Guest guest Posted December 7, 2007 Report Share Posted December 7, 2007 Dear grp . Now this is available records of gr8 indian astrologers who are also wel versed in astronomy and astrology . because since jyothisha come into practise from rishi laghadha of bc 8000 much of the real records has been lost or replaced by commentaries ,as many of the students will use commendaries and then forgets originals to copy and keep also to keep all literature by oneself is not humanly possible ,see our vedas and uapanishats .any body can keep all copeis of that itself .In olden times astrologer is sidhanthi (means who can calculate all planetary movements himself ) and also he has to predict and also do remedial measuse (pooja part ) also advise kings on various affairs .means a all rounder . Now the new generation is SW astologers and anything to change their mind is possible . this basjing ppl cannot produce one book of astro from any country outside india . where we deal with lot of dasa ,signs ,varga chart and planetary degrees and ashtavarga .How a borrowed sistem exceld and waster than the originals . Moreover jyothisha is used in various other sastras .esp in ayurveda to cure a patient and prepare medicines and also in martial arts also in educating a kid on various aspects .in short we say cradle to cremation in every aspect of life .even agriculture . so read it ,as this is recordicaly available . also i know one kerala brahmin used to predict 1000 years thunder and lightning muhurtha (as in shubh muhurtha it shud be avoided -muhurtha is max 48minits and astrologrs uses max 10 to 12minits) ,i was searching for that book ,it happened 1000 years back and now that book is of no use as the period is finished .No body contradicted him and u cannot fool ppl for 1000years . This are all working examples . regrds sunil nair . This article is prepared by chandrahari who is a real scientist and blver of astrology and who is doing reserch in jyothisha and who bring out true ayanamsa of varahamihira and surya sidhantha (astronomical treatise which was existed pre varahmihira as he said 18 rishis were the jyothisha pravarthkas from pitha maha brahma to parashara -he also said lack of revising technics many sidhnathas got obselet .) ============================================================ Eclipse Observations of Parame´svara K. Chandra Hari* 1. Introduction Parame´svara, the great Kerala astronomer as well as astrologer, was the resident of Alattur (10N51, 076E08) situated on the banks of the river Nila or Bharatappuzha. He was a prolific writer on both astronomy as well as astrology and is best known for his original work Drgganita, which was formulated after taking into account the astronomical observations of a period of 55 years. A detailed account of his original works and commentaries are available in the Drgganita[1] critically edited by K.V. Sarma. His date can be gleaned of the dates of the two texts – Drgganitam bearing ´Saka 1353(1431AD) and Goladipika II inscribed with ´Saka 1365 (1443 AD). Further we have got the evidence of different Kalikhandas employed in Parame´svara's works and the list he has given of the eclipse observations to ascertain his period to be between 1350 and 1450. Parame´svara has produced three works exclusively dealing with eclipses viz., Grahanamandana, Grahanastaka and Grahananyayadipika and has made a mention of the important eclipses that have taken place during 1398 to 1431 AD in a long discussion at the end of the chapter on Eclipses in his commentary `Siddhantadipika' on the Mahabhaskariya-Bhasya of Govindasvamin. 2. Significance of these Eclipse Records These eclipse observations formed the basis of the refinement of the age-old Parahita system by Parame´svara in 1431AD to formulate the Drgganitam. Parame´svara's disciple Nilkantha also used these observations in the formulation of his work Tantrasangraha. This record as such throws light on to certain salient features of the medieval phase of Kerala astronomy. The following statements of Parame´svara are noteworthy in this context:[2] 1. Drgganita (I.2-4) "Parahita planetary positions have been found to deviate from the observed ones; the sastra declares the observed positions to be the true ones. Times of auspicious rites can be fixed only by means of the true positions and the inaccurate positions are inappropriate. Hence the twice-born who are adept in astronomy must strive for obtaining positions agreeing with observations". 