IKS 5 Astronomy Handouts PDF

Society of St. Francis Xavier, Pilar’s Fr. Conceicao Rodrigues College of Engineering Fr. Agnel Technical Education Complex Bandstand Bandra (West) Mumbai -400 050 स!वता य&(ै∶ प,ृ थवीमर1णाद4क1भने स!वता 9याम:हं त ् I अ?व@मवाधC...

Society of St. Francis Xavier, Pilar’s Fr. Conceicao Rodrigues College of Engineering Fr. Agnel Technical Education Complex Bandstand Bandra (West) Mumbai -400 050 स!वता य&(ै∶ प,ृ थवीमर1णाद4क1भने स!वता 9याम:हं त ् I अ?व@मवाधC ु 9धDु नम&तEरCमतत ू G बं9ध स!वता समI ु म ् II Dr. Surendra Singh Rathod Principal, Fr. Conceicao Rodrigues College of Engineering [email protected] 1 Moulding Engineers Who Can Build the Nation स!वता य&(ै∶ प,ृ थवीमर1णाद4क1भने स!वता 9याम:हं त ् I अ?व@मवाधC ु 9धDु नम&तEरCमतत ू G बं9ध स!वता समI ु म ् II When Copernicus had his theory on heliocentric system, it was regarded as a revolutionary discovery by the scientific community. However, historians of Vedic science have dated the Earth orbiting the Sun long before Copernicus. 2 Moulding Engineers Who Can Build the Nation 3 Moulding Engineers Who Can Build the Nation List of Instruments Gifted 4 Moulding Engineers Who Can Build the Nation  Indian contributions in astronomy vThe celestial entities are an integral part of all living beings on Earth. There is a strong sense of mutual dependence between the earthly and the celestial entities. vAstronomy, a study of the celestial entities and phenomena is interconnected with cultural practices and daily life. Many events and planning of activities are done with reference to the celestial entities. ‘Kālanirṇaya’ (Determination of time) was considered the purpose of astronomy. Consulting the Pañcāṅga is a daily necessity and often the day begins with this activity. 5 Moulding Engineers Who Can Build the Nation Indian contributions in astronomy vAstronomy is not a study of some alien entities but an integral and important aspect of one’s life. Several concepts and models were developed by ancient Indians to address this requirement. This partly explains the growth and maturity of astronomical thinking in Indian society right from early times. vIndians developed a systematic procedure of study, observation, data collection, codification, pattern recognition, and analysis. This led to the development of advanced mathematics including arithmetic, geometry, algebra, trigonometry, and the basics of calculus. 6 Moulding Engineers Who Can Build the Nation  Indian contributions in astronomy vThe Vedic living required methods for fixing an auspicious time for performing various rituals and activities. Knowledge of the cardinal directions is also required to set theVedic altars. vIn ancient times, there were two major wealth-generating activities: Agriculture and Trade. Agriculture was the main driver of the economy and wealth creation. Ability to predict the weather conditions and understand the mechanism of season formation was a key requirement to improve agricultural productivity. 7 Moulding Engineers Who Can Build the Nation Indian contributions in astronomy vThe other economic activity is related to international trade. This required a good understanding of the latitude, longitude, and loxodrome. Moreover, there was a need for a calendar as well. vAstronomy plays a crucial role in navigation. The basic idea in navigation is to follow rising or setting location of a particular constellation for a certain period and then turn towards another constellation. Therefore, knowledge of astronomy becomes crucial. Indians have been regularly using astronomy for maritime purposes and some studies suggest that details of this have been well documented. 8 Moulding Engineers Who Can Build the Nation  Astronomy References in Vedic Texts and Their Dating The concept of Yuga was introduced to synchronize the Solar and Lunar calendars. 9 Moulding Engineers Who Can Build the Nation Indian Astronomers and Their Seminal Contributions 10 Moulding Engineers Who Can Build the Nation  Indian Astronomers and Their Seminal Contributions 11 Moulding Engineers Who Can Build the Nation Indian Astronomers and Their Seminal Contributions 12 Moulding Engineers Who Can Build the Nation  The celestial coordinate system ü Ecliptic is an imaginary line depicting the Sun’s movement around earth. ü The zenith is an imaginary point directly ‘above’ a particular location (highest point), on the celestial sphere and nadir is 180° from zenith (the lowest point). ü The vector from an observer to a point of interest (such as a star or any celestial body) is projected perpendicularly onto a reference plane. The angle between the projected vector and a reference vector on the reference plane is called the azimuth. 