{"id":400,"date":"2018-12-04T11:29:05","date_gmt":"2018-12-04T11:29:05","guid":{"rendered":"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=400"},"modified":"2018-12-04T12:00:51","modified_gmt":"2018-12-04T12:00:51","slug":"horizon-and-equatorial-coordinate-systems","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/chapter\/horizon-and-equatorial-coordinate-systems\/","title":{"rendered":"Horizon and Equatorial Coordinate Systems"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/NA\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n&nbsp;\r\n\r\n<strong>1. Learning Outcomes<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">After studying this module, you should be able to<\/p>\r\n\r\n<ul>\r\n \t<li style=\"text-align: justify\">explain the essential requirement of an astronomical coordinate system<\/li>\r\n \t<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">describe the Horizon System of coordinates<\/span><\/li>\r\n \t<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">locate horizon for any observer<\/span><\/li>\r\n \t<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">show that the altitude of the Pole star is equal to the latitude of the observer<\/span><\/li>\r\n \t<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">appreciate the convenience of the Horizon System<\/span><\/li>\r\n \t<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">understand the shortcomings in the Horizon System<\/span><\/li>\r\n \t<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">describe the Equatorial System of coordinates<\/span><\/li>\r\n \t<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">reason out the need for both the coordinates to be independent of time and location<\/span><\/li>\r\n \t<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">explain the Universal Equatorial System and its importance to astronomy<\/span><\/li>\r\n \t<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">describe the apparent annual motion of the Sun<\/span><\/li>\r\n \t<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">define the local sidereal time<\/span><\/li>\r\n<\/ul>\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<strong>2.\u00a0Introduction<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">In Module 01 we discussed the essential requirement of an astronomical system of coordinates for celestial objects.\u00a0 These requirements are:<\/p>\r\n&nbsp;\r\n\r\nI.\u00a0 A fundamental great circle, and\r\n\r\nII. A reference point, or origin.\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">As an example of these requirements, we discussed the terrestrial coordinate system in which equator is the fundamental great circle and the point of intersection of the prime meridian with the equator is the origin. By this system we assign longitude and latitude to places on the earth. We now discuss the <strong>Horizon System <\/strong>for which the fundamental great circle is the horizon and the origin is either the north point or the south point of the horizon. It is a simple system and is used by most small telescopes. However, the system has two shortcomings: the coordinates differ from observer to observer at the same point of time, and for the same observer at different times.\u00a0 These shortcomings are sought to be rectified in the <strong>Equatorial System <\/strong>of coordinates.<\/p>\r\n&nbsp;\r\n\r\n<strong>3. The Horizon System of Astronomical Coordinates\u00a0<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">In this system the fundamental great circle is the <strong>horizon<\/strong>.\u00a0 Let us see how we can locate our horizon.\u00a0 The point vertically overhead the observer on the celestial sphere is called the <strong>zenith<\/strong>, and the point vertically below the observer is called the <strong>nadir <\/strong>(Fig. 2.1). The horizon is the plane perpendicular to the line joining ZZ\u00b4.\u00a0 Let us see how we can locate it.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">Suppose an observer at latitude ?.\u00a0 The point exactly overhead the observer is called the <strong>zenith<\/strong>. Draw the line joining the zenith with the centre of the earth (Fig. 2.1).\u00a0\u00a0 A plane perpendicular to this line is the horizon of the observer at latitude ?. As long as an object is above the horizon, it is visible to us. \u00a0When it goes below the horizon, the object is no longer visible, we say it has set.<\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-413\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.1.png\" alt=\"\" width=\"679\" height=\"526\" \/>\r\n\r\n<strong>Exercise 2.1<\/strong>:\u00a0 Locate the horizon for an observer at the North Pole.\r\n\r\n&nbsp;\r\n\r\n<strong>Exercise 2.2<\/strong>:\u00a0 Locate the horizon for an observer stationed at the Equator.\r\n\r\n<img class=\"aligncenter size-full wp-image-412\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.2.png\" alt=\"\" width=\"624\" height=\"276\" \/>\r\n<p style=\"text-align: justify\"><span style=\"font-size: 1em;text-align: initial\">Projected on the celestial sphere with the earth as centre, the horizon is a great circle which\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">appears as shown in Fig. 2.3.\u00a0 Z and Z\u00b4 are the poles of the horizon, while P and Q are the north\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">and south celestial poles, respectively.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-411\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.3.png\" alt=\"\" width=\"669\" height=\"424\" \/>\r\n\r\nIn Fig. 2.4, N and S are the north and south points of the horizon.\u00a0 To fix coordinates of an object\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">X, we draw the half great circle ZXLZ\u00b4.\u00a0 One of the coordinates of X is then the arc length LX, called the <strong>altitude <\/strong>?.\u00a0 It is measured from zero to +90\u00b0 from L to Z and from zero to -90\u00b0 from L to Z\u00b4.\u00a0 To fix the other coordinate either N or S is chosen as the origin.\u00a0 If N is the origin, then the arc length NL, or the spherical angle NZL, is the second coordinates of X, called the <strong>azimuth<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong>A.\u00a0<\/strong>In this case the azimuth is measured from 0 to 180 degrees east or west.\u00a0 If S is chosen as the origin, the azimuth is measured from 0 to 360 degrees through west. It must be remembered that the refraction of light due to the earth\u2019s atmosphere increases slightly the altitude of a star. Necessary correction due to atmospheric refraction must, therefore, be applied to the measured altitudes of celestial objects. The complement of the altitude, the arc length ZX, is called the zenith distance of the object.