{"id":32,"date":"2018-11-16T04:46:17","date_gmt":"2018-11-16T04:46:17","guid":{"rendered":"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=32"},"modified":"2018-11-16T06:03:48","modified_gmt":"2018-11-16T06:03:48","slug":"coordinate-systems-measurement-of-time","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/chapter\/coordinate-systems-measurement-of-time\/","title":{"rendered":"Coordinate Systems, Measurement of Time"},"content":{"raw":"
\r\n\r\n \r\n\r\n1.\u00a0\u00a0<\/strong>Learning\u00a0 Outcomes <\/strong>\r\n\r\n \r\n\r\nAfter studying this module, you should be able to\r\n
    \r\n \t
  • transform coordinates from Alt \u2013 Azimuth system to Right \u2013 Ascension system and\u00a0vice versa<\/em><\/li>\r\n \t
  • understand the essential requirements of the ecliptic system of coordinates<\/li>\r\n \t
  • describe the ecliptic system<\/span><\/li>\r\n \t
  • appreciate the galactic plane as a great circle of the celestial equator<\/span><\/li>\r\n \t
  • discuss the galactic system<\/span><\/li>\r\n \t
  • grasp the concept of time<\/span><\/li>\r\n \t
  • comprehend the diurnal motion of celestial objects<\/span><\/li>\r\n \t
  • explain how solar time is derived from the diurnal motion of the Sun<\/span><\/li>\r\n<\/ul>\r\n \r\n\r\n2.\u00a0\u00a0<\/strong>Introduction<\/strong>\r\n\r\n \r\n

    We have already noted that locating celestial objects in space is important from the point of view of studying their kinematics, their motion in space for example.\u00a0 \u00a0Since our eye does not give a reliable estimate of distance, an objects is located in terms of two directions, or angles, on the celestial sphere. We have so far studied two of such coordinate systems. There is an obvious need to be able to transform from one system of coordinates to another. For this purpose, we need to solve spherical triangles, formulae for which were given in Module 01.\u00a0 <\/span>We shall also describe two other coordinate systems.<\/p>\r\n\r\n<\/div>\r\n

    \r\n\r\n \r\n\r\n3.\u00a0 Inter conversion\u00a0 from\u00a0 horizon\u00a0 system\u00a0 to\u00a0 equatorial\u00a0 system\u00a0 and \u00a0<\/b>vice\u00a0 versa<\/strong> <\/em>\r\n\r\n \r\n\r\n3.1.\u00a0<\/strong>\u00a0Conversion\u00a0 from Alt \u2013 Azimuth to Right Ascension \u00a0\u2013\u00a0 Declination <\/strong>\r\n\r\n \r\n

    The inter-conversion can be done with the help of Equations (1.1) to (1.5) in Module 01 pertaining to a spherical triangle.\u00a0 In Fig. 3.1 are shown the two sets of coordinates. Suppose<\/p>\r\n\r\n<\/div>\r\n

    \r\n\r\n\"\"\r\n\r\nFig. 3.1. Two sets of coordinates of the same object X.\u00a0 Solution of triangle PZX will give the relation between the two sets.\r\n\r\n \r\n

    zenith distance ?(= 90\u00b0 \u2013 a) and the azimuth ?(measured from N) are given. To find the hour angle ? and declination ?, we use the relations (1.2) and (1.3) applied to the spherical triangle\u00a0<\/span>PZX.\u00a0 In writing these relations we shall use the fact that the <\/span>altitude of the pole star is equal to\u00a0<\/strong>the latitude of the observer<\/strong>, which we have already proved. Accordingly, arc length NP = ?\u00a0<\/span>and arc length PZ = 90\u00b0 \u2013 ?.<\/span><\/p>\r\n\r\n<\/div>\r\n

    \r\n\r\n\"\"\r\n\r\n \r\n\r\n1.1.\u00a0 Conversion from Right Ascension \u2013 Declination to Alt \u00a0\u2013 Azimuth<\/strong>\r\n\r\n \r\n\r\n\"\"\r\n\r\n \r\n\r\n2.\u00a0 The\u00a0 Ecliptic\u00a0 System of Coordinates<\/strong>\r\n\r\n \r\n