2. "The planets have been observed by me for fifty-five years and they differ from the positions derived of Parahita-ganitam"(Quoted by Nilkantha Somayaji in his Aryabhatīya-Bhasya). 3. "Since ´Saka 1315 (AD 1393) I have observed a number of eclipses, all occurred at times prior to the computed ones. This necessitated a correction in the computational process". (Siddhantadipika)[3] 4. "Many more solar eclipses, other than those enumerated above have been observed by me and on the basis of such detailed observations I have found the correct the positions of the Sun, Moon, Higher apsis and Node to be[4]…" 5. Nilkantha Somayaji has spoken about Parame´svara as follows: "Parame´svara had his studentship well in mathematics and astronomy under able hands such as Rudra, Narayana and Madhava. He could understand the factors that caused difference between the computed and observed planetary positions. After deliberating over the principles of earlier teachers and verifying them through observations of eclipses and planetary conjunctions, he composed his accurate work Drgganita". 6. Further, he has spoken of the use of eclipses vis-à-vis the refinement of computational methods in the following words: "The eclipses cited in Siddhantadipika can be computed and the details verified. Similarly, other eclipses traditionally known as well as those currently observable are to be studied. In the light of such experience future ones can be computed and predicted. Or, eclipses occurring at other places can be studied taking into account the longitude and latitude of the place and on this basis the method for true Sun, Moon, Apsis and Node can be perfected. Based on these past and future eclipses of one's own place can be studied and verified with appropriate refinement of the technique". It is apparent from the above that the eclipses recorded by Parame´svara have played an important role in the progress achieved by the Kerala School of astronomy. 3. Parame´svara's Works on Eclipses As we have noted in the introduction Parame´svara has produced three works on eclipses: (1) Grahanastaka consisting of only 10 verses (2) Grahanamandana of 100 verses and (3) Grahananyayadipika of 85 verses Present author could make use of only the latter two works as references in the preparation of this paper. Grahanamandana (`Ornament of Eclipses') is a karana text that deals with computational aspects while Grahananyayadipika – a subsequent work - presents the underlying theory of eclipses: Both these works do not contain any information on the eclipses observed by him. The account on eclipses is available in his commentary Siddhantadipika on the Mahabhaskariya-Bhasya of Govindaswamin at the end of the chapter on Eclipses. Parame´svara's efforts were directed towards the refinement of the traditional constants employed in the computation of eclipses and has claimed no innovations of his own in the treatment of eclipses. But his scientific outlook is well evident from the criticism he has aired of Varahamihira in Grahanamandana in the following verses: "Unatiriktakale phalamuktam purva´sastradrstatvat" Itigaditam grahanaphale Varahamihirena samhitayam ca [97] ´Sastradalabdha ekah samskaro grahanakarmani ravindoh Astyeveti ca kalpyah ganakavarairyuktividdhiratah [98] Drstva bahuparagan sancintya ca golayuktimiha ganakaih Kalpyah sa tu samskarastasmadathava gurupade´sena [99] K.V. Sarma has rendered these verses into English as follows: (97) "Predictions of the effects (of eclipses) occurring (a little) earlier or later than the times due are given (by me) on the authority of ancient texts on the subject" – so says Varahamihira in his (Brhat-) Samhita in the section entitled `Prediction of effects of eclipses'. (98) "This being the case, it is to be postulated by learned astronomers well versed in (astronomical) theory that in the computation of eclipses of the Sun and Moon a correction not stated in old texts must exist". (99) "Such a correction has to be postulated by astronomers after observing a