Lec 01 - Introduction & Brief History of Astronomy - Mohan Apte

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<p>PROMINENT ANCIENT INDIAN ASTRONOMERS1&gt; Acharya Lagadha Vedang Jyotish 1500 BC2&gt; Aryabhat Aryabhatiya 500 AD3&gt; Varahamihir Panchsiddhantika 505 AD4&gt; Bhaskara 1 Mahabhaskriya 600 AD5&gt; Lallacharya Shishadhivridhidatantra 638 AD6&gt; Brahmagupta Brahmasphutsiddhanta 628 AD7&gt; Vateshwar Vateshwarsiddhanta 880 AD8&gt; Munjala Laghumanasam 932 AD9&gt; Aryabhat 2 Mahasiddhanta 950 AD10&gt; Bhaskaracharya 2 Siddhantashiromani 1150 AD11&gt; Ganesh Daivadna Grahalaghav 1520 AD||i-|| |-|= |i|= || +-|-|r|- +|i|:|-|||i-|= ||i|:|- ir|-|: :ccc PROMINANT ASTRONOMERS FROM KERALA1&gt; Madhavan of Sangamagram (1340-1425) Karanapaddhati(1375)2&gt; Narayana Pandit (1340-1400) Ganita Kaumudi3&gt; Parameshvara (1370-1460) Drigganita4&gt; Nilakantha Somayaji (1444-1544) Tantrasangraha5&gt; Jyesthadeva (1500-1610) Yuktibhasa6&gt; Sankara Variar (1500-1560) Kriya-kramakari7&gt; Sankar Varman (1774-1839) SadratnamalaCONCEPT OF YUGASKali 432000 YearsDwapar 864000 YearsTreta 129600 YearsKrita 1728000 YearsMahayuga = Kali + Dwapar + Treta + Krita= 4320000 Years Manavantar = 71 Mahayugas + 1 Krita= 71 x 4320000 + 1728000= 308448000 YearsKalpa = 14 Manvantaras + 1 Krita= 14 x 308448000 + 1728000= 4320000000 YearsKali Yuga started on 17/18 Feb 3102 BCCONCEPT OF NAKSHTRASPeriod of revolution of Moon = 27 DaysTotal angle covered in this period = 360 degreesSpeed of revolution per day = 360/27 = 13.33 deg/dayOne Nakshtra = 13.33 degreesThere are 27 NakshtrasMoon crosses one Nakshtra per dayNames of 27 Nakshtras1&gt; Ashvini 10&gt; Magha 19&gt; Mula2&gt; Bharani 11&gt; Purva Phalguni 20&gt; Purvashadha3&gt; Krittaka 12&gt; Uttara Phalguni 21&gt; Uttarashadha4&gt; Rohini 13&gt; Hasta 22&gt; Shravana5&gt; Mrigashirsha 14&gt; Chitra 23&gt; Dhanishta6&gt; Aardra 15&gt; Swati 24&gt; Shatataraka7&gt; Punarvasu 16&gt; Vishakha 25&gt; Purvabhadrapada8&gt; Pushya 17&gt; Anuradha 26&gt; Uttarabhadrapada9&gt; Ashlesha 18&gt; Jyeshta 27&gt; Revati--|| |ir--|-| -|ir-|||| -|||-|| -|||| ||-|+ |i| ||-|-||| -||| |||;| =| |:|r| |r| r-|--+| -+| i|i|||-|| -|ir-|: |+ : i|-|z |||= s =|i-=s |= a -||||||. |||c :c |||a &gt;|||| :: -|||c ||:+: :z =|-|-||: +|i|-|-|| || -|-|+||| ||= |-| || -|-|+|| -||| -|ir-||-|| :||- |-|||i|-|-|| |+| - - -|-|+ i:|-|: -|-|+-||| :|| i-|| ||| -|-| .|| -|-|+ ||||||=| SIGNS OF ZODIAC1&gt; MESH ARIES 14 APRIL2&gt; VRISHABHA TAURUS 14 MAY3&gt; MITHUN GEMINI 14 JUNE4&gt; KARKA CANCER 14 JULY5&gt; SIMHA LEO 14 AUGUST6&gt; KANYA VIRGO 14 SEPTEMBER7&gt; TULA LIBRA 14 OCTOBER8&gt; VRISHIKA SCORPIUS 14 NOVEMBER9&gt; DHANU SAGITTARIUS 14 DECEMBER10&gt; MAKAR CAPRICORNUS 14 JANUARY11&gt; KUMBHA AQUARIUS 14 FEBRUARY12&gt; MEENA PICES 14 MARCHINDIAN WESTERN ENTRY OF SUNDECLINATION OF THE SUN THROUGHOUT AN YEARi-|| Angular speed of Sun = 1 degree per dayAngular speed of Moon = 13.33 degrees per