    This system has the ecliptic <\/strong>\u2013 the intersection of the apparent annual orbit of the Sun round the earth with the celestial sphere \u2013 as the fundamental great circle. We know that most planets and other objects in the solar system have orbits which are close to the ecliptic and make only small angles with its plane. Therefore, the choice of ecliptic as the reference great circle makes this\u00a0system very useful in representing the positions and orbits of these objects. \u00a0<\/span>Objects outside the solar system are far off and move slowly; for these objects this system is not very useful.<\/span><\/p>\r\n \r\n

    The ecliptic is inclined to the celestial equator at an angle of about ? = 23\u00b0 27\u00b4. Points M and M\u00b4 are the poles of the ecliptic. The point of intersection of the ecliptic and the celestial equator,\u00a0<\/span>the First point of Aries (vernal equinox, or spring equinox), denoted by <\/span>\u03d2, <\/strong>is taken as the reference point for this system of coordinates (Fig. 3.2). The coordinates of the object X are\u00a0<\/span>found in the usual way by drawing a half great circle joining M and M\u00b4 and passing through X.<\/span><\/p>\r\n\r\n<\/div>\r\n

    <\/div>\r\n
    \r\n\r\n\"\"\r\n

    Fig. 3.2.\u00a0 Ecliptic system of coordinates gives ecliptic longitude and ecliptic latitude.<\/p>\r\n \r\n

    The point of intersection of this half great circle with the ecliptic is L. Then the arc XL is called\u00a0celestial latitude <\/strong>(\ufffd), measured positive towards north and negative towards south of the\u00a0ecliptic. The arc <\/span>\u03d2L <\/strong>is the <\/span>celestial longitude <\/strong>(?) of the object X.\u00a0 It is measured eastwards (in the direction of earth\u2019s motion) from vernal equinox from 0\u00b0 to 360\u00b0.<\/span><\/p>\r\n \r\n

    The gravitational forces due to the Sun, moon and (to a lesser extent) other planets make the axis of the earth precess slowly. This results in the vernal equinox advancing towards west at the annual rate of about 50 arcseconds. Thus, the ecliptic longitude of celestial objects increases continuously at this rate.<\/span><\/p>\r\n\r\n<\/div>\r\n

    \r\n\r\n \r\n\r\n2.1.\u00a0 Transformation\u00a0 to\u00a0 Ecliptic\u00a0 System\u00a0 from\u00a0 the Equatorial System<\/strong>\r\n\r\n \r\n

    The ecliptic coordinates cannot be measured directly; they must be obtained by transforming coordinates from other systems. \u00a0Fig. 3.3 shows equatorial and ecliptic coordinates together. Solution of the spherical triangle MPX would give the transformational equations from one set to another set of coordinates.\u00a0\u00a0 Fig. 3.3 also shows, incidentally, that the maximum declination of the Sun is \u221323\u00b0 27\u00b4, and at equinoxes its declination is zero.<\/p>\r\n \r\n\r\nConversion from equatorial coordinates to the ecliptic coordinates can be done by applying Equations (1.1), (1.2) and (1.3) discussed in Module 01 to triangle MPX. The equation we get for conversion from (?, ?) to (?, ?) are:\r\n\r\n\"\"\r\n\r\n<\/div>\r\n

    \r\n\r\n\"\"\r\n

    Fig. 3.3.\u00a0 The equatorial set of coordinates and the ecliptic set for the same object X are shown here. Solution of the spherical triangle gives the transformational equations.<\/p>\r\n \r\n\r\n3.\u00a0 The\u00a0 Galactic System\u00a0 of Coordinates<\/strong>\r\n\r\n \r\n

    The great circle formed by the intersection of the plane of our galaxy, the Milky Way Galaxy <\/strong>or just the Galaxy<\/strong>, is called the galactic equator <\/strong>(Fig. 3.4).<\/strong><\/p>\r\n\r\n<\/div>\r\n

    \r\n\r\n\"\"\r\n

    Fig. 3.4.\u00a0 Side on view of the Milky Way Galaxy. (Credit: NASA)<\/p>\r\n\"\"\r\n

    Fig. 3.5.\u00a0 A sketch of the side on view of the Milky Way Galaxy.\u00a0 The central plane, which appears a line seen side on. is called the galactic equator.<\/span><\/p>\r\n\r\n<\/div>\r\n

    \r\n\r\n \r\n

    The use of galactic equator as the basis for a system of coordinates gives us another system of celestial coordinates. This system, called the galactic system<\/strong>, is used extensively in the study of galactic structure and galactic rotation.<\/p>\r\n \r\n