large number of eclipses and with due consideration to the principles of spheres, or in the light of instructions of masters (who would have arrived at such a correction in a similar manner)" [5] 4. Date of Observations Available in Grahanamandana Grahanamandana make use of the Kalikhandam of 1648157 days, which K.V. Sarma has indicated, as corresponding to the Kali year 4512, Kataka17 i.e., 15th July 1410 AD. Modern computation suggests that the epoch actually is 17 July 1411 AD. We can have some idea of the accuracy of computations in this manual by comparing the mean longitudes accurately determined by the Acarya himself for the sun, moon, moon's apogee and node: Kalidinam = 1648157 days: 17 July 1411 AD, Friday, Ujjain sunrise 05:25:36, JD (TDT) = 2236622.5201. Ayanam´sa of Parame´svara It can be understood from Nilkantha's remarks in Jyotirmimamsa that Parame´svaracarya had precisely fixed the ayanam´sa to be 150 in Kali year 4536 or AD 1435.[6] If we adopt this determination the ayanam´sa for AD 1411 turns out to be 14036'. Planets Parame´svara's Sidereal l Col.2+14049' Col.2+14036' Modern mean l Modern True l True l of Parame´svara 1 2 3 4 5 6 7 Sun 108015'07" 123004'07" 122051'07" 122042'07" 121044'45" 121044'40" Moon 60017'1" 75006'01" 74053'01" 74027'43" 75043' 75049'45" Apogee 65023'18" 80012'18" 79059'18" 79052'36" 75045'22" --- Node 331041'04" 346030'04" 346017'04" 346004'12" ------ --- By comparison of columns 3 and 4 with column 5 it appears that the mean sun of Parame´svara and modern l differed by 9 minutes of arc when contrasted using his own ayanam´sa. But the true sun of Parame´svara is precisely equal to the modern true Sun, a fact that reflects the ingenuity of Parame´svara. Column (3) suggests that the traditional value of ayanamsa was in surplus by nearly 13 minutes (after accounting for the difference in equation of center) and Parame´svara rightly and precisely fixed the siddhantic ayanam´sa to be 150 in AD 1435. It is possible that at the time of writing Grahanamandana in 1411 AD, Parame´svara probably had only the traditional value of 14049' at hand and under such a circumstance the Sayana longitudes of Parame´svara would have been in error by a quarter-degree. As regards the accuracy of the results of this treatise on eclipses, Parame´svara himself has made the following observation in the concluding part: Iti purva´sastrayuktya siddhamidam grahanakarma nirdistam Kalo anena ca siddha kadacidiha bhidyate svalpam II "Thus has been enunciated the computation of eclipses according to principles derived from the ancient texts. The times (of contact etc.) as obtained from this (calculation) may, at times, differ slightly (from observation)". The fact that Parame´svara could fix the ayanam´sa to be 150 in AD 1435 – a value that made the true Sun to be as precise as the observation and modern true l, by correcting the ayanam´sa by (-) 13 minutes – is ample testimony for the diligent observations and use of the same for correcting the computational process. 5. Solar Eclipses Observed at Nila Parame´svara has altogether made a mention of eight solar and five lunar eclipses that have occurred during his times. The solar eclipses have been examined with planetarium software based on the VSOP87 theory. Location of Parame´svara's Village As regards the actual location of Parame´svara's village precise information is available in Parame´svara's work Goladipika: Samarekhayah pa´scadastÄda´sa yojanantare grame Svarakrtasat tuliteakse vasata… [Goladipika IV.91] Scholars[7] have interpreted this verse to mean a place 18 Yojanas West of Ujjain of longitude 75E43 at the latitude of 10N51 i.e., nearly one degree west of Ujjain (74E43), which is impossible for his village Alattur, near Palghat. Actually, Paramesvara's village (Alattur) was situated 18 Yojanas ahead of the Ujjain meridian and it had a sine latitude of 647, which corresponds to north latitude 10051'. 