\u00a0 Obviously, in degrees<\/p>\r\n&nbsp;\r\n<p style=\"text-align: center\">?= ?<strong>0<\/strong>\u2212 ?<strong>.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (2.1)<\/strong><\/p>\r\n\r\n<\/div>\r\n<div><img class=\"aligncenter size-full wp-image-410\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.4.png\" alt=\"\" width=\"715\" height=\"575\" \/><\/div>\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<strong>3.1. Altitude of the Pole star is equal to the Latitude of the Observer\u00a0<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">We immediately apply the horizon system to derive an important result: \u00a0<strong>The altitude of the Pole star is equal to the latitude of the observer. \u00a0<\/strong>Fig. 2.5 shows horizon for an observer at latitude ?.\u00a0 Z is the pole of the horizon and so the zenith for the observer is at ?to the equator.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">North Celestial Pole, P, is the pole of the equator and is in the direction of the Pole star. The great circle PZRQZ\u00b4T is called the <strong>observer\u2019s meridian<\/strong>, or <strong>local meridian<\/strong>. The arc length RZ is equal to ?by the definition of latitude. The arc length ZP is, therefore, 90 \u2212 ?<strong>, <\/strong>because the arc RP equals 90 degrees<strong>. <\/strong>This makes the arc length NP, which is actually the altitude of the Pole star in accordance with the horizon system, equal to the latitude ?.\u00a0 Thus, the altitude of the Pole\u00a0<span style=\"text-align: initial;font-size: 1em\">star at any place is equal to the latitude of that place.\u00a0\u00a0 So, to locate pole star, look in the north direction at an altitude equal to your latitude.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-409\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.5.png\" alt=\"\" width=\"614\" height=\"593\" \/>\r\n\r\n&nbsp;\r\n\r\n<strong>3.2. Convenience of the Horizon System\u00a0<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The horizon system is a very convenient system.\u00a0 Most small telescopes for amateur astronomers are based on this and use <strong>alt \u2013 azimuth mounting<\/strong>.\u00a0 The azimuth of an object gives the direction in which to look for the object.\u00a0 The altitude then gives the angle by which the telescope is to be raised from the horizontal to locate the object (Fig. 2.6).<\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-408\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.6.png\" alt=\"\" width=\"646\" height=\"388\" \/>\r\n\r\n<strong>3.3. Drawbacks of the Horizon System\u00a0<\/strong>\r\n\r\n&nbsp;\r\n\r\nEven if it is convenient, the horizon system suffers from two drawbacks:\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">(i) Since the horizon at different locations on the earth is different (Fig. 2.7), the coordinates of the same object at the same time are different for observers at different places. In other words, the coordinates of an object are location specific.<\/p>\r\n<p style=\"text-align: justify\">(ii) As the earth rotates, the celestial objects move in planes normal to the polar axis.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">Since these planes are generally inclined to the horizon, the coordinates of an object keep changing with time for any observer.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">These shortcomings are sought to be eliminated in the equatorial system of coordinates.<\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-407\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.7.png\" alt=\"\" width=\"730\" height=\"589\" \/>\r\n\r\n&nbsp;\r\n\r\n<strong>4.\u00a0 The Equatorial System\u00a0<\/strong>\r\n\r\n&nbsp;\r\n\r\n<strong>4.1.\u00a0 <\/strong><strong>Local Equatorial System<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The fundamental great circle chosen here is the celestial equator, whose plane is parallel to the equatorial plane of the earth.\u00a0 The <strong>north celestial pole <\/strong>(<strong>NCP<\/strong>) P and the <strong>south celestial pole <\/strong>(<strong>SCP<\/strong>) Q are the poles of the celestial equator, (Fig. 2.8).\u00a0 The great circle PTQR is the <strong>observer\u2019s meridian, or the local meridian. \u00a0<\/strong>Any half great circle through the two celestial poles is called an <strong>hour circle <\/strong>as it measures the time elapsed since an object on it crossed the observer\u2019s meridian.\u00a0 To get the coordinates of the object X we draw an hour circle through it.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"font-size: 1em;text-align: initial\">Then one coordinate of X is the arc length LX on its hour circle. The coordinate is called the\u00a0<\/span><strong style=\"text-align: initial;font-size: 1em\">declination <\/strong><span style=\"text-align: initial;font-size: 1em\">of X, denoted by ?. It is measure from zero to +90\u00b0 north of the celestial equator<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-406\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.8.png\" alt=\"\" width=\"590\" height=\"596\" \/>\r\n<p style=\"text-align: justify\">and from zero to -90\u00b0 to the south of the celestial equator. The other coordinate is the <strong>hour angle\u00a0<\/strong><strong>(<\/strong>?<strong>) <\/strong>measured from the point R on the observer\u2019s meridian westward (clockwise when viewed from the north celestial pole.) to L, the intersection of the hour circle of X with the celestial equator.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">It will be noticed that as the object appears to rotate from east to west, the declination remains unchanged while the hour angle increases steadily from zero to 360\u00b0 in 24 hours. For this reason, the hour angle is expressed in terms of hours rather than degrees, 1 hour corresponding to 15\u00b0.\u00a0\u00a0 In this system, too, one of the coordinates, namely the hour angle, keeps changing with\u00a0<span style=\"text-align: initial;font-size: 1em\">time as the object moves across the sky. \u00a0That is the reason the system is called <\/span><strong style=\"text-align: initial;font-size: 1em\">local equatorial system.