13 Moulding Engineers Who Can Build the Nation The celestial coordinate system Motion of the Sun in the Background of Stars 14 Moulding Engineers Who Can Build the Nation  The celestial coordinate system ü A solstic occurs when the sun’s path crosses the extreme north or south points on the earth’s equator. ü Southernmost point (S4) with respect to the equator is ‘winter solstice’. ü Northernmost point (S2) with respect to the equator is ‘summer solstice’. 15 Moulding Engineers Who Can Build the Nation The celestial coordinate system ü At S1 and S3, the ecliptic intersects the equator, and these points are known as the equinoxes. ü When the Sun is at equinox it is equinoctial day (viṣuvat) is mentioned in Aitareya-brāhmaṇa (18.4) ü Methods to compute the nth equinox is available inVedāṅga-jyotiṣa. ü Between S4 and S2, the Sun moves northwards (known in the Indian system as Uttarāyaṇa) ü Between S2 and S4, the Sun moves southwards (known as Dakṣiṇāyana). Taittirīya-saṃhitā (6.5.3) observes8, ‘Thus the Sun moves southwards for six months and northwards for six months’. 16 Moulding Engineers Who Can Build the Nation  The Zodiac Signs on the Ecliptic 17 Moulding Engineers Who Can Build the Nation The ‘sidereal period’ of an object is the time taken by it to complete one revolution in the background of stars. The Moon’s sidereal period is close to 27.32 days, which constitutes one lunar cycle. The 27 nakṣatras are mapped on to the 12 rāśis. Therefore, each rāśi is associated with two and a quarter (27/12) nakṣatra. In the Indian system, the zodiac has been divided into 27 equal parts from a fixed initial point in the ecliptic in order to trace the trajectory of the Moon in the context of the stars. Each such division is known as nakṣatra, measuring 13° 20′ or 800 minutes of arc of the ecliptic (360/27). Each division is named after a selected star that is generally prominent or traditionally well-known and is broadly equally spaced in the zodiac. 18 Moulding Engineers Who Can Build the Nation 19 Moulding Engineers Who Can Build the Nation 20 Moulding Engineers Who Can Build the Nation  Elements of the Indian calendar Notion of years and months The Notion of a Year Alternative Classification of Year Cycles in the Indian Tradition 21 Moulding Engineers Who Can Build the Nation Solar and Lunar Months Sūrya-siddhānta Solar month as the time taken by the Sun to traverse a rāśi, A lunar month (cāndra-māsa) is the time interval between two new Moons (Amāvāsyā), or two full Moons (Pūrṇimā). Lunar month (Pakṣas): Śukla-pakṣa (bright fortnight) from Amāvāsyā to Pūrṇimā Kṛṣṇa-pakṣa (dark fortnight) from Pūrṇimā to Amāvāsyā. 22 Moulding Engineers Who Can Build the Nation  Lunar Months Hindu Gregorian Chaitra Mar-Apr Vaishaka Apr-May Jyestha May-Jun Ashada Jun-Jul Shravan Jul-Aug Bhadrapada Aug-Sep Ashvina Sep-Oct Kartik Oct-Nov Margashirsha Nov-Dec Pausha Dec-Jan Megha Jan-Feb Phalgun Feb-Mar 23 Moulding Engineers Who Can Build the Nation The Notion of Tithi o Tithi captures the angular separation between the Sun and the Moon. o It is a time-unit during which the angle between the Sun and the Moon (as viewed from the Earth) increases by 12° or its integral multiples. o The actual duration of a particular tithi may vary from 26 hours 47 minutes to 19 hours 59 minutes. 24 Moulding Engineers Who Can Build the Nation 25 Moulding Engineers Who Can Build the Nation 26 Moulding Engineers Who Can Build the Nation  Āryabhaṭīya and the Siddhāntic Tradition Organisation of Āryabhaṭīya and the Issues Covered 27 Moulding Engineers Who Can Build the Nation According to Āryabhaṭa, the Earth is a sphere at the center of the framework in which stars and planets move. According to a verse in Āryabhaṭīya: “The globe of the Earth stands (supportless) at the center of the circular frame of asterisms surrounded by the orbits (of the planets); it is made up of water, earth, fire, and air and is spherical.” According to the earlier astronomical works in India and