    The galactic equator is inclined to the celestial equator at an angle of 62.6\u00b0 (Fig. 3.8). The reference point, A, is the direction of the centre of the Galaxy whose coordinates are (? = 17 h 42 m and\u00a0 ? = - 28.9\u00b0). The North galactic pole has coordinates: ? = 12 h 49 m, ? = +27\u00b0 24\u00b4.<\/p>\r\n \r\n

    The declination of the north galactic pole can be easily inferred from Fig. 3.8. The centre of the Galaxy is in the direction of the constellation Sagittarius. \u00a0It is to be noted that the centre of the Galaxy is not visible through optical wavelengths. \u00a0It is visible in radio, infrared and x-ray region of the spectrum.<\/p>\r\n\"\"\r\n

    Fig. 3.6. \u00a0Milky Way as it would appear if seen from the top. (Credit: NASA). The Milky Way Galaxy is a spiral galaxy.\u00a0 We cannot actually photograph our own galaxy.\u00a0 This photographs and the one in Fig. 3.4 are the impressions we have formed by observing similar other galaxies. The nearest spiral galaxy, believed to be quite like our own, is the Andromeda Galaxy.<\/span><\/p>\r\n\r\n<\/div>\r\n

    \r\n\r\n \r\n\r\n\"\"\r\n\r\n \r\n

    Fig. 3.7.\u00a0 Teapot of the Sagittarius is a part of the constellation Sagittarius. The centre of the Milky Way Galaxy lies in the direction of the constellation Sagittarius.<\/p>\r\n \r\n

    Points G and H in Fig. 3.8 are the poles of the galactic equator. \u00a0A half great circle joining G and H and passing through X intersects the galactic equator at L. Then the arc length AL is called the\u00a0<\/span>galactic longitude <\/strong>of X, measured from 0\u00b0 \u2013 360\u00b0 eastward along the galactic equator.<\/span><\/p>\r\n\r\n<\/div>\r\n

    \r\n\r\n\"\"\r\n\r\n<\/div>\r\n
    \r\n\r\n \r\n

    Fig. 3.8.\u00a0 Galactic system of coordinates.\u00a0 Galactic equator is the central plane of the Milky Way Galaxy.\u00a0 It makes an angle of 62.6\u00b0 with the celestial equator.\u00a0 The reference point is A, the direction of the centre of the Galaxy.<\/p>\r\n \r\n

    Galactic longitude is denoted by ???. The arc length LX is called the galactic latitude <\/strong>of X. It is denoted by ???. It is measure from 0\u00b0 \u2013 90\u00b0 positive (+) towards north or 0\u00b0 \u2013 90\u00b0 negative (-) towards south of the galactic equator. \u00a0Notice that galactic longitude and galactic latitude are defined in a similar way as longitude and latitude of a place on the earth. Earlier the galactic longitude and latitude (??, ??), used to be reckoned from the point of intersection of the galactic equator with the celestial equator.\u00a0 Unlike A, this point had no physical significance.<\/p>\r\n\r\n<\/div>\r\n

    \r\n\r\n\"\"\r\n\r\n<\/div>\r\n
    \r\n\r\n \r\n

    Fig. 3.9.\u00a0 Galactic coordinates. Direction to the galactic centre defines the reference point of the system. Angle ??? is in the plane of the Galactic equator and angle ??? is perpendicular to this plane.<\/p>\r\n \r\n\r\n4. <\/span>Summary<\/span><\/strong>\r\n\r\n<\/div>\r\n

