Determining Great Circle Distance & Initial Course

Determine the Great Circle Distance and initial course from LAT 24° 52' N; LONG 078° 27' W to LAT 47° 19' N; 006° 42' W.

Given:

   Lat_{1 =} 24° 52' N               

   Lat_{2 =} 47° 19' N

Long_{1 =} 078° 27' W

Long_{2 =} 006° 42' W

_{What is asked?}

_{Great Circle Distance and initial course}

_Solution:

_{1. Solve first for the DLO.}

           

             _{Rule:   If same name -Minus}

                     _{Different name - Plus}

            _{And then affix the name of direction. If the DLO is greater than 180, minus it to 360 then affix the name of Long1.}

           Long_{1 =}  078° 27' W

           Long_{2 =}- 006° 42' W  

             DLO =  071 45' E

2. Proceed to the formula for the great circle distance.

    Cos GCD = (Cos Lat1 × Cos Lat2 × Cos Dlo) ± (Sin Lat1 × Sin lat2)

         Rule:

                 Plus when not crossing the equator

                 Minus when crossing the equator

   Cos GCD = Cos 24° 52' × Cos 47° 19' × Cos 71° 45') + (Sin 24° 52' × Sin 47° 19')

   Cos GCD = 0.50174

          GCD = inv Cos 0.50174

          GCD = 59° 53'

                        × 60    to convert it into miles

          GCD =  3593 miles  

3. Solving for the Initial Course

        Sin IC = Cos Lat2 × Sin Dlo 

                          Sin Distance

        Sin IC = Cos 47° 19' × Sin 71° 45' 

                          Sin 59° 53'

        Sin IC = 0.74432

              IC = inv Sin 0.74432

              IC = 48.1 degrees