elsewhere, the Earth was stationary, and all the celestial objects rotated in the sky, completing one rotation in one day. The celestial objects rise in the eastern part of the sky, and set in the western part, and are visible when they are above the horizon. However, Āryabhaṭīya presented a different view. The diurnal motion of the celestial objects was mentioned in one of the verses as follows: “Just as a man in a boat moving forward sees the stationary objects as moving backward, just so are the stationary stars seen by people at Lanka (on the equator), as moving exactly towards the west.” What is implied in this verse is that though it appears that objects in the sky are moving from east to west, they are indeed stationary, and it is the Earth which is moving (rotating) along with the entities situated on it. 28 Moulding Engineers Who Can Build the Nation  The beginning of the current Kali-yuga was on a Friday (18 February, 3102 BCE). Planetary Revolutions in a Mahā-yuga and the Inferred Sidereal Periods in Āryabhaṭīya 29 Moulding Engineers Who Can Build the Nation The apparent motions of the Sun, Moon, and planets in the background of stars are not uniform. Two corrections have to be applied to the ‘mean longitude, θ0 to obtain the ‘true’ (geocentric) longitude. 1. Manda-saṃskāra: ü This is due to the non-uniformity of motion due to the eccentricity of the planet’s orbit. It is called the ‘Equation of centre’ in modern astronomy. ü This is the only correction to the Sun and the Moon (for Moon, there are some other minor corrections specified in later texts). ü In the case of the actual planets called tārāgrahas in India (traditionally only Mercury, Venus, Mars, Jupiter, and Saturn), we obtain the true heliocentric longitude, that is, the longitudes with respect to the Sun after the manda-saṃskāra. 30 Moulding Engineers Who Can Build the Nation  2. Śīghra-saṃskāra: This correction is done only for the planets. This converts their heliocentric longitudes (as observed from the Sun) to the geocentric longitudes (as observed from the Earth). 31 Moulding Engineers Who Can Build the Nation Nīlakanṭha Somayāji’s Planetary Model (1500 CE) (Tantra-saṅgraha) According to this model, the planets move in eccentric orbits around the Sun (that is, the centers of the orbits will be slightly displaced from the Sun), which itself orbits around the Earth. Same as Tycho Brahe’s model for the planetary motion proposed around 1580 CE 32 Moulding Engineers Who Can Build the Nation  Pañcāṅga – The Indian Calendar System Pañcāṅga, as the name suggests has five components: tithi, nakṣatra, vāra, karaṇa, and yoga. Pañcāṅga – Calculations: ü Use Sūrya-siddhānta ü In recent times, o Graha-lāghava of Gaṇeśa Daivajña o Siddhānta-darpaṇa of Candraśekhara Sāmanta 33 Moulding Engineers Who Can Build the Nation Tithi Let θM and θS be the true Longitudes of the Moon and the Sun in degrees respectively at any instant. Let, where I is an integer, and f is the fractional part. Then I is the number of tithis that have elapsed in the lunar month. 34 Moulding Engineers Who Can Build the Nation  Karaṇa This is half of a tithi. In one karaṇa, the angular separation between the Moon and the Sun increases by 6°. There are 60 karaṇas in a lunar month. At any instant, the procedure to find the number of karaṇas elapsed, and the time elapsed in the current karaṇa is the same as for the tithi except that 12 should be replaced by 6. 35 Moulding Engineers Who Can Build the Nation Nakṣatra The ecliptic is divided into 27 equal parts called nakṣatras beginning with Aśvinī and ending with Revatī. Hence each nakṣatra corresponds to along the ecliptic. The nakṣatra at any instant refers to the particular portion of the ecliptic in which the Moon is situated. If we consider the above example, the nakṣatras for the two longitudes of the Moon will be as follows: To find the nakṣatra, we first convert θM into minutes and divide it by 800. 