18 yojanas ahead of Ujjain means one degree east of Ujjain or 76E43 as per the diameter of earth specified by Parame´svara in Grahananyayadipika. Modern Astronomical Data of Solar Eclipses Recorded by Parame´svara Location: 10N51, 76E43 [Alattur] UT+ 05:00 Date Eclipse Visibility Beginning Maximum Magnitude Moon/Sun End Time Sun's altitude 9 Nov. 1398 Annular Partial 08:18 09:56 0.906 0.938 11:57 600 19 Oct.1408 Hybrid Partial 15:27 16:36 0.551 1.001 17:37 00.9 1 Feb. 1413 Total Partial 07:39 08:47 0.675 1.045 10:04 470.4 23 Jan. 1422 Total Partial 07:11 07:43 0.141 1.035 08:18 230.5 8 Aug. 1431 Annular Partial 06:41 07:56 0.674 0.946 09:26 490.7 2 Feb. 1432 Partial Partial 07:59 08:25 0.070 1.014 08:53 320.3 10 Nov.1425 --- No Eclipse 19 Aug.1430 --- No Eclipse Location: 14N32, 74E20 [Gokarnam] UT+ 04:57 10 Nov. 1425 Partial Partial 15:24 15:59 0.087 0.946 16:32 110.9 19 Aug.1430 Partial Partial 06:45 07:18 0.077 0.935 07:53 290.5 Observational Data of Paramesvara [10N51, 76E43] No. Kalidina Date Beginning End Duration (Parame´svara) Modern Data Gnomon shadow Time Beginning End 1 1643524 9 Nov.1398 11 08:13 11:49 3h36m[9nadikas] 08:18 11:57 2 1647156 19 Oct.1408 --- --- 17:31 --- 15:27 17:37 3 1648722 1 Feb. 1413 24 07:45 --- --- 07:39 10:04 4 1652000 23 Jan. 1422 35 07:15 --- --- 07:11 08:18 5 1655484 8 Aug. 1431 --- --- --- --- 06:41 09:26 6 1655662 2 Feb. 1432 15 08:05 --- --- 07:59 08:53 7 1653387 10 Nov.1425 No eclipse --- --- --- No eclipse --- 8 1655130 19 Aug.1430 No eclipse --- --- --- No eclipse --- 6. Discussion on the Eclipses · Solar eclipse of Kalidina 1643524 This ahargana corresponds to the sunrise prior to the eclipse and the date is Nov. 09, 1398: Gnomon shadow at the beginning is 11. Beginning of the eclipse therefore will be at 5.666 nadikas (2h16m) after sunrise i.e at 05:57+ 2h16m = 0813. Duration is 9 nadikas or 3h36m, which puts the end of the eclipse at 11:49. With modern algorithms the eclipse had its beginning at 08:18 LMT and ended at 11:57 LMT - hence the duration will be 3 hours 39 minutes as against 3h36m or 9 nadikas mentioned by Paramesvara. Upper transit of the Sun as per modern algorithms happened at 11:46 and this agrees well with Parame´svara's observation that the end of the eclipse took place after noon. Nilkantha's Observations on this Eclipse Nilkantha has referred to this eclipse in Jyotirmimam´sa and has given the mean and true sun along with mean moon and its apogee. Translation of Nilkantha's detailed account is available on pages 15-16 of the "Indian Astronomy – A Source Book"[8] and the following information can be extracted out of it: Introductory part of Nilkantha's disquisition is quoted below followed by data relevant to our present discussion: "The Bhata-correction enunciated through the verse commencing with the expression Vagbhavona is referred to here as ´Sakabda-samskara. Since the system of Parame´svara (AD 1360-1455) is posterior to that of Siddhanta´sekhara (of Sripati, AD c.1000), the mean positions of planets computed according to the former would accord (better) with observation. Hence, for (the eclipses) enumerated (by Parame´svara) in his Siddhantadipika and of those observed and enumerated by me in various contexts, compute: (i) the mean Sun etc., as directed by Parame´svara (ii) their true positions as directed by Sripati and (iii) by the special process explained by me in my (Bhasya) on the Kalakriya and Golapadas of the Aryabhatīya. Take as the first case the following instance: `On Kali day 16,43,524…." Manuscript error has led to a wrong record of the mean Sun in Katapayadi notation as – "Madhyam Suksmamhyarkah" which on decoding gives 0r 110 57' 15". This cannot be true as the reference is to a solar eclipse and Moon's mean longitude is given as "Manye Vanasthah", which is 7r 4015'. Obviously, the Sun's mean position is 7r 11057'15". On page 35 of the Jyotirmimamsa[9] also the manuscript error has made its successful appearance. Examination of Nilakantha's Values in the light of Modern Astronomy In continuation of the introductory remarks quoted earlier, Nilkantha has explained the accurate determination of the mean Sun, Moon, Rahu and True Sun and has given the following values for Kalidina of 1643524. Comparison of these values with the modern require the ayanamsa as used by Nilakantha, a clue towards which is available in Jyotirmimamsa as discussed earlier in the context of our discussion on Grahanamandanam. Nilkantha has referred to 150 as the ayanam´sa of AD 1435 as fixed precisely by Acarya Parame´svara and accordingly the ayanam´sa