\u00a0 <\/strong><span style=\"text-align: initial;font-size: 1em\">This shortcoming is rectified by choosing as origin a point on the celestial equator<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-405\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.9.png\" alt=\"\" width=\"616\" height=\"553\" \/>\r\n<p style=\"text-align: justify\">which is not stationary but moves with the same speed and in the same direction as the object. This ensures that there is no relative motion between the two.<\/p>\r\n&nbsp;\r\n\r\n<strong>4.2. Universal Equatorial System\u00a0<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The point, or origin, chosen for this purpose is the <strong>first Point of Aries<\/strong>, or the <strong>vernal equinox <\/strong>(<strong>\u03d2). First Point of Aries is the point of intersection of the apparent annual path of the Sun and the celestial equator<\/strong>. The arc length measured from the vernal equinox eastwards (counterclockwise when viewed from the north celestial pole) to the hour circle of the object, the arc length <strong>\u03d2L, <\/strong>is known as the right ascension (?) (Fig. 2.9)<strong>. <\/strong>It is also measured in hours because the vernal equinox completes one round of the sky in 24 hours as does any other object\u00a0<span style=\"text-align: initial;font-size: 1em\">in the sky. Thus, the right ascension remains unchanged as the object appears to move across the sky. \u00a0We have already noted that the declination of an object is unaffected by the motion of the object across the sky. Since both the coordinates remain unchanged as the object changes its position in the sky, this system is called the <\/span><strong style=\"text-align: initial;font-size: 1em\">universal equatorial system. This system is suitable for making catalogues of stars.<\/strong><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<strong>5. Annual Motion of the Sun\u00a0<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Let us briefly look at the apparent annual motion of the Sun.\u00a0 The plane of this motion is called the ecliptic.\u00a0 It makes an angle of 23.5\u00b0 with the plane of the celestial equator. The ecliptic plane intersects the plane of the equator at two points, called the vernal equinox (<strong>\u03d2<\/strong>) and the autumn equinox ( ? ). Around 21 June the Sun is at its northern most point in its apparent annual orbit. P<\/p>\r\n\r\n<\/div>\r\n<div><img class=\"aligncenter size-full wp-image-404\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.10.png\" alt=\"\" width=\"588\" height=\"541\" \/><\/div>\r\n<div>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Its declination is 23.5\u00b0. The event is called the <\/span><strong style=\"text-align: initial;font-size: 1em\">summer solstice<\/strong><span style=\"text-align: initial;font-size: 1em\">. It then moves southwards; in\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">India we call it <\/span><strong style=\"text-align: initial;font-size: 1em\"><em>Dakshinayan <\/em><\/strong><span style=\"text-align: initial;font-size: 1em\">(towards south). Around 23 September, it crosses the equator and\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">moves into the southern hemisphere.\u00a0 On this day the duration of day and night is equal, hence it is called <\/span><strong style=\"text-align: initial;font-size: 1em\">autumn equinox. <\/strong><span style=\"text-align: initial;font-size: 1em\">For those living on the equator, the Sun rises exactly in the east on this day. Around 23 December, the Sun reaches its southern most point, <\/span><strong style=\"text-align: initial;font-size: 1em\">the winter solstice<\/strong><span style=\"text-align: initial;font-size: 1em\">. Its\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">declination then is -23.5\u00b0. Then it reverses its direction and begins moving northwards; in India\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">it is called <\/span><strong style=\"text-align: initial;font-size: 1em\"><em>Uttarayan.\u00a0 <\/em><\/strong><span style=\"text-align: initial;font-size: 1em\">Around 21 March, the Sun crosses from the southern hemisphere into the\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">northern hemisphere. This point of intersection between the equator and the ecliptic is called the <\/span><strong style=\"text-align: initial;font-size: 1em\">first point of Aries<\/strong><span style=\"text-align: initial;font-size: 1em\">, or the <\/span><strong style=\"text-align: initial;font-size: 1em\">vernal equinox<\/strong><span style=\"text-align: initial;font-size: 1em\">. <\/span><strong style=\"text-align: initial;font-size: 1em\">It is this point that we use as the origin for the universal equatorial system of coordinates. There is no celestial object at this point in the sky; it is just a reference point. \u00a0<\/strong><span style=\"text-align: initial;font-size: 1em\">On the day of vernal equinox, the duration of day and night is equal, and for those living on the equator, the Sun rises exactly in the east. It must be noted that the Sun rises exactly in the east only for two days in the whole year, and that too for people\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">living in the tropics, the region between the Tropic of Cancer and the Tropic of Capricorn.\u00a0 On all other days of the year the Sun rises either in the north of east or the south of east. A few week\u2019s observations of the rising Sun should confirm this. Throughout the year the rising point of the\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">Sun keeps oscillating between 23.5\u00b0 north and 23.5\u00b0 south.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong><span style=\"text-align: initial;font-size: 1em\">6. Local Sidereal Time\u00a0<\/span><\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Since the coordinates of an object on the universal equatorial system do not change with time or location, this system is widely used for preparing catalogues of celestial objects. The hour angle of <\/span><strong style=\"text-align: initial;font-size: 1em\">\u03d2 <\/strong><span style=\"text-align: initial;font-size: 1em\">is called the <\/span><strong style=\"text-align: initial;font-size: 1em\">local sidereal time (LST), the time measured with reference to the distant\u00a0<\/strong><strong style=\"text-align: initial;font-size: 1em\">stars. <\/strong><span style=\"text-align: initial;font-size: 1em\">The relation between ?and ?is through the sidereal time (Fig. 2.9):<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: center\"><span style=\"text-align: initial;font-size: 1em\">LST = ?+ ?.