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Figure  15-1.-Reference  lines. - 14070_337
Figure  15-3.Terrestrial  and  celestial  coordinate  system. - 14070_339

Engineering Aid 1 - Advanced Structural engineering guide book
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below  the  equator.  Latitudes  are  expressed  in  degrees and are measured from 0° to 90° north or south. The conventional  symbol  for  latitude  used  in  computation  is the Greek letter  @. As shown also in figure 15-2, the longitude of a point is the angular distance measured along the equator between the meridian passing through a point and a reference  meridian.  The  chosen  reference  meridian  is the Greenwich meridian that passes through Greenwich, England. That meridian is known as the primary or prime meridian. Longitude is also expressed in degrees but is measured from 0° to 180° west or east from the prime meridian. The conventional symbol for longitude is the Greek letter  k  (lambda). Celestial system of Coordinates To  explain  the  celestial  system,  let’s  first  suppose that the earth is a glass sphere, with meridians and parallels traced in black and a light placed at the center. Suppose, too, that this sphere is placed at the center of another infinitely larger sphere, as shown in figure 15-3. This larger sphere is the imaginary celestial sphere on which  all  the  heavenly  bodies  are  presumed  to  be located. The celestial sphere is a mathematical concept of a sphere of infinite radius whose center is at the center of the earth The points at which the earth’s prolonged axis of rotation pierces the celestial sphere are known as the celestial  poles.  The  plane  of  the  earth’s  equator, extended to the celestial sphere, coincides with the celestial equator. Great  circles  through  the  celestial poles,  comparable  to  the  earth’s  meridians,  are  called hour circles.  The angle between hour circles is the hour angle. Even though the earth rotates and the stars appear stationary among themselves, it is easier to think of the earth as being stationary, while the celestial sphere, with the celestial bodies attached, rotates from east to west, This is actually its apparent motion. When reference is made to a star’s path or motion, it is this apparent motion that is referred to. DECLINATION.— Similar   to   latitude,   the declination  of  a  celestial  body  (star,  sun,  or  planet)  is its  angular  distance  north  or  south  of  the  celestial equator. As with latitude, declination is expressed in degrees and is measured horn 0° to 90° north or south from the celestial equator. North and south declination values are given plus and minus signs, respectively. The conventional  symbol  for  declination  is  the  Greek letter 6  (delta). RIGHT ASCENSION.—  The vernal equinox, also known as the first point of Aries, is an imaginary point on the celestial sphere where the  ecliptic  (or apparent path of the sun) crosses the equator from south to north on or about 21 March of each year. The vernal  equinox  moves  westward  along  the  equator about  50  seconds  of  arc  per  year.  The  right  ascension of the sun or any star is the angular distance measured eastward  along  the  celestial  equator  between  the vernal equinox and the hour circle passing through the celestial  body.  Right  ascension  is  normally  expressed in units of time from 0 to 24 hours, although it can be expressed   in   degrees   with   1   hour   of   time corresponding  to  15°.  The  conventional  symbol  for right ascension is the Greek letter a (alpha), or it can be abbreviated RA. HOUR ANGLE.— Right  ascension  and  declination are independent coordinates of the celestial system, whereas the hour angle is a dependent coordinate. Hour angle is the angle between celestial meridians, or hour circles; but its origin is the meridian that passes through the  observer’s  zenith  (or  point  on  the  celestial  sphere directly above the observer). The hour angle of a star is defined as the angular distance, measured  westward along the celestial equator, between the observer’s meridian and the hour circle or meridian of the star. This angle is often called the local hour angle (LHA), which will  be  discussed  later. GREENWICH  HOUR  ANGLE.—  The  coordi- nate for a heavenly body that corresponds to longitude is called the  Greenwich  hour  angle  (GHA).  The Greenwich hour angle is the angular distance from the Greenwich meridian to the meridian of the heavenly body.  It  is  always  measured  westward   from  the Greenwich meridian and is expressed in degrees from 0° to 360°. Another point to remember is that, while the longitude of a point on the earth always remains the same, the GHA of the celestial object is constantly increasing as the body moves westward on the celestial sphere. Horizon System of Coordinates To  connect  the  celestial  and  terrestrial  coordinates, you  must  have  a  third  system,  descriptive  of  the observer’s  position.  The  fundamental  reference  of  this 15-4







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