of Nilkantha for AD 1398 will be 150 - 0037' = 14023' instead of the traditional value 14036'. Mean sun at sunrise preceding the eclipse = 221057'15" Mean sun (sidereal) according to modern astronomy =236013' 11".4 – 14023' = 221050'11".4 Mean moon (Nilakantha's) = 214015' Mean moon (sidereal) modern l = 228030'18" – 14023' = 214007'18" Mean apogee of moon (Nilakantha's) = 269026' Mean apogee of moon (sidereal) modern l = 283043'53" –14023' = 269020'53" Nilakantha's true sun at the beginning of the eclipse =220045'12". The modern value turns out to be: 23508'45" – ayanam´sa = 220045'45" at 0813 hrs. But we have seen above that the sidereal Moon given by Nilkantha was more by (+) 7 minutes of arc. According to modern astronomy the apogee was at 91040' and as such the equation of center amounted to 01010' while in the Siddhantic astronomy the equation of center was 01018' and thus arose the error in mean Sun of Nilkantha. But that error got nullified in the sphutīkarana to obtain the true longitude. The exactness that we see here in Nilakantha perhaps has no parallel in the pre-telescopic era of astronomy. Nilkantha has also given the following details about this eclipse: Kalalagnam or Sayana Ravi for Local Noon as 236038' which according to modern astronomy is 236028' and the Lagna at the beginning of the eclipse as 266006' against the modern computational result of 265020' for w = 23.5173 degrees. Drksepalagna = 176026'[Vrtribha]; Sphutagati of Sun 60'59" [modern value =60'47".5]; True Moon=219043'40" while the modern algorithms give 219030'38.7"(sidereal) [i.e. 233053'38".7-14023'] and the sphutagati of Moon = 749'09" [modern value = 739'26"]. These values given by Nilakantha have got only insignificant errors when compared to modern computer derived longitudes based on the latest theories of planetary dynamics. It is apparent from the above that in terms of accuracy of the planetary longitudes the epicyclic theory was not far behind the theory of Kepler, when it was handled by researchers like Parame´svara and Nilkantha[10]. · Solar eclipse of Kalidina 1647156 Date is October 19, 1408: According to Parame´svara's observation, sunset occurred at quarter nadi (6 minutes) after the end of the eclipse. The partial eclipse had its beginning at 1527 LMT and end at 1737 LMT. Sunset was at 17:37, i.e. modern algorithms make sunset and the end of the eclipse coincident. This discrepancy can be explained as due to lack of observational aids for Parame´svara or to the atmospheric factors that affect visibility. In respect of other eclipses Parame´svara gives only little information: 3. Feb.1, 1413: Gnomon shadow at first contact = 24. 4. Jan.23, 1422: Gnomonic shadow at first contact 40 or 35. 5. Wed. Aug.8, 1431: Gnomonic shadow at last contact = 5.5. 6. Feb.2, 1432: Gnomon shadow at first contact: 15, last contact: 9.5. As mentioned by Paramesvara the eclipse magnitude was very small. Parame´svara has also mentioned two solar eclipses, which were observable at Gokarnam (14N32, 74E20), but not at his place. 7. Kalidina = 1653387: New moon of 10th Nov.1425 AD, 14:31:52.12 (LMT) of Gokarnam (JD [TDT] = 2241852.9032688). The discs came in slight contact between 1524 LMT and 1632 LMT. 8. Kalidina = 1655130: New moon of 19 Aug.1430 AD, 09:00:56.24 (LMT) of Gokarnam (JD [TDT] = 2243595.6733523). Discs were in slight contact between 0645 and 0753. 7. Lunar Eclipses Observed by Parame´svara No: Kalidina Date and LMT of Full Moon Beginning of phase Maximum End of phase Total Partial Total Partial 1 1655647 17.01.1942, 21:22 20:50 19:38 21:26 22:02 23:13 2 1655293 28.01.1431, 19:14 --- 17:03 19:27 --- 21:51 3 1652694 17.12.1423, 20:03 --- 19:51 20:13 --- 20:36 4 1654614 21.03.1429, 04:00 03:35 02:16 03:56 04:16 05:35 5 1653403 25.11.1425, 02:29 01:53 00:44 02:25 02:57 04:06 Parame´svara's account of lunar eclipses has the mention of Kalidina only and the modern astronomical data of the lunar eclipses mentioned by him are given in the above Table. 8. Mean Luni-Solar Positions Given by Parame´svara Parame´svara's account of eclipses ends with the accurate mean positions of Sun, Moon, Moon's apogee and Node for Kalidina = 1651700: Saturday, March 29, 1421AD 05:47 Ujjain sunrise. JD (TDT) = 2240165.53472291. 