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (2.2)<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">We shall discuss the sidereal time a little later.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong><span style=\"text-align: initial;font-size: 1em\">7.\u00a0\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">Summary\u00a0<\/span><\/strong><\/p>\r\n\r\n<\/div>\r\n<div>\r\n<ul>\r\n \t<li style=\"text-align: justify\">Essential requirements for an astronomical coordinate system are a reference great circle and a reference point.<\/li>\r\n \t<li style=\"text-align: justify\">For Horizon System the reference great circle is the horizon and the reference point\u00a0is the intersection of the horizon and half great circle ZXZ<span style=\"text-align: initial;font-size: 1em\">\u00b4.<\/span><\/li>\r\n \t<li style=\"text-align: justify\">The arc length along ZXZ<span style=\"text-align: initial;font-size: 1em\">\u00b4 <\/span>from the horizon to X is called the altitude of X.<\/li>\r\n \t<li style=\"text-align: justify\">Either the North point or the South point of the horizon is used the reference point\u00a0for measuring the azimuth of X.<\/li>\r\n \t<li style=\"text-align: justify\">Horizon System is a very convenient system and most small telescopes use alt \u2013 azimuth mounting.<\/li>\r\n \t<li style=\"text-align: justify\">Horizon for each observer is different. Moreover, the horizon for the same observer changes as the earth rotates on its axis.<\/li>\r\n \t<li style=\"text-align: justify\">The two drawbacks of the horizon system are that the coordinates change with the observer and with time for the same observer.<\/li>\r\n \t<li style=\"text-align: justify\">These drawbacks are sought to be rectified in the Equatorial coordinate system.<\/li>\r\n \t<li style=\"text-align: justify\">Equatorial system uses celestial equator as the reference great circle and its intersection with the observer\u2019s meridian (great circle through the poles and the zenith) as the reference point for measuring the hour angle of X.<\/li>\r\n \t<li style=\"text-align: justify\">In hour angle \u2013 declination system, declination of an object is fixed, while the hour angle of the object changes as the earth rotates on its axis.<\/li>\r\n \t<li style=\"text-align: justify\">This shortcoming, a coordinate changing with time, is rectified by choosing the first Point of Aries as the reference point.<\/li>\r\n \t<li style=\"text-align: justify\">The first Point of Aries moves just like the object X, so the coordinate measured from this point to the hour circle of X stays fixed. This coordinate is called the right ascension.<\/li>\r\n \t<li style=\"text-align: justify\">The right ascension \u2013 declination system is called the universal equatorial system.<\/li>\r\n \t<li style=\"text-align: justify\">Since both the coordinates of a star in this system remain unchanged as the star moves about in the sky, this system is suitable for making catalogues of stars.<\/li>\r\n \t<li style=\"text-align: justify\">The annual path of the Sun (ecliptic) is inclined to the equator at an angle of 23.5<span style=\"text-align: initial;font-size: 1em\">\u00b0<\/span>.<\/li>\r\n \t<li style=\"text-align: justify\">At summer solstice the Sun is at 23.5\u00b0 N and at winter solstice it is at 23.5\u00b0 S. This\u00a0motion of the Sun is responsible for the shifting point of Sunrise during the year.<\/li>\r\n \t<li style=\"text-align: justify\">Sidereal time is the time reckoned with respect to the distant fixed stars.<\/li>\r\n \t<li style=\"text-align: justify\">Right ascension and hour angle are related through the local sidereal time.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<table style=\"height: 34px\" width=\"742\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 655.063px\"><strong>You can view video on Horizon and Equatorial Coordinate Systems<\/strong><\/td>\r\n<td style=\"width: 58.0625px\"><a href=\"https:\/\/www.youtube.com\/watch?v=NA&amp;feature=youtu.be\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<strong>Websites discussing the material in this module<\/strong>\r\n<ul>\r\n \t<li>http:\/\/www.skyandtelescope.com\/astronomy-resources\/what-are-celestial-coordinates\/<\/li>\r\n \t<li>http:\/\/www.telescope.com\/Celestial-Coordinates\/p\/99817.uts<\/li>\r\n \t<li>http:\/\/physics.gmu.edu\/~jevans\/astr103\/CourseNotes\/earthSky_coordinateSystems.html<\/li>\r\n \t<li>https:\/\/www.astronomyhouston.org\/sites\/default\/files\/presentations\/HAS_Novice_Program_Celestial_Coordinates.pdf<\/li>\r\n \t<li>https:\/\/www.tcnj.edu\/~pfeiffer\/AST261\/AST261Chap2,CelCord.pdf<\/li>\r\n<\/ul>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/NA\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<p>&nbsp;<\/p>\n<p><strong>1. Learning Outcomes<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">After studying this module, you should be able to<\/p>\n<ul>\n<li style=\"text-align: justify\">explain the essential requirement of an astronomical coordinate system<\/li>\n<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">describe the Horizon System of coordinates<\/span><\/li>\n<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">locate horizon for any observer<\/span><\/li>\n<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">show that the altitude of the Pole star is equal to the latitude of the observer<\/span><\/li>\n<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">appreciate the convenience of the Horizon System<\/span><\/li>\n<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">understand the shortcomings in the Horizon System<\/span><\/li>\n<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">describe the Equatorial System of coordinates<\/span><\/li>\n<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">reason out the need for both the coordinates to be independent of time and location<\/span><\/li>\n<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">explain the Universal Equatorial System and its importance to astronomy<\/span><\/li>\n<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">describe the apparent annual motion of the Sun<\/span><\/li>\n<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">define the local sidereal time<\/span><\/li>\n<\/ul>\n<div>\n<p>&nbsp;<\/p>\n<p><strong>2.\u00a0Introduction<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">In Module 01 we discussed the essential requirement of an astronomical system of coordinates for celestial objects.\u00a0 These requirements are:<\/p>\n<p>&nbsp;<\/p>\n<p>I.\u00a0 A fundamental great circle, and<\/p>\n<p>II. A reference point, or origin.