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Page Title: The Relationship between Time and Longitude
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The Relationship between Time and Longitude Background Information Ordinarily,  we  use  mean  solar  time,  which  is  measured  by  the  motion  of the  mean  Sun  around  the  Earth.  Let’s  suppose  your  ship  is  on  longitude 60°W.  When  the  Sun  is  on  your  longitude  or  meridian,  it  is  noon.  As  the Sun  continues  to  move  west  and  crosses  over  longitude  61°W,  it  is  noon there  and  the  time  on  your  meridian  is  later.  In  fact  it  is  the  time equivalent  of  1°  later.  But  you  can’t  measure  1°  on  your  watch;  you  must convert this 1° of arc to units of time. To  have  a  standard  reference  point,  every  celestial  observation  is  timed according  to  the  time  at  the  Greenwich  meridian.  Usually  this  is determined  by  means  of  the  chronometer  which  is  set  to  GMT.  To  clarify the relationship between time and arc, let’s consider a situation in which you know your longitude exactly at noon, and you want to find out the time  in  Greenwich. Arc to Time When  the  Sun  is  on  a  particular  meridian,  it  is  noon  at  that  meridian.  In other words, when the Sun is on the Greenwich meridian (0°), it is noon by  Greenwich  time.  To  make  the  problem  easier,  let’s  say  you’re  in  90°W longitude.  It’s  noon  where  you  are,  so  the  Sun  must  also  be  in  90°W longitude.  So,  since  leaving  Greenwich,  the  Sun  has  traveled  through  90° of  arc.  Because  it  was  1200  (noon)  Greenwich  time  when  the  Sun  was  at 0°, the time at Greenwich now must be 1200 plus the time required for the Sun to travel through 90° of arc. The  following  information  provides  all  the  elements  of  a  problem  for converting  arc  to  time.  If  you  know  that  it  takes  24  hours  for  the  Sun  to travel 360° or one complete revolution, it should be easy to find how long it  takes  it  to  go  90°.  If  the  Sun  goes  360°  in  24  hours,  it  must  go  15°  in 1  hour.  If  it  goes  15°  in  1  hour,  it  must  go  1°  in  4  minutes.  Then,  to  go 90°, it takes 90 x 4 minutes, or 360 minutes, which is the same as 6 hours.  Six  hours  ago  it  was  1200  Greenwich  time;  therefore,  the  time  at Greenwich  now  must  be  1800.  You  actually  have  converted  90°  of  arc  to 6  hours  of  time.  In  doing  so,  you  discovered  the  basic  relationship between  arc  and  time.  This  relationship  is  stated  as  15°  of  longitude  (arc) equals 1 hour of time. Your  problem  could  be  converting  time  to  arc--the  reverse  of  the  one  we worked  out.  Tables  for  converting  either  way  are  in  The  Nautical Almanac  and in  Bowditch,  but if you acquire the following easy methods of  converting,  you  won’t  have  to  refer  to  publications.  First,  you  must memorize the values for arc and time. 5-7

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