36 Moulding Engineers Who Can Build the Nation  Yoga üYoga means addition, which indicates the period during which the sum (yoga) of the nirayana longitudes of the Sun and the Moon amounts to 13° 20′ or integral multiples. üThe yoga at any moment can be found by dividing the sum of the longitudes of the sun and moon at the moment by 13° 20′. üThe quotient will give the serial number of the yoga expired and the remainder will give the elapsed part of the current yoga in units of arc. üIt pertains to a 27-fold division of the ecliptic. θS + θM in degrees is found (if the number exceeds 360, we can subtract 360 from it). It is converted into minutes (by multiplying this by 60) and then divided by 800. The quotient (Q) represents the number of yogas completed, and Q + 1 represents the currentYoga. 37 Moulding Engineers Who Can Build the Nation Yoga 38 Moulding Engineers Who Can Build the Nation  Vāra Vāra is the day of the week as we know it in modern parlance. Āryabhaṭa I was the first astronomer in the world to conceive the brilliant idea of counting continuously the days without the involvement of months and years which varies from one calendar to another.This system is named ‘ahargaṇa’, literally meaning ‘count of days’. As per Āryabhaṭīya, the beginning of the current Kali-yuga was on a Friday (18 February, 3102 BCE). Let A be the ahargaṇa corresponding to a given day. Divide A by 7. If the remainder is 0, the given day is a Friday, if it 1, it is a Saturday, etc.This is used to check the computed value of A. Suppose the ahargaṇa of the day for which we need to compute the pañcāṅga is 18,70,348. The day of the week is determined as follows: The ahargaṇa of the day is 18,70,348. Dividing this by 7 we get a quotient of 2,67,192 and a reminder of 4. For reminder 4, the day of the week is Tuesday. 39 Moulding Engineers Who Can Build the Nation Indian Astronomical Instruments Gati- yantra Nara or Sanku A drone (bowl-shaped) water- (The Gnomon) made of Ivory or a Gola-yantra clock with a hole at its bottom. metal (The armillary sphere) A sphere in which all movable and fixed circles are designed and serves the purpose of an astrolabe. 40 Moulding Engineers Who Can Build the Nation  Indian Astronomical Instruments Procedure for Fixing the Cardinal Direction Determination of the East-West Line Using a Gnomon The simplest instrument is just a straight, vertical stick (Sanku) which has a pointed tip (called a ‘gnomon’ in astronomy). vPlace a Gnomon OX exactly vertical level on the ground, so that its tip at X points at the Zenith Z. vDraw a circle with a suitable radius with the base of the gnomon O as the centre. vMark the points ‘W’ and ‘E’ where the tips of the shadow of the gnomon are on the circle, in the forenoon and the afternoon, respectively. 41 Moulding Engineers Who Can Build the Nation Indian Astronomical Instruments Nadivalaya Yantra ü The Nāḍīvalaya is a larger circular wooden disc with an axis in the centre. ü Divided into 60 ghatikas and also into 12 signs of the ecliptic with variable arcs corresponding to the periods of their risings in the place of observation. ü The disk is rotated around the axis so that the shadow of the axis falls on the mark made for the position of the Sun at sunrise. ü The number of ghatis will be seen between the point of sunrise to the position of the shadow Nāḍīvalaya – A Simple Illustration which will also indicate the lagna. 42 Moulding Engineers Who Can Build the Nation  Indian Astronomical Instruments Nadivalaya Yantra Nāḍīvalaya – A Simple Illustration 1. The Nāḍīvalaya is a larger circular wooden 3. The disk is rotated around the axis so that the disc with an axis in the centre. shadow of the axis falls on the mark made for 2. Divided into 60 ghatikas and also into 12 the position of the Sun at sunrise. signs of the ecliptic with variable arcs 4. The number of ghatis will be seen between corresponding to the periods of their risings in the point of sunrise to the position of the the place of observation.. shadow which will also indicate the lagna. 43 Moulding Engineers Who Can Build the Nation 44 Moulding Engineers Who Can Build the Nation  Cakra-Yantra CapaYantra Half the structure of Cakra Yantra TuriyaYantra (one quadrant of the Cakra) A Simple Representation of Cakra-Yantra 45 Moulding Engineers Who Can Build the Nation Jantar Mantar of Rājā Jai Singh Sawai (1686-1743 CE) East Side of Samrāṭ-yantra 2 at Delhi Jantar Mantar The Samrat Yantra is an enormous sundial: a 27m-high triangular wall with two semi-circular ramps that radiate like A Simple Sketch of Samrāṭ-yantra wings from its sides 46 Moulding Engineers Who Can Build the Nation 47 Moulding Engineers Who Can Build the Nation આભાર ‫ﺷﮑرﯾہ‬ধন&বাদ ਤੁ ਹਾਡਾ ਧੰਨਵਾਦ நன்7ధన: ;