      \r\n \t
    • Coordinates can be transformed from one system to another by solving relevant spherical triangle.<\/li>\r\n \t
    • Ecliptic system of coordinates is used extensively in studying the solar system.<\/li>\r\n \t
    • Objects of the solar system have orbits quite close to the ecliptic. Therefore, the reference great circle for the ecliptic system is the ecliptic.<\/li>\r\n \t
    • The reference point is the First Point of Aries, or Vernal equinox.<\/li>\r\n \t
    • A half great circle joining the two poles of the ecliptic is drawn through the object whose coordinates are required.<\/li>\r\n \t
    • The celestial latitude is the arc length from the ecliptic to the object along this great half circle.<\/li>\r\n \t
    • The celestial longitude is the arc length from vernal equinox along the ecliptic to the point of intersection of this great half circle with the ecliptic.<\/li>\r\n \t
    • Another system of coordinates, the galactic system, is used in the study of galactic structure and galactic rotation.<\/li>\r\n \t
    • The reference circle for the galactic system is the great circle parallel to the plane of our Milky Way galaxy.<\/li>\r\n \t
    • This plane is inclined to the celestial equator at an angle of 62.6\u00b0.<\/li>\r\n \t
    • The reference point is the direction of the galactic centre in the direction of the constellation Sagittarius.<\/li>\r\n \t
    • The two coordinates on this system are called galactic longitude and galactic latitude.<\/li>\r\n \t
    • Our Galaxy is a spiral galaxy. Seen side-on it shows the characteristic bulge at the centre.\u00a0 The solar system is near the edge of the Galaxy.<\/li>\r\n \t
    • Seen from the top the spiral structure of the Galaxy is clearly seen.<\/li>\r\n<\/ul>\r\n \r\n\r\nKNOW \u2013 MORE<\/strong>\r\n\r\n \r\n\r\nMaterial for further reading on the topics discussed in this module is available on the following\u00a0websites:\r\n
        \r\n \t
      • https:\/\/en.wikipedia.org\/wiki\/Spherical_trigonometry<\/li>\r\n \t
      • http:\/\/www.krysstal.com\/sphertrig.html<\/li>\r\n \t
      • http:\/\/jwilson.coe.uga.edu\/EMAT6680Fa2013\/Lively\/Spherical%20Triangles\/Solving_Spherical_Triangles.pdf<\/li>\r\n \t
      • http:\/\/astrowww.phys.uvic.ca\/~tatum\/celmechs\/celm3.pdf<\/li>\r\n \t
      • http:\/\/faculty.trinityvalleyschool.org\/hoseltom\/labs\/Lab-01 %28Spherical%20Trigonometry%20Intro%29.pdf<\/li>\r\n \t
      • http:\/\/csep10.phys.utk.edu\/astr161\/lect\/celestial\/celestial.html<\/li>\r\n \t
      • http:\/\/stars.astro.illinois.edu\/celsph.html<\/li>\r\n \t
      • http:\/\/astro.wsu.edu\/worthey\/astro\/html\/lec-celestial-sph.html<\/li>\r\n<\/ul>","rendered":"
        \n

         <\/p>\n

        1.\u00a0\u00a0<\/strong>Learning\u00a0 Outcomes <\/strong><\/p>\n

         <\/p>\n

        After studying this module, you should be able to<\/p>\n

          \n
        • transform coordinates from Alt \u2013 Azimuth system to Right \u2013 Ascension system and\u00a0vice versa<\/em><\/li>\n
        • understand the essential requirements of the ecliptic system of coordinates<\/li>\n
        • describe the ecliptic system<\/span><\/li>\n
        • appreciate the galactic plane as a great circle of the celestial equator<\/span><\/li>\n
        • discuss the galactic system<\/span><\/li>\n
        • grasp the concept of time<\/span><\/li>\n
        • comprehend the diurnal motion of celestial objects<\/span><\/li>\n
        • explain how solar time is derived from the diurnal motion of the Sun<\/span><\/li>\n<\/ul>\n

           <\/p>\n

          2.\u00a0\u00a0<\/strong>Introduction<\/strong><\/p>\n

           <\/p>\n

          We have already noted that locating celestial objects in space is important from the point of view of studying their kinematics, their motion in space for example.\u00a0 \u00a0Since our eye does not give a reliable estimate of distance, an objects is located in terms of two directions, or angles, on the celestial sphere. We have so far studied two of such coordinate systems. There is an obvious need to be able to transform from one system of coordinates to another. For this purpose, we need to solve spherical triangles, formulae for which were given in Module 01.\u00a0 <\/span>We shall also describe two other coordinate systems.<\/p>\n<\/div>\n

          \n

           <\/p>\n

          3.\u00a0 Inter conversion\u00a0 from\u00a0 horizon\u00a0 system\u00a0 to\u00a0 equatorial\u00a0 system\u00a0 and \u00a0<\/b>vice\u00a0 versa<\/strong> <\/em><\/p>\n