dayAngular speed of Moon with respect Sun = 13.33 1 = 12 deg/dayOne Tithi = 12 degrees nearlyTithi is also angular difference between Sun and MoonAngular difference in white fortnight = 12 x TithiLet Tithi = 4, Angular difference = 4 x 12 = 48 degreesAngular difference in black fortnight = 180 12 x TithiLet Tithi = 3, Angular difference = 180 12 x 3 = 144 degreesTithi also indicates the Phase of the MoonFrom the Tithi, time of Moon rise can also be estimated.For example, in the third Tithi of dark fortnight Moon riseWill be about 2.5 ( 36/15) hours after Sunset.In the fifth Tithi of white fortnight MoonriseWill be about 4 (60/15) after Sunrise.From the Tithi time of high tide can also be estimated.i-|| |i: |i| -|| At the time of sunrise the current tirhi is the tithi of the day The tithi which exists at the consecutive sunrise is the case oftithi vriddhi or interval of tithi &gt; 24 hours. The tithi which falls between the two consecutive sunrises is thecase of tithi kshya or interval of tithi &lt; 24 hoursTithi Cycle ( Metonic Cycle) 19 tropical years = 19 x 365.2422 = 6939.602 days 235 synodic months of Moon = 235 x 29.3 = 6939.689 days Hence after 19 years sequence of tithis are repeated A difference of 1 day after 218.5 years.INTERCALARY MONTH (i|= -||| ) Lunar month is an interval between two successive new moons.Which is equal to 29.530589 days. one lunar year = 29.530589 x 12 = 354.36706 days one solar year = 365.25636 days. Difference between solar and lunar year = 10.8893 days. If the difference is allowed to accumulate, Lunar months will be out of steps with the seasons. Hence idea of intercalarymonth was introduced. When the difference adds up to a full lunar month, intercalarymonth is added in that particular lunar month. Intercalary month occurs after 10.8893 x 3 = 32.6679 months,or after about 33 months. Normal lunar year consists of 12 lunar months of 354 0r 355 days.In a lunar year in which there is intercalary month will have 13lunar months of 383 or 384 days. i|= -|||-|| -|||FORTNIGHTS AND ELONGATION(+-| |i| ;-||-) Two Fortnights White (|+-|) and Dark (=|) In White fortnight angular distance between Sun and Moon increases. In Dark fortnight angular distance between Sun and Moon decreases. In White fortnight Moon rises after sunrise and sets after sunset. In Dark fortnight Moon rises before sunrise and sets before sunset. Elongation is angular difference between longitudes of Sun and Planet/star. If longitude of a star or planet is greater than longitude of Sun, elongation is east. If longitude of a star or planet is less than longitude of Sun,elongation is west. If elongation is east star or planet will rise after sunrise. If elongation is west star or planet will rise before sunrise. Time of rise of a star or planet = elongation/15.KNOWING THE NAME OF THE MONTH, THE TYPE OF THE FORTNIGHTAND THE TITHI, ENTIRE SKY IS KNOWN.Angle between the Sun, Earth and Planet is called ElongationLongitude of Sun &gt; Longitude of planet : Elongation is westElongation = Longitude of Sun Longitude of planetIf Elongation is West then planet rises before sunrise and sets before sunsetLongitude of planet &gt; Longitude of Sun : Elongation is eastElongation = Longitude of planet Longitude of SunIf elongation is East then planet rises after sunrise and sets after sunsetELONGATIONelongation2.