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">As an example of these requirements, we discussed the terrestrial coordinate system in which equator is the fundamental great circle and the point of intersection of the prime meridian with the equator is the origin. By this system we assign longitude and latitude to places on the earth. We now discuss the <strong>Horizon System <\/strong>for which the fundamental great circle is the horizon and the origin is either the north point or the south point of the horizon. It is a simple system and is used by most small telescopes. However, the system has two shortcomings: the coordinates differ from observer to observer at the same point of time, and for the same observer at different times.\u00a0 These shortcomings are sought to be rectified in the <strong>Equatorial System <\/strong>of coordinates.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>3. The Horizon System of Astronomical Coordinates\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">In this system the fundamental great circle is the <strong>horizon<\/strong>.\u00a0 Let us see how we can locate our horizon.\u00a0 The point vertically overhead the observer on the celestial sphere is called the <strong>zenith<\/strong>, and the point vertically below the observer is called the <strong>nadir <\/strong>(Fig. 2.1). The horizon is the plane perpendicular to the line joining ZZ\u00b4.\u00a0 Let us see how we can locate it.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Suppose an observer at latitude ?.\u00a0 The point exactly overhead the observer is called the <strong>zenith<\/strong>. Draw the line joining the zenith with the centre of the earth (Fig. 2.1).\u00a0\u00a0 A plane perpendicular to this line is the horizon of the observer at latitude ?. As long as an object is above the horizon, it is visible to us. \u00a0When it goes below the horizon, the object is no longer visible, we say it has set.<\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-413\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.1.png\" alt=\"\" width=\"679\" height=\"526\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.1.png 679w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.1-300x232.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.1-65x50.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.1-225x174.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.1-350x271.png 350w\" sizes=\"auto, (max-width: 679px) 100vw, 679px\" \/><\/p>\n<p><strong>Exercise 2.1<\/strong>:\u00a0 Locate the horizon for an observer at the North Pole.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Exercise 2.2<\/strong>:\u00a0 Locate the horizon for an observer stationed at the Equator.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-412\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.2.png\" alt=\"\" width=\"624\" height=\"276\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.2.png 624w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.2-300x133.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.2-65x29.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.2-225x100.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.2-350x155.png 350w\" sizes=\"auto, (max-width: 624px) 100vw, 624px\" \/><\/p>\n<p style=\"text-align: justify\"><span style=\"font-size: 1em;text-align: initial\">Projected on the celestial sphere with the earth as centre, the horizon is a great circle which\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">appears as shown in Fig. 2.3.\u00a0 Z and Z\u00b4 are the poles of the horizon, while P and Q are the north\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">and south celestial poles, respectively.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-411\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.3.png\" alt=\"\" width=\"669\" height=\"424\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.3.png 669w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.3-300x190.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.3-65x41.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.3-225x143.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.3-350x222.png 350w\" sizes=\"auto, (max-width: 669px) 100vw, 669px\" \/><\/p>\n<p>In Fig. 2.4, N and S are the north and south points of the horizon.\u00a0 To fix coordinates of an object<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">X, we draw the half great circle ZXLZ\u00b4.\u00a0 One of the coordinates of X is then the arc length LX, called the <strong>altitude <\/strong>?.\u00a0 It is measured from zero to +90\u00b0 from L to Z and from zero to -90\u00b0 from L to Z\u00b4.\u00a0 To fix the other coordinate either N or S is chosen as the origin.\u00a0 If N is the origin, then the arc length NL, or the spherical angle NZL, is the second coordinates of X, called the <strong>azimuth<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong>A.\u00a0<\/strong>In this case the azimuth is measured from 0 to 180 degrees east or west.\u00a0 If S is chosen as the origin, the azimuth is measured from 0 to 360 degrees through west. It must be remembered that the refraction of light due to the earth\u2019s atmosphere increases slightly the altitude of a star. Necessary correction due to atmospheric refraction must, therefore, be applied to the measured altitudes of celestial objects. The complement of the altitude, the arc length ZX, is called the zenith distance of the object.\u00a0 Obviously, in degrees<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\">?= ?<strong>0<\/strong>\u2212 ?<strong>.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (2.1)<\/strong><\/p>\n<\/div>\n<div><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-410\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.4.png\" alt=\"\" width=\"715\" height=\"575\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.4.png 715w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.4-300x241.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.4-65x52.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.4-225x181.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.4-350x281.png 350w\" sizes=\"auto, (max-width: 715px) 100vw, 715px\" \/><\/div>\n<div>\n<p>&nbsp;<\/p>\n<p><strong>3.1. Altitude of the Pole star is equal to the Latitude of the Observer\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">We immediately apply the horizon system to derive an important result: \u00a0<strong>The altitude of the Pole star is equal to the latitude of the observer. \u00a0<\/strong>Fig. 2.5 shows horizon for an observer at latitude ?.