           <\/p>\n

          3.1.\u00a0<\/strong>\u00a0Conversion\u00a0 from Alt \u2013 Azimuth to Right Ascension \u00a0\u2013\u00a0 Declination <\/strong><\/p>\n

           <\/p>\n

          The inter-conversion can be done with the help of Equations (1.1) to (1.5) in Module 01 pertaining to a spherical triangle.\u00a0 In Fig. 3.1 are shown the two sets of coordinates. Suppose<\/p>\n<\/div>\n

          \n

          \"\"<\/p>\n

          Fig. 3.1. Two sets of coordinates of the same object X.\u00a0 Solution of triangle PZX will give the relation between the two sets.<\/p>\n

           <\/p>\n

          zenith distance ?(= 90\u00b0 \u2013 a) and the azimuth ?(measured from N) are given. To find the hour angle ? and declination ?, we use the relations (1.2) and (1.3) applied to the spherical triangle\u00a0<\/span>PZX.\u00a0 In writing these relations we shall use the fact that the <\/span>altitude of the pole star is equal to\u00a0<\/strong>the latitude of the observer<\/strong>, which we have already proved. Accordingly, arc length NP = ?\u00a0<\/span>and arc length PZ = 90\u00b0 \u2013 ?.<\/span><\/p>\n<\/div>\n

          \n

          \"\"<\/p>\n

           <\/p>\n

          1.1.\u00a0 Conversion from Right Ascension \u2013 Declination to Alt \u00a0\u2013 Azimuth<\/strong><\/p>\n

           <\/p>\n

          \"\"<\/p>\n

           <\/p>\n

          2.\u00a0 The\u00a0 Ecliptic\u00a0 System of Coordinates<\/strong><\/p>\n

           <\/p>\n

          This system has the ecliptic <\/strong>\u2013 the intersection of the apparent annual orbit of the Sun round the earth with the celestial sphere \u2013 as the fundamental great circle. We know that most planets and other objects in the solar system have orbits which are close to the ecliptic and make only small angles with its plane. Therefore, the choice of ecliptic as the reference great circle makes this\u00a0system very useful in representing the positions and orbits of these objects. \u00a0<\/span>Objects outside the solar system are far off and move slowly; for these objects this system is not very useful.<\/span><\/p>\n

           <\/p>\n

          The ecliptic is inclined to the celestial equator at an angle of about ? = 23\u00b0 27\u00b4. Points M and M\u00b4 are the poles of the ecliptic. The point of intersection of the ecliptic and the celestial equator,\u00a0<\/span>the First point of Aries (vernal equinox, or spring equinox), denoted by <\/span>\u03d2, <\/strong>is taken as the reference point for this system of coordinates (Fig. 3.2). The coordinates of the object X are\u00a0<\/span>found in the usual way by drawing a half great circle joining M and M\u00b4 and passing through X.<\/span><\/p>\n<\/div>\n

          <\/div>\n
          \n

          \"\"<\/p>\n

          Fig. 3.2.\u00a0 Ecliptic system of coordinates gives ecliptic longitude and ecliptic latitude.<\/p>\n

           <\/p>\n

          The point of intersection of this half great circle with the ecliptic is L. Then the arc XL is called\u00a0celestial latitude <\/strong>(\ufffd), measured positive towards north and negative towards south of the\u00a0ecliptic. The arc <\/span>\u03d2L <\/strong>is the <\/span>celestial longitude <\/strong>(?) of the object X.\u00a0 It is measured eastwards (in the direction of earth\u2019s motion) from vernal equinox from 0\u00b0 to 360\u00b0.<\/span><\/p>\n

           <\/p>\n

          The gravitational forces due to the Sun, moon and (to a lesser extent) other planets make the axis of the earth precess slowly. This results in the vernal equinox advancing towards west at the annual rate of about 50 arcseconds. Thus, the ecliptic longitude of celestial objects increases continuously at this rate.<\/span><\/p>\n<\/div>\n

          \n

           <\/p>\n

          2.1.\u00a0 Transformation\u00a0 to\u00a0 Ecliptic\u00a0 System\u00a0 from\u00a0 the Equatorial System<\/strong><\/p>\n

           <\/p>\n

          The ecliptic coordinates cannot be measured directly; they must be obtained by transforming coordinates from other systems. \u00a0Fig. 3.3 shows equatorial and ecliptic coordinates together. Solution of the spherical triangle MPX would give the transformational equations from one set to another set of coordinates.\u00a0\u00a0 Fig. 3.3 also shows, incidentally, that the maximum declination of the Sun is \u221323\u00b0 27\u00b4, and at equinoxes its declination is zero.<\/p>\n

