of proficiency, and ifPythagoras on his return had so little knowledge in geometry as toconsider the forty-seventh of Euclid as a great discovery, he certainly wasentirely incapable of acquiring the Indian method of calculation, throughhis deficiency of preparatory knowledge ……each teacher, or head of sect that drew his knowledge from Indiansources, might conceal his instructors to be reckoned an inventor.” -Reuben Burrow, ‘Hints concerning the observatory at Benares’ c. 1783.
- 140. General conclusions The principles underlying the rules for using the tables also supposesa deep knowledge of trigonometry and spherical trigonometry. That thesewere carried to a high level of perfection in Bharat-Varsha, is amplydemonstrated by the ancient Sanskrit texts, the Surya Siddhanta.**See, for example, John Playfair, “Observations on the trigonometrical tables of the Brahmins”,Transactions of the Royal Society of Edinburgh, Vol. IV. (1798).
- 141. General conclusions The classic problem of the quadrature of the circle, or the ratio of thecircumference to the diameter of the circle (commonly known as π), wassolved in India much before the Greek mathematicians, and to muchgreater precision.*“…the Hindoos suppose the diameter of a circle to be to its circumferenceas 1250 to 3927, and where the author, who knew that this was moreaccurate than the proportion of Archimedes, (7 to 22), … expresses hisastonishment, that among so simple a people, there should be found atruth, which, among the wisest and most learned nations, had beensought for in vain.”* Also see, “On the Hindu quadrature of the circle, and the infinite series of the proportion ofthe circumference to the diameter exhibited in the four Sastras, the Tantra Sangraham, YuctiBhasha, Carana Padhati, and Sadratnamala”, by Charles M. Whish, published in theTransactions of the Royal Asiatic Society of Great Britain and Ireland, Vol. III (1835).
- 142. Comparison of the days of the week in the Indian systemand the European system (Table scanned from the book ‘Sketches chiefly relating the history, religion, learning, and manners, of the Hindoos’, Vol. I, by Quentin Craufurd, 1792. “the days are arranged exactly in the same order that has been adopted by the Europeans.”)
- 143. “If to this we add the great extent of geometrical knowledge requisite tocombine this, and the other principles of their astronomy together and todeduce from them the just conclusions; the possession of a calculusequivalent to trigonometry; and, lastly, their approximation to thequadrature of the circle, we shall be astonished at the magnitude of thatbody of science, which must have enlightened the inhabitants of India insome remote age, and which, whatever it may have communicated to thewestern nations, appears to have received nothing from them.”
- 144. Final reflections
- 145. Final reflections It should be noted that Playfair’s article discussed in this presentationsets only a lower limit for the antiquity of Indian astronomy, and in noway rules out the possibility that it could be much more ancient. Indeed,considering the level of mathematical and astronomical skills used inmaking these tables, this certainly seems to be the case.
- 146. Final reflections It should be noted that Playfair’s article discussed in this presentationsets only a lower limit for the antiquity of Indian astronomy, and in noway rules out the possibility that it could be much more ancient. Indeed,considering the level of mathematical and astronomical skills used inmaking these tables, this certainly seems to be the case. In spite of there being abundant evidence concerning the achievementsof Bharat-Varsha in the mathematics and the sciences, all references toIndian science and technology have been either eliminated or ignored;not just by the world at large, but by the majority of Indians themselves.
- 147. Final reflections It should be noted that Playfair’s article discussed in this presentationsets only a lower limit for the antiquity of Indian astronomy, and in noway rules out the possibility that it could be much more ancient. Indeed,considering the level of mathematical and astronomical skills used inmaking these tables, this certainly seems to be the case. In spite of there being abundant evidence concerning the achievementsof Bharat-Varsha in the mathematics and the sciences, all references toIndian science and technology have been either eliminated or ignored;not just by the world at large, but by the majority of Indians themselves. It is time to undo this damage by learning about the true history andcontributions of Bharat-Varsha, instead of depending on borrowedhistories and identities.
- 148. AcknowledgementsA deep sense of appreciation is expressed to Shri Dharampal (1922-2006), for having compiled several publications on Indian science andtechnology in the book, ‘Indian science and technology in the eighteenthcentury’. The article discussed in this presentation is included in thisbook.This book, and several others, can be downloaded for free from thewebsite: www.samanvaya.com/dharampal/Most of the references mentioned in this presentation are available forfree at www.books.google.com. The effort in making these documentsavailable to the general public is sincerely appreciated.

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