What is the shortest distance between two points #(61^@40.177',33^@23.101')# and #(59^@26.266',13^@03.807')# #("latitude","longitude")# on earth?

First of all here angles (latitudes and longitudes) are given here in degrees and minutes and hence need to converted into degrees (with decimals) so that I can use scientific calculator provided with MS Windows. Further, I will be using up to six places (or more) of decimal for accuracy.

Hence #33^@23.101'=(33+23.101/60)^@=33.385016^@#.

Similarly #13^@03.807'=13.06345^@#, #61^@40.177'=61.669616# and #59^@26.266'=59.437767^@#

Further, although we are using degrees as longitudes and latitudes are available in degrees, #d# should be found in radians, to get great circle distance (GCD - it is the shortest distance between two points on the surface of a sphere, here earth) and then this distance would be #d xx R#. Now using the formula,

#d=cos^(-1)(sin33.385016^@sin13.06345^@+cos33.385016^@cos13.06345^@ cos(61.669616 – 59.437767)^@#

= #cos^(-1)(0.5502624xx 0.2260299+0.8349918xx0.97412xxcos(2.231849))#

= #cos^(-1)(0.5502624xx 0.2260299+0.8349918xx0.97412xx0.9992414)#

= #cos^(-1)(0.12437576+0.8127652)#

= #cos^(-1)(0.93714096)#

= #0.35645154# - in radians

#GCD=0.35645154xx3960=1411.55# miles.