-|||| |i| :i-||||-| After Winter Solstice uttarayan starts. At present Uttarayan starts on 22 December every year After Summer Solstice Dakshinayan starts At present Dakshinayan starts on 22 June every year. After onset of Uttarayan day length increases night length decreases. After onset of Dakshinayan day length decreases night length increases. Lengths of day and night are equal on Vernal Eqinox (||-|+|-) andAutumnal Equinox (|:|+|-).longitude22 Dec22 JunSummer SolsticeWinter SolsticeNiryanAYANANSHA(i|+|)|:|| ||i-|||| i|r|| -|||||-| -||||-||-| -|||| |||-|| || ||+|||-| ||i-|-| -||i-| i-=i-|||| -|||EVENT JULIAN GREGORIANWINTER SOLSTICE 03 JAN 1752BC 19 DEC 1753 BCFUL MOON DAY 17 JAN 1752 BC 02 JAN 1752VERNAL EQUINOX 04 APL 1752 BC 20 MAR 1752 BCSUMMER SOLSTICE 05 JUL 1752 BC 20 JUN 1752 BCDIFFERENCE BETWEEN GREGORIAN AND JULIAN 15 OR 16 DAYSGREGORIAN AND JULIAN CALENDAR DATES OF VEDANGA JYOTISHWINTER SOLSTICENOW 22 DECEMBERSUMMER SOLSTICENOW 22 JUNE SUNMOON3 JANUARY 1752 BC NEW MOON DAY IN DHANISHTA17 JANUARY 1752 BC FULL MOON DAY IN MAGHA4 APRIL 1752 BC VERNAL EQUNOX IN BHARANI5 JULY 1752 BC DAKSHINAYAN IN MID OF ASHLESHA SUNSHIFT OF VERNAL EQUINOX1 : Earth rotates2 : PI = 3.14163 : Sidereal day = 23hrs 56 min 4.1 sec4 : Diameter of Earth = 12810 km5 : Earth is round6 : length of Earths shadow = 1392000km7 : Solution of first order indeterminate equation 8 : Sidereal year = 365.25639 : Revolution of Moon = 27.3216 days11 : Period revolutions of the planets (days)planet Aryabhat modernSun 365.25868 365.25636Moon 27.32167 27.32166Mercury 87.96988 87.9693Venus 224.69814 224.7008Mars 686.99974 686.9797Jupiter 4332.2721 4332.5887Saturn 10766.06465 10759.201GLIMPSES ARYABHATIYAARYABHAT : BORN IN 476 ADSines in terse verse : Roddam Narasingh : Nature 20/27 DEC 2001-|i= |i= =i= |i= -|i= |i= =i= r:| =i= i=| |i= i=|-|i= i=| r+| |i= i=| | :|| =| +-| - = = =-|||||arc ABC = radius R Angle AOC = 57deg 17 min 44 sec = 3438 minutesAll reference circles will have, Radius 3438For example: sin(3.75deg) = sin(225min) = 225/3438 = 0.0654radianRRR|-- r||| |-|||| |||=-| |||||||=-||- |-|| ||i- |||:||- i:-|+|weekdaysHOURS OF A DAY(HORA)1 2 3 4 5 6 78 9 10 11 12 13 14 15 16 17 18 19 20 2122 23 24 SATURNSUNSATURNJUPITERMARSSUNVENUSMERCURYMOONSLOWESTFASTESTTHE OF THE WEEK: |-i|= |--| ||-| = 104 x 8 = 832z :||i-|| |r+|||-| = 62000 (1) + (2) = 62000 + 832 = 62832|-:| = 20000 = 62832/20000 = 3.146 (approximately)\The most accurate value among those of ancients.