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Tacheometric Surveying NPR COLLEGE OF ENGINEERING & TECHNOLOGY, DINDIGUL DEPARTMENT OF CIVIL ENGINEERING GI-8013-ADVANCED SURVEYING-III-CIVIL PRESENTED BY, MRS.S.PREMASUNDARI ASSISTANT PROFESSOR UNIT IV ASTRONOMICAL SURVEYING UNIT I -ASTRONOMICAL SURVEYING Astronomical terms and definition – Motion of sun and stars – Celestial co-ordinate System - Time system - Nautical Alamance – Apparent attitude and corrections – Field observations and determinations of time, longitude, latitude and azimuth by attitude and Hour angle method. 2 ASTRONOMICAL SURVEYING UNIT IV ASTRONOMICAL SURVEYING CONTENTS • Celestial sphere • Astronomical terms and definitions • Motion of sun and stars • Apparent altitude and corrections • Celestial co-ordinate systems • Different time systems • Use of Nautical almanac • Star constellations • Calculations for azimuth of a line 4 UNIT IV ASTRONOMICAL SURVEYING Shape and Size of Earth Shape of the earth is sphere regular figure for simplified calculation Equatorial radius of earth (a) = 6378.388 km Polar radius of earth (b)= 6356.912 km Survey of India gives a =6377.3097 km and b=6356.1087 km Ellipticity factor = a2 b2 a India : 1/300-80 Mean radius of earth is 6367.272km 5 UNIT IV ASTRONOMICAL SURVEYING Celestial sphere The celestial sphere is an imaginary sphere of arbitrarily large radius, concentric with the observer •All objects in the observer's sky can be thought of as projected upon the inside surface of the celestial sphere, as if it were the underside of a dome or a hemispherical screen. •The celestial sphere is a practical tool for spherical astronomy, allowing observers to plot positions of objects in the sky when their distances are unknown or unimportant. 6 UNIT IV ASTRONOMICAL SURVEYING Astronomical terms and definitions Zeinth (z) : It is a point on the upper portion of celestial sphere immediately above the overhead of an observer Nadir (z’) : It is the intersection of a vertical line through the observer’s station to the lower portion of the celestial sphere Celestial or Rotational Horizon (Geocentric or true horizon): It is a great circle traced upon the celestial sphere by that plane which is perpendicular to zeinth-nadir line and which passes through the centre of the earth Sensible Horizon : It is a circle in which a plane passes through the point of observation and tangential to earth’s surface intersects with celestial sphere. The line of sight of an accurately levelled telescope lies in this plane Visible Horizon: 7 UNIT IV ASTRONOMICAL SURVEYING 8 UNIT IV ASTRONOMICAL SURVEYING Fig 1 Fig 2 9 UNIT IV ASTRONOMICAL SURVEYING Sivapriya Vijayasimhan 10 UNIT IV ASTRONOMICAL SURVEYING Motion of SUN and STAR Sun Located at a distance 93,005 km from earth Dia of Sun = 109 Dia of earth Mass of Sun = 3,32,000 of earth Temperature of earth = 20 million degrees Motions: Two apparent motion of earth 1. With respect to earth east to west 2. With respect to fixed stars in celestial sphere Motion of sun is along the great circle – ecliptic Obliquity of Ecliptic – angle between the plane of equator and the ecliptic ( 23027’) Equinoctial Point : Point of intersection of ecliptic with equator. Here declination of sun is zero Vernal Equinox : First point of aeries in which the sun’s declination changes from south to north Autumnal Equinox : First point of libra in which the sun’s declination changes from north to south Solstices : Sun’s declination is maximum Summer solstices : north declination is maximum at a point Winter Solstices : South declination is maximum 11 UNIT IV ASTRONOMICAL SURVEYING Star Moon rerates the earth in elliptical orbit(average angle 508’)inclined to the plane of ecliptic, which is intersected at points called Nodes Motions: 1. With respect to earth east to west 2. With respect to fixed stars it is from west to east Moon rotates about its polar axis. New and full occur when sun, earth and moon lie in same vertical plane (not necessarily in same straight line) Conjunction : in new moon ,moon lies between sun and earth and has same latitude as sun Opposition : In full moon , earth lies between sun and moon Waxing : Illuminated limb increase in size of moon between the time interval of new and full moon period Waning : Illuminated limb decrease in size of moon between the time interval of full and new moon period Lunar Month : Time taken between two successive new moons (27 ⅓ days) Siderial Month : One complete revolution relative to stars (29.5 days) Solar Eclipse: moon passes in front of sun’s disc Lunar Eclipse: Shadow of earth passing over the moon 12 UNIT IV ASTRONOMICAL SURVEYING 13 UNIT IV ASTRONOMICAL SURVEYING 14 UNIT IV ASTRONOMICAL SURVEYING 1. Spherical Triangle It is formed by surface of the sphere by interaction of three arcs of great circle The angle subtended by the axes at the vertices of the triangle