\u00a0 Z is the pole of the horizon and so the zenith for the observer is at ?to the equator.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">North Celestial Pole, P, is the pole of the equator and is in the direction of the Pole star. The great circle PZRQZ\u00b4T is called the <strong>observer\u2019s meridian<\/strong>, or <strong>local meridian<\/strong>. The arc length RZ is equal to ?by the definition of latitude. The arc length ZP is, therefore, 90 \u2212 ?<strong>, <\/strong>because the arc RP equals 90 degrees<strong>. <\/strong>This makes the arc length NP, which is actually the altitude of the Pole star in accordance with the horizon system, equal to the latitude ?.\u00a0 Thus, the altitude of the Pole\u00a0<span style=\"text-align: initial;font-size: 1em\">star at any place is equal to the latitude of that place.\u00a0\u00a0 So, to locate pole star, look in the north direction at an altitude equal to your latitude.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-409\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.5.png\" alt=\"\" width=\"614\" height=\"593\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.5.png 614w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.5-300x290.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.5-65x63.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.5-225x217.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.5-350x338.png 350w\" sizes=\"auto, (max-width: 614px) 100vw, 614px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong>3.2. Convenience of the Horizon System\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The horizon system is a very convenient system.\u00a0 Most small telescopes for amateur astronomers are based on this and use <strong>alt \u2013 azimuth mounting<\/strong>.\u00a0 The azimuth of an object gives the direction in which to look for the object.\u00a0 The altitude then gives the angle by which the telescope is to be raised from the horizontal to locate the object (Fig. 2.6).<\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-408\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.6.png\" alt=\"\" width=\"646\" height=\"388\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.6.png 646w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.6-300x180.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.6-65x39.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.6-225x135.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.6-350x210.png 350w\" sizes=\"auto, (max-width: 646px) 100vw, 646px\" \/><\/p>\n<p><strong>3.3. Drawbacks of the Horizon System\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Even if it is convenient, the horizon system suffers from two drawbacks:<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">(i) Since the horizon at different locations on the earth is different (Fig. 2.7), the coordinates of the same object at the same time are different for observers at different places. In other words, the coordinates of an object are location specific.<\/p>\n<p style=\"text-align: justify\">(ii) As the earth rotates, the celestial objects move in planes normal to the polar axis.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Since these planes are generally inclined to the horizon, the coordinates of an object keep changing with time for any observer.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">These shortcomings are sought to be eliminated in the equatorial system of coordinates.<\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-407\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.7.png\" alt=\"\" width=\"730\" height=\"589\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.7.png 730w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.7-300x242.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.7-65x52.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.7-225x182.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.7-350x282.png 350w\" sizes=\"auto, (max-width: 730px) 100vw, 730px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong>4.\u00a0 The Equatorial System\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>4.1.\u00a0 <\/strong><strong>Local Equatorial System<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The fundamental great circle chosen here is the celestial equator, whose plane is parallel to the equatorial plane of the earth.\u00a0 The <strong>north celestial pole <\/strong>(<strong>NCP<\/strong>) P and the <strong>south celestial pole <\/strong>(<strong>SCP<\/strong>) Q are the poles of the celestial equator, (Fig. 2.8).\u00a0 The great circle PTQR is the <strong>observer\u2019s meridian, or the local meridian. \u00a0<\/strong>Any half great circle through the two celestial poles is called an <strong>hour circle <\/strong>as it measures the time elapsed since an object on it crossed the observer\u2019s meridian.\u00a0 To get the coordinates of the object X we draw an hour circle through it.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"font-size: 1em;text-align: initial\">Then one coordinate of X is the arc length LX on its hour circle. The coordinate is called the\u00a0<\/span><strong style=\"text-align: initial;font-size: 1em\">declination <\/strong><span style=\"text-align: initial;font-size: 1em\">of X, denoted by ?. It is measure from zero to +90\u00b0 north of the celestial equator<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-406\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.8.png\" alt=\"\" width=\"590\" height=\"596\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.8.png 590w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.8-297x300.png 297w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.8-65x66.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.8-225x227.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.8-350x354.png 350w\" sizes=\"auto, (max-width: 590px) 100vw, 590px\" \/><\/p>\n<p style=\"text-align: justify\">and from zero to -90\u00b0 to the south of the celestial equator. The other coordinate is the <strong>hour angle\u00a0<\/strong><strong>(<\/strong>?<strong>) <\/strong>measured from the point R on the observer\u2019s meridian westward (clockwise when viewed from the north celestial pole.) to L, the intersection of the hour circle of X with the celestial equator.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">It will be noticed that as the object appears to rotate from east to west, the declination remains unchanged while the hour angle increases steadily from zero to 360\u00b0 in 24 hours. For this reason, the hour angle is expressed in terms of hours rather than degrees, 1 hour corresponding to 15\u00b0.