|-i|= |--| ||-| :||i-|| |r+|||-||-:| i|=-|| ||--| |-|+i|VALUE OF The gods living at north pole and demons living at south poleSee the Sun for six months when it rises.The ancestors living on Moon see the Sun for half of the lunarmonth i.e. for 15 days.The people living on Earth see the Sun for half of the day i.e.for 12 hours. The meaning of this verse is,On north and south pole the day and night cycle is of six months.On Moon the day and night cycle if of 15 days.On Earth the day and night cycle is of 12 hours.Day and night cycle On north and south pole, on Moon and the Earthi||||| :|| +|i- .i:- i| -|| +-||i|-||||| i+- |i||| =i:-||| ;r -|-|||Planet Bhagana Sidereal time of revolution (days)Aryabhata ModernSun 4320000 365.25868 365.25636Moon 57753336 27.32167 27.32166Mercury 17937020 87.96988 87.9693Venus 7022388 224.69814 224.7008Mars 2296824 686.99974 686.9797Jupiter 364224 4332.27217 4332.5887Saturn 146564 10766.06465 10759.201Ascending node 232226 6794.74951 6793.39108BHAGANANumber revolutions around the Earth in MahayugaSYNODIC TIME = NUMBER OF YEARS IN YUGA/NUMBER OF CONJUNCTIONSNUMBER OF YEARS IN YUGA = 4320000NUMBER OF CONJUNCTIONSIN YUGA = N1 N2 N= REVOLUTIONSSYNODIC TIME OF SUN AND MOON = 4320000/(57753336 4320000)= 4320000/5343336 = .0808484 X 365.25868= 29.530582 daysPlanet Aryabhatiya ModernMercury 0.375 0.387Venus 0.725 0.723Mars 1.538 1.523Jupiter 5.16 5.2Saturn 9.41 9.54Heliocentric distances of the planetsin terms of Earth to Sun distancePlanet Aryabhatiya(days) Modern(days)Mercury 115.88 115.975Venus 583.89 585.92Mars 779.92 779.93Jupiter 398.89 398.75Saturn 378.08 378.00SYNODIC TIMES OF THE PLANETSPLANET AVERAGE DAILY SPEED(DEG)ARYABHAT MODERNMoon 13.176333 13.178029Mercury 4.092029 4.0953717Venus 1.6019858 1.6013164Sun 0.9856377 0.9861002Mars 0.524014 0.5234908Jupiter 0.0830973 0.0833221Saturn 0.0334383 0.03330AVERAGE DAILY SPEEDS OF THE PLANETSEpycycleMV = Equation of Center ( -|:=-| )At A and CSun : 840 minMoon : 1920 minAt B and DSun : 820 minMoon ; 1900 min.-| ||lanka-p23.|;i-|i||||-|-|=|:i-|| || (|z||-|-|).|;i-| -|=||| -- |-| |-||-|-.|;i-| -||| zza .-| (||-| zs:)LANKA AND FOUR CARDINAL CITIES.:|| -|=|||-| | --|| |i|- | i|:+-|||--| ||=||| |-|=i||| ||+ ||-four-citiesi|:+|-|=-|=|||=|i||i=|||i=|Brahmagupta occupies an important place in the historyof Oriental culture. Brahmagupta taught astronomy tothe Arabs before they came to know Ptolemys work, since, references to the works, Sindhind , and Al-Arkand frequently occur in Arabic literature. These are the translations of Brahmaguptas works, BrahmaSiddhanta, and Khandakhadyka .Prof.Sachau, in the translation of Al-Birunis IndiaBRAHMAGUPTA (BORN IN 598 AD)BRAHMAGUPTA (BORN IN 598 AD)First to give the formula for the area of Cyclic QuadrilateralIn trigonometry,the Brahmagupta interpolation formulais a special case of the Newton-Stirling interpolation formula,which calculates the values of sine at different intervals.The formula was developed by Brahmagupta in 665, which