1 2 3 5 6 Mean l of Parame´svara's Col.2+ 14046' Modern l Difference Col.3- 4 Sun 00015' 15001' 14051' 10' Moon 304006' 318052' 318037' 15' Apogee 279057' 294043' 294036' 7' Node 143055' 158041' 158027' 14' When compared with the modern values the differences average to be only 11.5 minutes of arc. Truly speaking the mean ls of the Siddhantic tradition cannot be compared with modern mean ls as the equation of center and other corrections based on which the mean longitude is arrived at from the true observed positions are different. As for example, here in the case of Sun the difference is (+) 10 minutes of arc and this error gets nullified when true ls are compared as the siddhantic equation of center is deficient by 11.8 minutes for anomaly of nearly (-) 780. These accurate positions were probably obtained by applying additional correction to the method outlined in Grahanamandana as can be noted from the Drgganita II.47-50: "Additional corrections required for the mean positions of Grahanamandana, which was not stated there-in, I shall mention now: One second should be subtracted for every two hundred years from the Sun of Grahanamandana while for Moon addition of one second is required for every 41 years. For apogee the correction is (+) one second for every 135 years and in the case of Rahu one minute needs to be subtracted for every three years." If we go by the Kalikhandam of 1648157, Grahanamandana's formulation took place in 1411 AD – quite early in the career of Parame´svara. Kalikhandam given above in the correction mentioned falls after 10 years and hence these corrections may be the fruits of his constant observation of astronomical phenomena like eclipses. 9. Epoch of Drgganita A discussion on Parame´svara shall remain incomplete without a reference to his magnum opus – Drgganitam. According to the information available in the text (´Sloka 46) the composition took place in ´Saka 1353 corresponding to AD 1431. The epoch as such will be the expiry of the Kali year 4532: Kalidina = 1655352.34: JD[TDT] =2243817.54490972; Thursday, March 29, 1431, 05:55 LMT[ Ujjain Sunrise]. Comparison of the Mean Elements Kalidina: 1655352: 29thMarch 1431AD, Thursday, Ujjain sunrise 05:55 Drk l+A Tropical l Sun 14036' 14027' Moon 199004' 199012' Apogee(Moon) 350008' 217044' Rahu 329047' 325004' Mars 211031' 211030' Mercury 118048' 113011' Jupiter 45005' 46006' Venus 08011' 07035' Saturn 292050' 291040' Derivation of the mean longitudes from observed positions calls into play both the observational skills as well as the mathematical genius of an astronomer. Strictly speaking, the modern mean longitudes and the siddhantic madhyamams are not entirely the same even if the precession is accounted for. True positions decremented by the equation of center formed the siddhantic madhyamams while in modern astronomy the mean positions are arrived at after scores of other corrections, which represent the perturbations to the mean orbit. Obviously equality cannot be looked for while comparing the epochal mean co-ordinates. But even then the contrast, siddhantic versus modern, of the different epochs have been employed by earlier scholars to gain a prima facie understanding of the merits of the siddhantic works. True picture can be gained only by comparing the true longitudes as per Drgganita with those of modern algorithms. Those who are adept in the Siddhantic computational process may attempt a comparison of the Drgganita output with the modern true longitudes provided below: Planet True l b dl per day db per day Sun 16°21' -00°00' 00°58'41" -00'00".08 Moon 195°44' -03°53' 12°06'45" -42'19".53 Mercury 35°52' 02°37' 01°06'11" 06'27".13 Venus 12°22' -01°17' 01°14'13" 01'04".14 Mars 212°09' 01°54' -00°17'56" -01'37".83 Jupiter 44°10' -00°48' 00°13'19" 00'08".16 Saturn 294°39' -00°01' 00°02'44" -00'04".82 The Kalikhanda of 4532 years (of 365.2586806 days) constitute 1655352.34 days. To remove the fraction 0.34 of a day Parame´svara introduced the Kali-dhruva of 20'22" for mean sun, for the first time in the history of siddhantic astronomy. At no time earlier has there been a correction applied to Sun in terms of Kali-dhruva. Perhaps, Parame´svara is the first astronomer of the Aryabhatan tradition of Kerala, who has postulated zero correction for the planets at the beginning of Kaliyuga. In Drgganitam he has given: Sun: 20'22"; Moon: +3015'2"; Mars: +3'; Mercury:(-) 3044"; Jupiter:(-) 2059'; Venus: (-) 40;Saturn: + 408'; and Node: 182036'.