           <\/p>\n

          Conversion from equatorial coordinates to the ecliptic coordinates can be done by applying Equations (1.1), (1.2) and (1.3) discussed in Module 01 to triangle MPX. The equation we get for conversion from (?, ?) to (?, ?) are:<\/p>\n

          \"\"<\/p>\n<\/div>\n

          \n

          \"\"<\/p>\n

          Fig. 3.3.\u00a0 The equatorial set of coordinates and the ecliptic set for the same object X are shown here. Solution of the spherical triangle gives the transformational equations.<\/p>\n

           <\/p>\n

          3.\u00a0 The\u00a0 Galactic System\u00a0 of Coordinates<\/strong><\/p>\n

           <\/p>\n

          The great circle formed by the intersection of the plane of our galaxy, the Milky Way Galaxy <\/strong>or just the Galaxy<\/strong>, is called the galactic equator <\/strong>(Fig. 3.4).<\/strong><\/p>\n<\/div>\n

          \n

          \"\"<\/p>\n

          Fig. 3.4.\u00a0 Side on view of the Milky Way Galaxy. (Credit: NASA)<\/p>\n

          \"\"<\/p>\n

          Fig. 3.5.\u00a0 A sketch of the side on view of the Milky Way Galaxy.\u00a0 The central plane, which appears a line seen side on. is called the galactic equator.<\/span><\/p>\n<\/div>\n

          \n

           <\/p>\n

          The use of galactic equator as the basis for a system of coordinates gives us another system of celestial coordinates. This system, called the galactic system<\/strong>, is used extensively in the study of galactic structure and galactic rotation.<\/p>\n

           <\/p>\n

          The galactic equator is inclined to the celestial equator at an angle of 62.6\u00b0 (Fig. 3.8). The reference point, A, is the direction of the centre of the Galaxy whose coordinates are (? = 17 h 42 m and\u00a0 ? = – 28.9\u00b0). The North galactic pole has coordinates: ? = 12 h 49 m, ? = +27\u00b0 24\u00b4.<\/p>\n

           <\/p>\n

          The declination of the north galactic pole can be easily inferred from Fig. 3.8. The centre of the Galaxy is in the direction of the constellation Sagittarius. \u00a0It is to be noted that the centre of the Galaxy is not visible through optical wavelengths. \u00a0It is visible in radio, infrared and x-ray region of the spectrum.<\/p>\n

          \"\"<\/p>\n

          Fig. 3.6. \u00a0Milky Way as it would appear if seen from the top. (Credit: NASA). The Milky Way Galaxy is a spiral galaxy.\u00a0 We cannot actually photograph our own galaxy.\u00a0 This photographs and the one in Fig. 3.4 are the impressions we have formed by observing similar other galaxies. The nearest spiral galaxy, believed to be quite like our own, is the Andromeda Galaxy.<\/span><\/p>\n<\/div>\n

          \n

           <\/p>\n

          \"\"<\/p>\n

           <\/p>\n

          Fig. 3.7.\u00a0 Teapot of the Sagittarius is a part of the constellation Sagittarius. The centre of the Milky Way Galaxy lies in the direction of the constellation Sagittarius.<\/p>\n

           <\/p>\n

          Points G and H in Fig. 3.8 are the poles of the galactic equator. \u00a0A half great circle joining G and H and passing through X intersects the galactic equator at L. Then the arc length AL is called the\u00a0<\/span>galactic longitude <\/strong>of X, measured from 0\u00b0 \u2013 360\u00b0 eastward along the galactic equator.<\/span><\/p>\n<\/div>\n

          \n

          \"\"<\/p>\n<\/div>\n

          \n

           <\/p>\n

          Fig. 3.8.\u00a0 Galactic system of coordinates.\u00a0 Galactic equator is the central plane of the Milky Way Galaxy.\u00a0 It makes an angle of 62.6\u00b0 with the celestial equator.\u00a0 The reference point is A, the direction of the centre of the Galaxy.<\/p>\n