was later expanded by Newton and Stirlingaround a thousand years later to developthe more general Newton-Stirling interpolation formula.The Brahmagupta interpolation formula is defined as:Angle Indian sine First difference Second difference0 015 39 3930 75 36 -345 106 31 -560 130 24 -775 145 15 -990 150 5 -10150Sine (67) = sine (60) + sine(7) = 130 + {(7/15)(15 + 24)/2 + (7/15)(15 24)/2}= 130 + 8.12 = 138.12Sine(67) = 138.12/150 = 0.9208 (=9205 actual)Glimpses of Siddhantshiromani1 : Idea of infinity : Khahara rashi2 : Numbers from one to 10^183 : PI = 3.14164 : Idea of calculus d(sin x) = cos x dx5 : Khandameru = Pascal trtiangle6 : Two line proof of so called Pythagoras hypothesis7 : General solution of Indeterminateequation of second order61x^2 + 1 = Y^2X=226153980 Y = 17663190498 : Circumference of Earth = 40000kmSIDDHANTASHIROMANI1 : Lilavati2 : Beejaganit3 : Ganiytadhyaya4 : GoladhyayaBHASKARACHARYA (1114 -1183 AD)BIRTH AND DATE OF WRITING SIDDHANTASHIROMANIRASA = 6 GUNA = 3 PURNA = 0 MAHI = 1BHASKARACHARYA WAS BORN IN SHAKE 1O36THAT IS 1036 + 78 = 1114 ADSIDDHANTASHIROMANI WAS WRITTEN AT THE AGE RASA = 6 GUNA = 3 THAT IS WHEN HE WAS 36 YEARS OLDVALUE OF PIbha = 27 nanda = 9 agni = 3 kha = 0 bana = 5 suryai = 12PI = 3927/1250 = 3.1416PI = 22/7OREDUCATION OF BHASKARACHRYANAMES OF THE NUMBERS THE PLACE AND THE TEACHER BHASKARACHARYAPERIODIC TIME OF THE PLANETSPlanet Revolutions in Kalpa Periodic Time (years)Sun 4,320,000,000 1Moon 57,753,300,000 27.3 daysMercury 17,936,998,984 87.96 daysVenus 7,022,389,492 224.76 daysMars 2,296,828,522 1.88 Jupiter 365,226,455 11.86Saturn 146,567,298 29.47Moons Node 2,323,111,698 18.56Moons Perigee 488,105,858 8.85TIME UNITES1 Muhurta = 24/30 hours = 48 minutes1 Ghatika = Muhurta = 24 minutes1 Kala = 1/30 Ghatika = 48 seconds1 Kashtha = 1/30 Kala = 8/5 seconds1 Nimesh = 1/18 Kashtha = 4/45 seconds1 Tatpar = 1/30 Nimesh = 2/675 seconds1 Truti = 1/100 Tatpar = 2/67500 seconds| =i-|i|- + -||||-| n||| --||- +|- .-|- -|i-|-| + n||-- -||-| -|| +|-- |||-| | -|+|-|- -|| +|- |||-||i-| -||-- -:| |=|| i=-| ;i-=-| ||ii| |||-||i-|lunar eclipseDD1LLength of the Earths shadow = L = (2Re x D)/(2Rs 2Re) = 1392000 kmRe = radius of Earth Rs = radius of Sun D = Earth - Sun distanceL = (Earths diameter x Earth-Sun distance)/(Suns diameter-Earths diameter)Diameter of Earths shadow at Moons distance=d = (L -D1)2Re/L = 9000 kmD1 = Earth - Moon distance 2Re = diameter of Earth|:|r|MADHAV OF SANGAMGRAMAM (1350 1435)Greatest of the Indian medieval Astronomer- MathematicianPOWER SERIESMadhav Gregory SeriesMadhav Newton SeriesSeries for PI|r-|||| Written by Ganesh Daivadna in 1520 AD. Accepted 11 year cycle to reduce number of days from the epoch. 11 year cycle consists of only 4016 days. Removed the use of trigonometry. Still calculations are correct. Simplified the calculations. Accepted all over India form almanac preparations. Epoch Chaitra Shukla Pratipada Shake 1...</p>