[11] Also for Suryasiddhanta: Sun: +5'35"; Moon: (-) 2'37"; Apogee: + 4017'13"; Mars: (-) 5'; Mercury: (-) 40;Jupiter: (-) 3045';Venus:(-) 4024';Saturn:+407';Rahu:+2035'. Parame´svara could disregard the traditional belief of zero mean longitudes at Yugadi only because of his scientific outlook and the knowledge he has gained about planetary motions through observations of the sky. 10. Conclusions In the above is presented a succinct account of the golden period of medieval Indian as well as Kerala astronomical tradition authored by the genius of Parame´svara. His record of astronomical observations, the refinement of astronomical parameters and the accompanying work of his disciple Nilakantha Somayaji, following the same footsteps to maximize the accuracy of planetary longitudes etc., are reflective of the past glory of Indian Science. The accuracy that we see in the Sun and Moon of Parame´svara and Nilkantha can be inferred as the result of eclipse observations as well as experimentation with the computational techniques. Planetary longitudes of Kujadis have relatively more deviation when compared to the results of modern algorithms, obviously due to the constraints of the pre-telescopic Age in the matter of observation * B – 204, Parth Avenue, Ahmedabad –5, Gujarat [1] Drgganita, Critically edited by K.V. Sarma, V.V.R.I, Hoshiarpur, 1963 [2] In the following translations I have given a resume in English rather than a literal translation. [3] Siddhantadipika, Commentary on Mahabhaskariya-Bhasya of Govindasvamin, p.321, ed. Madras, 1953. [4] Ibid p.331.Dr. K.V. Sarma has quoted this verse on page (xii) of his introduction to the translation of Grahanamandana [5] Sarma has added the note: "Perhaps the author has at the back of his mind Mu´njala's Laghumanasa Ganita, on which he himself has commented and which gives the correction to the Moon, known as `Evection' and envisages the possibility of others" [6] In making a contrast of the sidereal longitudes of Parame´svara with the results of modern lunar theory we need to determine the ayanamśa of the epochs of which computations are presented. The Siddhantic tradition of Kerala takes Kali 3623 or AD 522 as the coincidence of the vernal equinox with the zero point vis-à-vis the epoch of Aryabhatīya. The extra-long solar year of Siddhantic astronomy necessitated a rate of precession of nearly one minute per year and this amounts to one degree in sixty years. Ayanamśa of any year Y can therefore be computed as (Y-522)/60 degrees. Accordingly the ayanam´sa works out to be 14049'. [7] (1) Kripa Shankar Shukla, The Suryasiddhanta with the commentary of Parame´svara, p.64: "Its latitude is given to be 10050' north and longitude 18 yojanas west of the meridian of Ujjain". Published by Department of Mathematics and Astronomy, Lucknow University, (1957). (2) K.V. Sarma, Grahanamandana, Critically edited with translation, V.V.R.I, Hoshiarpur, p.xii: "It was, thus, 18 yojanas to the west of the Central (Ujjain) meridian and had a Sine latitude of 647, corresponding to10051', north latitude" [8] B.V. Subbarayappa and K.V. Sarma, Indian Astronomy – A Source Book, Nehru Centre, Bombay m [9] Jyotirmimamsa, ed. By Dr. K.V. Sarma, Pub: V.V.R.I, Panjab University, Hoshiarpur [10] Nilkantha has mentioned two other eclipses. (1) Kalidina = 1681472: Annular eclipse at Trivandrum(Syanandurapura) [08N29, 76E59]. New Moon: Saturday, 1st October 1502, 13:33:58.44 LMT. Eclipse had its beginning at 1250 PM, Middle:02:34PM and end at 04:10 PM. JD (TDT) = 2269936.8539206. (2) Kalidina = 1686847: Annular eclipse at Harihara of Karnataka state – exact location of this place could not be made out. At Bangalore [77E34, 12N58] the eclipse was total at 10:00 LMT. New Moon: Friday, June 19, 1517. JD(TDT) = 2275311.736119. [11] Indian Astronomy – A Source Book: ed. B.V. Subbarayappa and K.V.Sarma, p.153; Nehru Centre, Bombay Quote Link to comment Share on other sites More sharing options...
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