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?

1 Answer
Mar 31, 2017

Great circle distance is 1411.55 miles.

Explanation:

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.