           <\/p>\n

          Galactic longitude is denoted by ???. The arc length LX is called the galactic latitude <\/strong>of X. It is denoted by ???. It is measure from 0\u00b0 \u2013 90\u00b0 positive (+) towards north or 0\u00b0 \u2013 90\u00b0 negative (-) towards south of the galactic equator. \u00a0Notice that galactic longitude and galactic latitude are defined in a similar way as longitude and latitude of a place on the earth. Earlier the galactic longitude and latitude (??, ??), used to be reckoned from the point of intersection of the galactic equator with the celestial equator.\u00a0 Unlike A, this point had no physical significance.<\/p>\n<\/div>\n

          \n

          \"\"<\/p>\n<\/div>\n

          \n

           <\/p>\n

          Fig. 3.9.\u00a0 Galactic coordinates. Direction to the galactic centre defines the reference point of the system. Angle ??? is in the plane of the Galactic equator and angle ??? is perpendicular to this plane.<\/p>\n

           <\/p>\n

          4. <\/span>Summary<\/span><\/strong><\/p>\n<\/div>\n

            \n
          • Coordinates can be transformed from one system to another by solving relevant spherical triangle.<\/li>\n
          • Ecliptic system of coordinates is used extensively in studying the solar system.<\/li>\n
          • Objects of the solar system have orbits quite close to the ecliptic. Therefore, the reference great circle for the ecliptic system is the ecliptic.<\/li>\n
          • The reference point is the First Point of Aries, or Vernal equinox.<\/li>\n
          • A half great circle joining the two poles of the ecliptic is drawn through the object whose coordinates are required.<\/li>\n
          • The celestial latitude is the arc length from the ecliptic to the object along this great half circle.<\/li>\n
          • The celestial longitude is the arc length from vernal equinox along the ecliptic to the point of intersection of this great half circle with the ecliptic.<\/li>\n
          • Another system of coordinates, the galactic system, is used in the study of galactic structure and galactic rotation.<\/li>\n
          • The reference circle for the galactic system is the great circle parallel to the plane of our Milky Way galaxy.<\/li>\n
          • This plane is inclined to the celestial equator at an angle of 62.6\u00b0.<\/li>\n
          • The reference point is the direction of the galactic centre in the direction of the constellation Sagittarius.<\/li>\n
          • The two coordinates on this system are called galactic longitude and galactic latitude.<\/li>\n
          • Our Galaxy is a spiral galaxy. Seen side-on it shows the characteristic bulge at the centre.\u00a0 The solar system is near the edge of the Galaxy.<\/li>\n
          • Seen from the top the spiral structure of the Galaxy is clearly seen.<\/li>\n<\/ul>\n

             <\/p>\n

            KNOW \u2013 MORE<\/strong><\/p>\n

             <\/p>\n

            Material for further reading on the topics discussed in this module is available on the following\u00a0websites:<\/p>\n

              \n
            • https:\/\/en.wikipedia.org\/wiki\/Spherical_trigonometry<\/li>\n
            • http:\/\/www.krysstal.com\/sphertrig.html<\/li>\n
            • http:\/\/jwilson.coe.uga.edu\/EMAT6680Fa2013\/Lively\/Spherical%20Triangles\/Solving_Spherical_Triangles.pdf<\/li>\n
            • http:\/\/astrowww.phys.uvic.ca\/~tatum\/celmechs\/celm3.pdf<\/li>\n
            • http:\/\/faculty.trinityvalleyschool.org\/hoseltom\/labs\/Lab-01 %28Spherical%20Trigonometry%20Intro%29.pdf<\/li>\n
            • http:\/\/csep10.phys.utk.edu\/astr161\/lect\/celestial\/celestial.html<\/li>\n
            • http:\/\/stars.astro.illinois.edu\/celsph.html<\/li>\n
            • http:\/\/astro.wsu.edu\/worthey\/astro\/html\/lec-celestial-sph.html<\/li>\n<\/ul>\n","protected":false},"author":4,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["prof-v-b-bhatia"],"pb_section_license":""},"chapter-type":[],"contributor":[58],"license":[],"class_list":["post-32","chapter","type-chapter","status-publish","hentry","contributor-prof-v-b-bhatia"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/32","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/users\/4"}],"version-history":[{"count":5,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/32\/revisions"}],"predecessor-version":[{"id":49,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/32\/revisions\/49"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/32\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/media?parent=32"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapter-type?post=32"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/contributor?post=32"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/license?post=32"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}