\u00a0\u00a0 In this system, too, one of the coordinates, namely the hour angle, keeps changing with\u00a0<span style=\"text-align: initial;font-size: 1em\">time as the object moves across the sky. \u00a0That is the reason the system is called <\/span><strong style=\"text-align: initial;font-size: 1em\">local equatorial system.\u00a0 <\/strong><span style=\"text-align: initial;font-size: 1em\">This shortcoming is rectified by choosing as origin a point on the celestial equator<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-405\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.9.png\" alt=\"\" width=\"616\" height=\"553\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.9.png 616w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.9-300x269.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.9-65x58.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.9-225x202.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.9-350x314.png 350w\" sizes=\"auto, (max-width: 616px) 100vw, 616px\" \/><\/p>\n<p style=\"text-align: justify\">which is not stationary but moves with the same speed and in the same direction as the object. This ensures that there is no relative motion between the two.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>4.2. Universal Equatorial System\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The point, or origin, chosen for this purpose is the <strong>first Point of Aries<\/strong>, or the <strong>vernal equinox <\/strong>(<strong>\u03d2). First Point of Aries is the point of intersection of the apparent annual path of the Sun and the celestial equator<\/strong>. The arc length measured from the vernal equinox eastwards (counterclockwise when viewed from the north celestial pole) to the hour circle of the object, the arc length <strong>\u03d2L, <\/strong>is known as the right ascension (?) (Fig. 2.9)<strong>. <\/strong>It is also measured in hours because the vernal equinox completes one round of the sky in 24 hours as does any other object\u00a0<span style=\"text-align: initial;font-size: 1em\">in the sky. Thus, the right ascension remains unchanged as the object appears to move across the sky. \u00a0We have already noted that the declination of an object is unaffected by the motion of the object across the sky. Since both the coordinates remain unchanged as the object changes its position in the sky, this system is called the <\/span><strong style=\"text-align: initial;font-size: 1em\">universal equatorial system. This system is suitable for making catalogues of stars.<\/strong><\/p>\n<\/div>\n<div>\n<p>&nbsp;<\/p>\n<p><strong>5. Annual Motion of the Sun\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Let us briefly look at the apparent annual motion of the Sun.\u00a0 The plane of this motion is called the ecliptic.\u00a0 It makes an angle of 23.5\u00b0 with the plane of the celestial equator. The ecliptic plane intersects the plane of the equator at two points, called the vernal equinox (<strong>\u03d2<\/strong>) and the autumn equinox ( ? ). Around 21 June the Sun is at its northern most point in its apparent annual orbit. P<\/p>\n<\/div>\n<div><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-404\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.10.png\" alt=\"\" width=\"588\" height=\"541\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.10.png 588w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.10-300x276.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.10-65x60.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.10-225x207.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/12\/6.27.10-350x322.png 350w\" sizes=\"auto, (max-width: 588px) 100vw, 588px\" \/><\/div>\n<div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Its declination is 23.5\u00b0. The event is called the <\/span><strong style=\"text-align: initial;font-size: 1em\">summer solstice<\/strong><span style=\"text-align: initial;font-size: 1em\">. It then moves southwards; in\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">India we call it <\/span><strong style=\"text-align: initial;font-size: 1em\"><em>Dakshinayan <\/em><\/strong><span style=\"text-align: initial;font-size: 1em\">(towards south). Around 23 September, it crosses the equator and\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">moves into the southern hemisphere.\u00a0 On this day the duration of day and night is equal, hence it is called <\/span><strong style=\"text-align: initial;font-size: 1em\">autumn equinox. <\/strong><span style=\"text-align: initial;font-size: 1em\">For those living on the equator, the Sun rises exactly in the east on this day. Around 23 December, the Sun reaches its southern most point, <\/span><strong style=\"text-align: initial;font-size: 1em\">the winter solstice<\/strong><span style=\"text-align: initial;font-size: 1em\">. Its\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">declination then is -23.5\u00b0. Then it reverses its direction and begins moving northwards; in India\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">it is called <\/span><strong style=\"text-align: initial;font-size: 1em\"><em>Uttarayan.\u00a0 <\/em><\/strong><span style=\"text-align: initial;font-size: 1em\">Around 21 March, the Sun crosses from the southern hemisphere into the\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">northern hemisphere. This point of intersection between the equator and the ecliptic is called the <\/span><strong style=\"text-align: initial;font-size: 1em\">first point of Aries<\/strong><span style=\"text-align: initial;font-size: 1em\">, or the <\/span><strong style=\"text-align: initial;font-size: 1em\">vernal equinox<\/strong><span style=\"text-align: initial;font-size: 1em\">. <\/span><strong style=\"text-align: initial;font-size: 1em\">It is this point that we use as the origin for the universal equatorial system of coordinates. There is no celestial object at this point in the sky; it is just a reference point. \u00a0<\/strong><span style=\"text-align: initial;font-size: 1em\">On the day of vernal equinox, the duration of day and night is equal, and for those living on the equator, the Sun rises exactly in the east. It must be noted that the Sun rises exactly in the east only for two days in the whole year, and that too for people\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">living in the tropics, the region between the Tropic of Cancer and the Tropic of Capricorn.