is called spherical angles ABC – spherical triangle AB and AC are great circles with subtended angle BAC = A0 1.1Properties of spherical triangle 1. Any angle is less than two right angles or π 2. Sum of three angles is less than six right angles or 3 π and greater than two right angles or π 3. Sum of any two sides is greater than the third 4. If the sum of any two angles, is equal to two right angles to π, the sum of the angles opposite them is equal to two right angles or π 5. The smaller angle is opposite the smaller side and vice-versa 15 UNIT IV ASTRONOMICAL SURVEYING Sivapriya Vijayasimhan 16 UNIT IV ASTRONOMICAL SURVEYING 17 UNIT IV ASTRONOMICAL SURVEYING 18 UNIT IV ASTRONOMICAL SURVEYING 19 UNIT IV ASTRONOMICAL SURVEYING 1.Position of Stars Star of Elongation :When it is at greater distance east or west of meridian. Under this condition azimuth of star is maximum. Eastern or western elongation of a star is at its greatest distance to west or east of meridian respectively Star at Prime Vertical: When the observer, at zenith , the angle is right angled in the astronomical triangle. A = 90 deg Star of Horizon : Its altitude is zero and the zenith distance is equal to 90 deg Star at Culmination : When the star crosses an observer meridian the star is said to be culminate or transit. In one revolution, each star crosses a meridian twice. Upper culmination : altitude is maximum Lower culmination : altitude is minimum 20 UNIT IV ASTRONOMICAL SURVEYING Circumpolar Star : Stars which are always above the horizon and which evidently do not set. For an observer it is an circle above the pole Declination of such stars is always greater than the co-altitude of the place of observation M1 – circumpolar star having circular path A1A2 (path above horizon) M2 – circumpolar star having circular path B1B2 (path below horizon) 21 UNIT IV ASTRONOMICAL SURVEYING Co-ordinate Systems Position of heavenly body can be located by two-spherical co-ordinates, two angular distances measured along arcs of two great circles which cut each other at right angles One of great circle passing through the heavenly body is called Primary circle of reference, whereas the other is called as Secondary circle of reference Point M represents heavenly body with reference to a plane OAB O –origin of the co-ordinates A plane passing through OM shall cut a perpendicular plane OAB in line OB Two spherical co-ordinates of the point M are angles AOB and BOM at centre O Systems :1. Altitude and Azimuth , 2.Declination and right ascension system and 3. Declination and hour angle system 22 UNIT IV ASTRONOMICAL SURVEYING 1.Altitude and Azimuth System Also called as horizon system which is dependent on the position of the observer Horizon is a plane of reference and the co-ordinates of a heavenly body (azimuth and altitude) - It is the primary and secondary reference great circle in observer’s meridian - Horizontal and vertical angles are measured - theodolite - The heavenly body can be in eastern or western part of the celestial sphere Heavenly body in eastern part of celestial sphere. Let Z be the observer’s zenith and P be the celestial pole Great circle is passing through Z and M is drawn to cut the horizon plane at M’ The azimuth (A) angle between the observer’s meridian and the vertical circle through the body is the first co-ordinate Azimuth is equal to the angle at zenith between the meridian and the vertical circle through M. The co-ordinate of M is the altitude (α), which is measured above or below the horizon on vertical circle 23 UNIT IV ASTRONOMICAL SURVEYING Heavenly body in western part of celestial sphere. The concerned angles NOM(azimuth) and MOM’ (altitude) In northern hemisphere, the azimuth is always measured from north to east or west In southern hemisphere, the azimuth is measured from south to east or west Zenith Distance = ZM-MM’ Sivapriya Vijayasimhan 24 UNIT IV ASTRONOMICAL SURVEYING 2.Declination and Right Ascension System (Independent equatorial system) Two great circles : 1. Equatorial circle – primary circle 2. Declination circle – secondary circle The first co-ordinate of heavenly body is the right ascension It is the angle along the arc of celestial equator measured from the first point of aeries and also the angle between the hour circle through (γ) Declination (δ) is the angle of the body measured from equator along the arc of declination circle 25 UNIT IV ASTRONOMICAL SURVEYING 3.Declination and Hour angle System (Dependent equatorial system) Two great circles : 1. Horizon – primary circle 2. Declination circle – secondary circle The first co-ordinate of M is the hour angle It is the angle subtended at the pole, between observer's meridian and the declination of the body In northern hemisphere the hour angle is measured from south towards the west up to the declination circle.
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