\u00a0 On all other days of the year the Sun rises either in the north of east or the south of east. A few week\u2019s observations of the rising Sun should confirm this. Throughout the year the rising point of the\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">Sun keeps oscillating between 23.5\u00b0 north and 23.5\u00b0 south.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong><span style=\"text-align: initial;font-size: 1em\">6. Local Sidereal Time\u00a0<\/span><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Since the coordinates of an object on the universal equatorial system do not change with time or location, this system is widely used for preparing catalogues of celestial objects. The hour angle of <\/span><strong style=\"text-align: initial;font-size: 1em\">\u03d2 <\/strong><span style=\"text-align: initial;font-size: 1em\">is called the <\/span><strong style=\"text-align: initial;font-size: 1em\">local sidereal time (LST), the time measured with reference to the distant\u00a0<\/strong><strong style=\"text-align: initial;font-size: 1em\">stars. <\/strong><span style=\"text-align: initial;font-size: 1em\">The relation between ?and ?is through the sidereal time (Fig. 2.9):<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\"><span style=\"text-align: initial;font-size: 1em\">LST = ?+ ?.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (2.2)<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">We shall discuss the sidereal time a little later.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong><span style=\"text-align: initial;font-size: 1em\">7.\u00a0\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">Summary\u00a0<\/span><\/strong><\/p>\n<\/div>\n<div>\n<ul>\n<li style=\"text-align: justify\">Essential requirements for an astronomical coordinate system are a reference great circle and a reference point.<\/li>\n<li style=\"text-align: justify\">For Horizon System the reference great circle is the horizon and the reference point\u00a0is the intersection of the horizon and half great circle ZXZ<span style=\"text-align: initial;font-size: 1em\">\u00b4.<\/span><\/li>\n<li style=\"text-align: justify\">The arc length along ZXZ<span style=\"text-align: initial;font-size: 1em\">\u00b4 <\/span>from the horizon to X is called the altitude of X.<\/li>\n<li style=\"text-align: justify\">Either the North point or the South point of the horizon is used the reference point\u00a0for measuring the azimuth of X.<\/li>\n<li style=\"text-align: justify\">Horizon System is a very convenient system and most small telescopes use alt \u2013 azimuth mounting.<\/li>\n<li style=\"text-align: justify\">Horizon for each observer is different. Moreover, the horizon for the same observer changes as the earth rotates on its axis.<\/li>\n<li style=\"text-align: justify\">The two drawbacks of the horizon system are that the coordinates change with the observer and with time for the same observer.<\/li>\n<li style=\"text-align: justify\">These drawbacks are sought to be rectified in the Equatorial coordinate system.<\/li>\n<li style=\"text-align: justify\">Equatorial system uses celestial equator as the reference great circle and its intersection with the observer\u2019s meridian (great circle through the poles and the zenith) as the reference point for measuring the hour angle of X.<\/li>\n<li style=\"text-align: justify\">In hour angle \u2013 declination system, declination of an object is fixed, while the hour angle of the object changes as the earth rotates on its axis.<\/li>\n<li style=\"text-align: justify\">This shortcoming, a coordinate changing with time, is rectified by choosing the first Point of Aries as the reference point.<\/li>\n<li style=\"text-align: justify\">The first Point of Aries moves just like the object X, so the coordinate measured from this point to the hour circle of X stays fixed. This coordinate is called the right ascension.<\/li>\n<li style=\"text-align: justify\">The right ascension \u2013 declination system is called the universal equatorial system.<\/li>\n<li style=\"text-align: justify\">Since both the coordinates of a star in this system remain unchanged as the star moves about in the sky, this system is suitable for making catalogues of stars.<\/li>\n<li style=\"text-align: justify\">The annual path of the Sun (ecliptic) is inclined to the equator at an angle of 23.5<span style=\"text-align: initial;font-size: 1em\">\u00b0<\/span>.<\/li>\n<li style=\"text-align: justify\">At summer solstice the Sun is at 23.5\u00b0 N and at winter solstice it is at 23.5\u00b0 S. This\u00a0motion of the Sun is responsible for the shifting point of Sunrise during the year.<\/li>\n<li style=\"text-align: justify\">Sidereal time is the time reckoned with respect to the distant fixed stars.<\/li>\n<li style=\"text-align: justify\">Right ascension and hour angle are related through the local sidereal time.<\/li>\n<\/ul>\n<\/div>\n<table style=\"height: 34px; width: 742px;\">\n<tbody>\n<tr>\n<td style=\"width: 655.063px\"><strong>You can view video on Horizon and Equatorial Coordinate Systems<\/strong><\/td>\n<td style=\"width: 58.0625px\"><a href=\"https:\/\/www.youtube.com\/watch?v=NA&amp;feature=youtu.be\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p><strong>Websites discussing the material in this module<\/strong><\/p>\n<ul>\n<li>http:\/\/www.skyandtelescope.com\/astronomy-resources\/what-are-celestial-coordinates\/<\/li>\n<li>http:\/\/www.telescope.com\/Celestial-Coordinates\/p\/99817.uts<\/li>\n<li>http:\/\/physics.gmu.edu\/~jevans\/astr103\/CourseNotes\/earthSky_coordinateSystems.html<\/li>\n<li>https:\/\/www.astronomyhouston.org\/sites\/default\/files\/presentations\/HAS_Novice_Program_Celestial_Coordinates.pdf<\/li>\n<li>https:\/\/www.tcnj.edu\/~pfeiffer\/AST261\/AST261Chap2,CelCord.pdf<\/li>\n<\/ul>\n","protected":false},"author":4,"menu_order":27,"template":"","meta":{"_acf_changed":false,"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-400","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\/400","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":4,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/400\/revisions"}],"predecessor-version":[{"id":414,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/400\/revisions\/414"}],"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\/400\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/media?parent=400"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapter-type?post=400"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/contributor?post=400"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/license?post=400"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}